I wasn't going to put this page in, but I have to. I wanted to keep the website as free from handwavium as possible. However, while Faster-Than-Light travel is about as handwavium as you can get, it is unfortunately the sine qua non of interstellar space opera. Space opera with no StarDrive is like chocolate cake without the chocolate.

This page is about a science fiction author designing a faster-than-light system that logically allows the sort of science fiction background they want to write about. AND simultaneously is as free as possible from nasty unintended consequences that will allow their readers to point out logical inconsistencies and laugh.

The second FTL page is for samples of faster-than-light travel in various science fiction.


In the better scifi novels, the author uses a technique mentioned in the Fate Space Toolkit RPG: "blackboxing".

The FTL method that is part of the background of a science fiction novel is put into a black box, that nobody can look inside. This means the disruptive effects of the FTL technology are never explored in the novel, because it never occurs to any of the characters in the story to look. Functionally the only thing that penetrates the black box are the pre-established limits, not the operating mechanism.

In extreme cases, the author does not even mention how the FTL drive works. The author just gives the drive a technobabble name and leaves it at that. If any reader asks the author how the drive works, the answer is "Splendidly".

Using blackboxing the author can have the highly-unscientific FTL drive that their readers crave, but make the rest of the background ultra-hard science fiction. The only problem is readers asking awkward questions try to penetrate the blackbox, usually in the form of "If the FTL drive can do this, then it should be able to do {something that will utterly destroy the carefully crafted story background}".

An example of a blackbox breaking and ruining everything can be found in Star Wars: The Last Jedi. SPOILERS: Vice Admiral Holdo causes the lead Resistance ship to make the jump to lightspeed, which does something catastrophic to Snoke's flagship. The audience immediately wants to know why this tactic was not used in any of the seven earlier movies. Say, on the two Death Stars.

The Basic Problem

  1. Traveling between stars at speeds up to the speed-of-light can take centuries, which does not allow science fiction authors to write fast-paced novels

  2. That rat-bastard Albert Einstein's theory of relativity more or less forbids starships and other things from traveling faster than the speed-of-light. Bye-bye fast paced novels

  3. So authors who want to write hard science fiction but do not want to loose their audience are in a bit of a bind

If you want all the nitty-gritty details including savage equations with nasty pointed teeth, there is an great scientific paper here.

If you just want the Cliff Notes, read on.


The standard physics term for "the speed of light in a vacuum" is lower-case letter c. "Vacuum" is because light and other electromagnetic radiation travels slower in spaces filled with matter, such as water. Science fiction commonly uses "lightspeed" as a synonym for c. In case you were not aware, electromagnetic radiation includes light, infrared rays, ultraviolet rays, radio waves, microwave rays, x-rays, gamma-rays, radar, radio, laser beams and pretty much any other form of energy that can be called "rays".

  • Lightspeed: at the speed of light

  • FTL: Faster Than Light

  • STL: Slower Than Light

  • NAFAL: Not As Fast As Light. Non-relativistic flight, say below 14% c. (Ursula K. LeGuin)

  • AAFAL: Almost As Fast As Light. Relativistic STL flight, say, above 14% c but below 100% c.

  • AFAL: As Fast As Light. Exactly equal to c.

  • Superluminal: faster than light, from Latin terms for superior ("super") and pertaining to light ("luminal")

  • Sublight: slower than light

  • Fittled: to travel at FTL velocities. Term comes from trying to pronounce "FTL" as if it had vowels in it. (Ken MacLeod)

  • Tesser: to travel FTL by space warp. Term comes from Tesseract. (Madeleine L'Engle)

  • Wrinkle: to travel FTL by space warp. Synonym for Tesser. (Madeleine L'Engle)

For FTL drives that travel to their destination at a certain rate (as opposed to "jump" drives that appear instantly at the destination), science fiction authors generally talk about how much faster than the speed of light in a vacuum the starship travels. No jokes about Han Solo and the Kessel Run (see the frantic retconning at this website). This allows one to easily calculate how long the starship will take to travel a trip of x light years. Note that this assumes no complications from relativistic time dialation, but if you are traveling faster than light then relativity has been kicked to the curb already so don't worry about it.

  • 1,000 c: one thousand times the speed of light in a vacuum. 0.5 c is half lightspeed.

  • 100,000% lightspeed: one thousand times the speed of light in a vacuum, because the percentage is the factor times 100.

  • Mike 1,000: one thousand times the speed of light in a vacuum, from Robert Heinlein's Starship Troopers. Presumably "Mike" refers to Michelson–Morley. "Under Cherenkov drive she cranks Mike 400 or better—say Sol to Capella, forty-six light-years, in under six weeks."

  • 1 kilolight: one thousand times the speed of light in a vacuum, from Iain M. Banks Culture novels. The term "lights" is used like the navy term "knots". And it is in metric: 1 decalight = 10c, 1 megalight = 1,000,000c, etc.

  • Ninety parsecs an hour: 2,570,184 times the speed of light in a vacuum, in E. E. "Doc" Smith's LENSMAN series the starship speed at full blast in intragalactic space. The top extragalactic speed at full blast is 100,000 pc/hr or 2,855,760,000c.

Jump drives commonly have a maximum jump distance, a minimum time between successive jumps, but the jump proper is instantaneous. Or they have a maximum jump distance and the jump takes a certain amount of time. These two factors can be combined to give an effective speed. You calculate how long it takes to go a given distance, and divide that time by how long it takes light to go the same distance.


A Traveller jump-1 drive can travel 1 parsec in one week. What is it's effective FTL velocity?

1 parsec = 3.26 light-years. This is the jump distance.

There are 24 hours-in-a-day × 7 days-in-a-week = 168 hours in a week. This is the jump duration.

So the jump-1 drive travels 3.26 light-years-jump-distance / 168 hours-jump-duration = 0.0195 light-years per hour.

There are 24 hours-in-a-day × 365 days-in-a-year = 8,760 hours in a year.

So in one year the Jump-1 drive can travel 0.0195 light-year-per-hour × 8,760 hours = 171 light-years.

In one year light can travel 1 light-year, and the jump-1 can travel 171 light-years. So the jump-1 is 171 times as fast as light.

So the effective FTL velocity of the jump-1 drive is 171c.

In vintage SF, the propulsion was commonly termed "hyperdrive", since the starships evaded Einstein by entering a dimension called "hyperspace" where there was a higher speed limit. Star Trek has its "warp drive" that reduces the distance to be traveled by warping space. The RPG Traveller has its "jump" drive that teleports the ship from point A to point B. In his "Lucky Starr" novels, Isaac Asimov uses the term "Hyperatomic spaceships", presumably since the spacecraft had both a faster-than-light Hyperspace engine and a more conventional atomic engine. Go read the "Faster Than Light" entry in Wikipedia.

The two main catagories of science-fiction-invented FTL travel center around modifying one of the two terms in the travel time = distance / rate of travel equation. Modifying distance is usually called a "warp drive" while modifying rate-of-travel is usually called a "hyperspace drive", but not always. There are some modifying distance types that are called hyperspace drives because there is always one in every crowd.

Fred Kiesche says that a faster than light starship should have a license plate that reads "ME = MC2"


FTL. Faster than light. This is by far the most important item of HANDWAVIUM technology in Space SF, and is absolutely necessary for the communications, TRADE, and WARFARE of the KNOWN GALAXY. No one, after all, wants to take decades or centuries to get anywhere. For this reason, even HARD SF usually makes an exception for FTL. You just can't leave home without it.

TECHJARGON terms include Hyperspace, Subspace, and a host of meaningless names - such as my own Ashikaga Jump, named for its purported inventor. Warp was old-fashioned even when classic Trek used it, and is hardly encountered any more.  (Interestingly, though, it is one piece of Techjargon that has entered the everyday language; people who never heard of FTL know that warp speed means "really, really fast.")

FTL is primarily a form of rapid transit for space vehicles, needed to literally move the plot along. FTL radio is also common (the most frequent Techjargon term is Ansible), but is sometimes left out as not entirely necessary - you can always send a ship with a message, and the resulting haphazard communications are a rich source of plot complications. Ursula Le Guin has things the other way around - Ansibles, but no FTL drive.

FTL requires Handwavium because of that damned speed-of-light barrier to travel in normal space. Over the years, SF writers have grasped at any conceivable loophole in the laws of physics that might theoretically allow them to speed things up. The physicists have actually been - very marginally - helpful in this regard, what with wormholes, quantum tunneling, and so forth. Basically, though, FTL remains sheer Handwavium, in that its properties are wholly arbitrary. (Unlike, say, a matter-antimatter DRIVE, for which you can at least calculate energy-to-thrust ratios and the like.)

Broadly speaking, FTL environments fall into two classes, those that you "fly" through and those that you "jump" through. The first type allows you to actually navigate - change course, or even fight battles - while in FTL. It also favors artsy semi-streamlined spacecraft designs, a la Trek, presumably to slide cleanly through whatever it is you go through in FTL.

In contrast, "jump" FTL is a sort of rabbit hole that you hop through to get where you're going. Navigation is all done beforehand, in normal Space, as you line up to make the jump. Once you make it you have no further control till you pop back out, hopefully where you wanted to go. Jump FTL often limits movement to specific JUMP POINTS

Both types of FTL often require some kind of intuitive skill for successful navigation.  This is a convenient way to make automated drone STARSHIPS impossible, forcing them all to have crews.

Trek, of course, had a fly-through FTL, but on the whole the fashion in Space SF has been leaning toward jump FTL. This is for a couple of reason. The semi-demi-plausible wormhole and quantum-tunneling concepts seem to imply a jump. More important, though, jump FTL is less intrusive in stories.

This is desireable, because most Space SF writers — myself included — are basically guilt-ridden about FTL. We would like to make our stories seem plausible, and may go to a great deal of effort to research, say, what stars are likely to have HABITABLE PLANETS, how much thrust a fusion Drive can generate, or the economics of interstellar Trade. But right at the heart of the whole damn thing is what amounts to magic. So far as genuine scientific plausibility goes, a ship's FTL Drive might just as well be a pretty woman in a white dress who lights some candles and flips tarot cards while chanting in Welsh.

So the only decent thing to do with FTL is make it as inconspicuous as possible, act as if stars are really just a little farther apart than planets, and hope against hope that the physicists eventually turn up something solid. Till then? Keep chanting in Welsh, babe.

The Trouble With StarDrives

The important point is to keep the fracture under control. Hack writers will assume that "if we have to break a few laws of physics for FTL, why not just throw all the laws out the window?" Don't give in. Omitting physics will degrade your novel to a pathetic lack of accuracy worse than an average Space Ghost cartoon.

What to do? Keep all the physics you can. And when you break the laws for your FTL drive, at least establish some limitations and rules. Then stick to them! Internal self-consistency is better than nothing.

The general rule is what physicists call the correspondence principle or the Classical limit. This states that any new theory must give the same answers as the old theory where the old theory has been confirmed by experiment. Newton's laws and Einstein's Relativity give the same answers in ordinary conditions, they only give different answers in extreme conditions such as near the speed of light, refining the accuracy of the GPS system, or calculating the orbit of Mercury (none of which Newton could confirm by experiment).

The point is: you, as a science fiction author inventing a FTL drive, have to explain why current scientific theory didn't discover FTL travel decades ago. Harry Turtledove turned the problem on its head and turned the explanation into the plot of the short story.

As a general rule, a given science fiction novel has one faster than light method. Two notable exceptions are The Halcyon Drift by Brian Stableford and Startide Rising by David Brin. Both of those novels have half a dozen stardrives used by various races and factions, each with different capabilities and limitations.

The Light-Speed Barrier

No, this is not like the "sound barrier", it is much more fundamental.

That old spoil-sport Einstein ruined FTL travel when he created his theory of General and Special Relativity.

Now according to common sense (and as codified by Isaac Newton), velocities will add to each other. If you are travelling at twenty kilometers per hour due north, and you add five kilometers per hour northward to your velocity, you should now be travelling at twenty-five kilometers per hour due north. Everybody (including Newton) knows that 20 + 5 = 25.

Unfortunately for us, Einstein is not everybody. In Special Relativity, no matter how fast you are moving, a beam of light appears to be moving at exactly the speed of light (the technical term is The Principle of Invariant Light Speed). One of the unobvious consequences is that velocities do NOT add. At least not when one gets close to the speed of light. Only a percentage of the new velocity is actually added.

What percentage? Well, the faster you go, the lower the percentage. And at the speed of light, the percentage is zero. So in theory, once you are at light speed, no matter how much velocity you try to add, the amount actually added is zero. Which means you can never exceed lightspeed.

Almost every single FTL drive you read about in science fiction is based on some clever way to avoid the light speed barrier.

The basic assumption of special relativity, which is most strongly confirmed by observation, is that lightspeed is the same for every observer. So, as you speed up, lightspeed stays as far away from you as it ever was. Your time and distance coordinates distort to allow lightspeed to be equally far away from people moving with respect to each other, but the point remains, no matter how much you accelerate, you can never even approach lightspeed, let alone exceed it.

Even if you completely ignore things like mass and energy, and consider simply velocity, adding more velocity can never get you to lightspeed, no matter how much you add.

The tricksy parts are the "coordinates distort" things. But the basic concept is relatively simple; approaching lightspeed is worse than a red queens race. It takes all the speed possible to just stay the same distance away from it.

Wayne Throop

Note that in special relativity, velocities do not add. Instead, rapidities add. The velocity is the speed of light times the hyperbolic tangent of the rapidity. At low rapidities, the rapidity times the speed of light is almost the same as the velocity. However, no matter how high your rapidity gets, the hyperbolic tangent maxes out at 1 for very large rapidities so that your velocity can never be higher than the speed of light.

So imagine someone in a starship. As he burns propellant, the (delta-V) / (c) consumed adds to his rapidity. If he has a lot of delta-V, he can get a very high rapidity, but when you look at the velocity, it is always less than the speed of light.

Interestingly, the time dilation and length contraction factor is the hyperbolic cosine of the rapidity.

Luke Campbell


FTL Kills Causality

However, very few SF novels deal with the second problem. The aphorism at rec.arts.sf.written goes "Causality, Relativity, FTL travel: choose any two."

Your average physicist holds Relativity quite strongly. It has been tested again and again with an accuracy of many decimal places. Relativity explains why atom bombs go boom (E=mc2 and all that). GPS satellites require relativistic corrections or they give inaccurate results.

Physicists hold onto Causality even tighter. Without Causality the entire structure of physics crumbles. Causes must preceed effects, or it becomes impossible to make predictions. If it is impossible to make predictions, it would be best to give up physics for a more profitable line of work. Like flipping burgers.

Therefore, physicists choose to jettison FTL travel.

Be told: when I say "choose" I mean "choose to exist in the real world". Meaning that if you do not choose Relativity, it means Relativity is an utterly bogus scientific theory. It does NOT mean somehow avoiding near-lightspeed relativistic velocities while performing FTL travel.

Why only two?

Relativity proves that FTL travel is identical to Time travel.

Time travel makes Causality impossible, since it can be used to create paradoxes. Note that to a physicist, it is not enough that time travel never happens to be used to make a paradox. The mere fact it is possible is enough to utterly destroy Causality.

  1. So if you have Relativity and FTL, Causality is impossible
  2. If you do not have Relativity, then FTL is not Time travel, so you can have Causality.
  3. Or more mundanely you can have Relativity and Causality, but no FTL/Time travel

Causality, Relativity, FTL travel: chose any two.

Physicist Stephen Hawking calls #3 the chronology protection conjecture. To help your research, the technical term for time travel is "Closed timelike curve".

So what's the problem?

  1. If you have no Causality, suddenly you are living in Bizzaro-world.
  2. Relativity has withstood every test the scientists have thrown at it for about 120 years, and passed with flying colors and multiple decimal places. If it is eliminated, the Correspondence Principle mandates it will have to be replaced with a theory that will predict everything that relativity is predicting now. Good luck with that.
  3. If you eliminate FTL/Time-Travel you will make lots of science fiction writers angry.

Why have you not read about the causality FTL problem in any science fiction novel?

It is absent from some because the authors do not know enough relativity theory to spot the FTL equals Time Travel implication.

It is absent from the rest because of those authors who do know enough relativity, none of them wants to deal with the huge squirming can of worms opened by time travel. They just wants a quick and easy way to get their hero from star to star, not write a doctoral thesis.

This is why the time travel connection is the dirty little secret of science fictional FTL travel.

Time-Travel Paradox Example

The classic Time-travel paradox is the so-called "Grandfather paradox" (though it actually should be called the "Grandmother paradox"). Boris Badenov sneaks into Mr. Peabody's Wayback Machine (actually the WABAC machine, but who cares?) and travels back in time to when Boris' grandfather was a baby. Boris then gives his infant grandfather a lit stick of dynamite then cackles evilly as his grandfather is blown to bits. Bah-hah-hah!

But wait! Boris' grandfather is now smithereens, he'll never grow up, beget Boris' father, who will beget Boris. In other words, Boris will never exist.

But if Boris never exists, then he will never travel back in time to assassinate his grandfather. In which case grandpop will beget Poppa Boris, who will beget Boris. Who will then proceed to assasinate his grandfather. Start back at the beginning and repeat.

Does Boris' grandfather get blown up? Both Yes and No! A paradox.

And causality is killed stone dead. Because physics requires "Yes" or "No", an answer of "Both" is worthless.

Wormholes and Stargates Kills Causality Too

Please note that in this case the definition of FTL is "when you start at point A and can make an appearance at point B in a shorter time that a photon would take traveling through normal space". In other words, a Stargate from the Stargate Franchise or the Ring network from The Expanse counts as FTL. As does anything involving wormholes. It doesn't matter that they are making the adventurer or the spaceship vanish at one point and appear at another point without traveling through the space between. As far as Einstein's relativity is concerned, it is faster-than-light.

Also note that as far as Causality is concerned, FTL communication is every bit as bad as FTL travel.

FTL Loop-Hole: No Paradox Rule

Clever readers will have already spotted a possible loop-hole. What if there was some law of physics that prevented Time travel from creating paradoxes? In that case, FTL/Time Travel would not make Causality impossible. Which would give science fiction authors the gift of scientifically accurate FTL starships.

Hinson shows there are four ways of enforcing a "no-paradox" rule for time travel. Parallel Universes, Consistency Protection, Restricted Space-Time Areas, and Special Frames. In some ways Special Frames is the best, though it directly contradicts part of Relativity (the first postulate of special relativity is that there are no special frames, "no privileged inertial frames of reference"). Oh well. For details, you'd best read the Hinson article.

The latter three are examples of the Novikov self-consistency principle.

In some late-breaking news, physicists Daniel Greenberger and Karl Svozil have shown that the laws of quantum mechanics enforces Consistency Protection. You can read their paper here, but it makes my brain hurt. Translated into English, they maintain that time travellers going back into the past cannot alter the past (i.e., the past is deterministic). This is because quantum objects can act sometimes as a wave. When they go back in time, the various probabilities interfere destructively, thus preventing anything from happening differently from that which has already taken place.

Quick-and-Dirty Way to Deal With FTL Scientifically

It seems to me that an FTL drive ruled by the Novikov self-consistency principle would operate in a very strange and non-intuitive way. It might be that occasionally the starship pilot would try to start a trip and the FTL drive would refuse to operate. Or the pilot suddenly has a heart attack. Or there is a sudden call from the pilot's boss ordering the trip to be cancelled because of an unexpected IRS audit. Or suddenly a meteorite punctures the ship's fuel tank. Or some other annoying bit of bad luck is thrown up by the blind forces of the universe to prevent the trip.

Then the pilot would know that some how, some way, the proposed trip would cause a causality paradox. And the universe just won't have it.

Or even worse, after an FTL trip, the pilot and any passengers would discover that if they try certain actions the entire universe throws up random events preventing said actions. Indeed the entire universe might throw up random events forcing a passenger to perform some action. Because if certain actions happen or certain actions do not happen, given the events that occured during the FTL trip, a paradox will ensue. In other words it would be an example of the effect happening before the cause.

So the quick-and-dirty way for a science fiction author to have an FTL drive that acts semi-plausibly: use whatever FTL drive you want. But at dramatic moments have the drive fail (as per above) while the protagonists turn white with fear while screaming "OH NO! A NOVIKOV VIOLATION! WE'RE TRAPPED!"

This could be real exciting if, for instance, an interstellar grand admiral was orchestrating an ambush of an enemy starship battlefleet, and Novikov's principle unexpectedly prevented some or all of the ambush fleet from arriving. Oops.


In science fiction, it is pretty standard fare to introduce some form of faster-than-light communication or travel. After all, space is big, and you can't write your swashbuckling Hornblower-in-space novel if you have to wait for a generation ship to crawl painfully slowly between the nearest stars, much less try to cross a galaxy.

However, faster-than-light communication (which includes travel) breaks something very fundamental about physics, something that is often ignored by sci-fi, and difficult for non-physicists to understand. If you allow faster-than-light (FTL), then you break causality: you are allowing time-travel. One pithy way of saying this is:

Pick two:

  • Relativity
  • Causality
  • FTL

The Universe has picked relativity and causality, it seems. Thus, we cannot travel or communicate faster than light. 

But why is this? Why does FTL imply time travel. To demonstrate this, it's handy to draw some diagrams. We're going to work with "spacetime diagrams." They look like this:

Here I'm trying to draw all four dimensions of the Universe: three space and one time. Now, I can't draw four dimensions. I can't even really draw three (it's a 2D screen, after all). So I've suppressed two space dimensions, drawing all of space as just a line. It won't matter much for what I'm trying to do, but it's good to keep that in mind.

With that in mind, I'm showing here my spacetime diagram: I'm stationary at the center, and so I see time tick forward "orthogonal" (perpendicular) to the space directions around me. As you'll see, other people have different spacetime diagrams, and different time and space axes, relative to me. That's the point of relativity, after all.

The special thing about relativity is that everyone measures the speed of light to be the same. We show this in a spacetime diagram by saying that every spacetime diagram has light traveling at 45 degrees relative to the time axis. Light travels on lines that are called "null."

Here I'm showing the null lines of light emitted from an event at the time I'm calling t=0 (when the time and space axis cross).

Remember I'm suppressing most of the space dimensions: these rays of light are really emanating out in a sphere around me. Because light travels at 45 degrees, anything traveling slower than light from this t=0 event is closer to the time axis than the light rays, and anything faster than light is further away from the time axis.

The light rays define the future lightcone. This is the set of spacetime events that can perceive the event at t=0, and so, in a Universe without FTL, all the events that can be affected by whatever happened at this event at t=0. There is also a past lightcone, which would be the 45 degree lines extending backwards in time from the event: in a Universe without FTL this defines all the events that could have effected that t=0 event, because the light (and thus things moving slower than light) from those other events had time to reach the t=0 event.

So now let me move from general spacetime diagrams to an example that will indicate why FTL implies time travel. Let's consider a specific example: Let's say we on Earth have built a FTL communication device that let's us talk to the inhabitants of the planet Proxima Centauri B, 4.25 lightyears away. Again, this is what a FTL and slower-than-light set of communications would appear like in a spacetime diagram.

Critically, I've drawn the time axis for the Proximal Centaurians parallel to our own time. This is because Proxima Centauri is moving at essentially the same velocity as Earth (the differences are small compared to the speed of light). Thus, there are no big relativistic effects between our counting of time and the Proximal Centaurians. 

Now, let's imagine that some event occurs away from Earth, oriented in such a way that the light from the event hits us before it reaches Proxima Centauri. The spacetime diagram for that would look like what I've shown. First we see the light, then the light reaches Proxima Centauri. Notice I've drawn the light rays from the event traveling at 45 degrees to my time axis. After all, it is light, and light travels at 45 degrees on spacetime diagrams.

So, now, let's add in FTL communication.

We see the event, we get on the FTL phone, and we tell the Proximal Centaurians. They get the phone call, and now have years to prepare for the arrival of the light from whatever the event is (let's say it's a supernovae, or the launch of relativistic attack vehicles. We are playing with sci-fi tropes here).

Now, this is the image most people have of FTL communication. There appears to be no problem: we all agree that the event happened "first," then Earth calls Proxima Centauri, then the light reaches Proxima Centauri. No problem: though the Proximal Centaurians hear about the event "early," no causality has been violated. After all, we all agree on what happened first, don't we? No effect precedes its cause.


But we've forgotten relativity. This only works when everyone is moving in the same frame of reference, like us and Proxima Centauri (really we're not in the same rest frame, but its close enough not to matter). So, to see the problem, let's add a new observer, moving at high speeds relative to Earth and Proxima Centauri. It's sci-fi, so we add a relativistic spaceship. It's moving with v<c but v>>0, so it's trajectory on my spacetime diagram is highly skewed relative to my time axis: it's nearly moving at the speed of light.

Here's where the relativistic effects start coming into play. Relativity tells us that everyone moving with constant velocity is totally justified in saying they are stationary. Thus, we think we're stationary (ignore the rotation of the Earth, or its orbit around the Sun). The Proximal Centaurians think they're at rest. The people on the relativistic spaceship think they are at rest. So they can draw their spacetime diagram, with their own time axis. That time axis, like mine, is always where they are: on the ship. So I think their time axis is aligned with the ship trajectory.

In addition, they have a space-axis, just like I do. Relativity mixes up space and time, so their space axis I perceive as slanted - just like their time axis is skewed. It turns out that the space axis is flipped across the 45 degree null line, but I'm not going to prove that. This weird mixture of space and time of observers I perceive as moving is a necessary part of relativity. It is the only way everyone can agree that light moves at c

Now, if I wanted to, I could draw the spacetime diagram of the spaceship in its frame of reference. It would have othogonal space and time axes, the light from the event would travel at 45 degree, and they would see Earth's axes highly skewed (pointing toward the left if I kept the same orientation as in this set of diagrams). That's relativity. But we will not draw that diagram here, as it's not necessary for the story.

So what happens now. Let's ask when the spaceship sees the various events in this diagram. To do that, we need to know the lines of constant time for the ship. That's not too hard: lines of constant time for us are lines in the spacetime diagram parallel to the space axis. So it is for the spaceship. Their lines of constant time look like this:

Now do you see the problem?

According to us, on Earth, the order of events is thus: we see the light from the event hit us. We call Proxima Centauri on the FTL phone. The Proximal Centaurians do whatever they want to do in response to that call, and then they see the light of the event. 

What does the ship see? They see the phone call received on Proxima Centauri. Then they see the phone call placed from Earth. Effect precedes cause: causality is violated. In fact, if the ship had a FTL phone set up in the right way, they could call Earth before Earth placed the call. They could even tell Earth "hey, don't make that call to Proxima Centauri we just saw you make." Then what?

Now, you might say "wait, light takes a finite amount of time to travel. You've just shown what times the spaceship will assign to various events, but they can't see it immediately. That'll save us!" Sadly no. Here's when the ship actually gets the light from the events.

As you can see, the light from the phone call reception arrives well before the light from the placing of the phone call. Again: causality is violated.

So you see the problem: if we could just say that there was only one frame of reference where we needed to set up cause and effect, then we could have FTL without worrying about causality. However, there is no special frame of reference, there cannot be one if relativity is to be true. And relativity is true, because we all measure light to travel at the same speed (also, you need relativity for electromagnetism to work, which you probably do want).

If you could travel or communicate FTL, you can time travel, or at least communicate backwards in time. And that would be troubling - and doesn't seem to be the Universe we live in.

From WHY FTL IMPLIES TIME TRAVEL by Matthew Buckley (2016)

1. The Unique and Constant Speed of Light.

Many science fiction stories simply assume you can travel faster than light, using one means or another, and don’t worry about the consequences. This assumption, of course, gets us into trouble with Einstein’s Principle of Relativity, which, for a number of reasons, forbid spaceships to travel faster than the speed of light.

Other stories (notably The Left Hand of Darkness, by Ursula LeGuin) try to be more careful, and properly apply the Principle of Relativity to the motion of the spaceships. As a result, these ships can only travel slower /than light, the time dilation being used to let the ship travel over interstellar distances in a reasonable ship-board time. But at the same time some of these authors assume there is some Way of transmitting a signal faster than light—even instantaneously—over interstellar distances. I want to show in this article that if you make the above assumptions, then what you are doing is combining two incompatable concepts—the Principle of Relativity and faster-than-light communication. As a result it is possible to get into paradoxical situations where very peculiar combinations of events can take place. But before we can understand these paradoxes it is necessary to show why the speed of light is something so special.

Einstein’s Principle of Relativity is based on the observation that the speed of light is the same to all observers. That is, anybody who measures the speed of light is going to get exactly the same number, no matter how fast he is moving, or how fast the source of the light is moving. For this reason we call the speed of light an invariant quantity.

The invariance of the speed of light has some remarkable consequences. For example, suppose Richard Seaton, on board Skylark III, is traveling towards the star Capella at one half the speed of light, while John Star, on Spaceship Orion, is traveling away from Capella at half the speed of light. The observer on each ship measures the speed of the light received from Capella and finds it to be 299,792.458 kilometers per second, even though one ship is traveling toward the source of the light and the other ship is traveling away. This is the same speed that would be measured even if the ships were at rest relative to the star emitting the light.

What is perhaps more surprising, John Star finds that a light beam sent to him from Skylark III also travels with the normal light speed (which we call c), even though the two ships are moving toward each other. At the same time, Richard Seaton, on the Skylark, measuring the speed of the light beam he himself is transmitting, finds that it, too, travels with the same velocity. Everybody gets the same number for the speed of light.

Now this is an unsettling phenomenon to someone only familiar with classical (pre-Einstein) concepts. Sound waves do not behave like this at all. The speed of a sound wave depands not only on the velocity of the source relative to the air, but also on the velocity of the observer doing the measuring. An airplane pilot measuring the speed of sound transmitted to him from another airplane will measure different speeds, depending on where the other plane is located—whether it’s in front or to the side. But the speed of light depends on neither the velocity of the source nor of the observer. Any observer will measure the same light speed regardless of the source. (From here on it will be understood that we are dealing only with light traveling through a vacuum.)

The statement that the speed of light is a constant is not just theory. It is based on a very large number of experimental observations, which in recent years have become extremely accurate. It must be understood that simple measurements of the speed of light are not enough to say that this speed is a constant. This is because measurements of light speed are usually made by finding the time it takes for the light to travel back and forth over a closed path. Averaging over the two directions of travel washes out most of the change that would occur if the speed of light depended on the motion of the apparatus.

Therefore measurements having to do with the constancy of the speed of light are so-called “second order” experiments, usually involving comparison of the speed of two light beams traveling in different directions relative to the motion of the earth in its orbit. The classical experiment of this kind, of course, was the Michelson-Morley experiment, performed about 1887.

I don’t want to go into details here about the experiments. (For such details see my book, Discovering the Natural Laws, Doubleday, 1972.) It should be mentioned, however, that the Michelson-Morley experiment, by itself, is not sufficient to prove the constancy of the speed of light. In 1949 the well-known relativist H. P. Robertson, of the California Institute of Technology, proved that three independent types of experiments are needed to nail down the proposition that the speed of light is absolutely a constant. These three experiments test the following three hypotheses:

1. The total time required for light to traverse a given distance and then to return to its origin is independent of the direction of travel of the light beam.

2. The total time required for a light beam to traverse a closed path is independent of the motion of the source and of the observer.

3. The frequency of a moving light source (or radio transmitter) is altered by a time dilation factor that depends in a certain way on the velocity of the source relative to the observer.

All three of these statements have been verified by hundreds of experiments during the past century. The Michelson-Morley experiment tests only the first statement. The Kennedy-Thorndike experiment (1929) was the first to test the second, while the Ives-Stillwell experiment (1938) was the prototype of the third.

A traditional way of rating the accuracy of such experiments has been to go back to the old idea of light being a vibration of a hypothetical ether. If the Earth were traveling through this ether, then a Michelson-Morley type of experiment would detect the motion of the Earth through the ether. Experiments of this type always fail to find such a motion. But there is some error in every experiment, and so we describe the amount of error by saying how much ether motion could be detected by the experiment if it were there.

The original M-M experiment was precise enough to detect an "ether drift” of about 1 kilometer per second, while the actual velocity of the Earth in its orbit around the sun is 30 km/sec. Therefore the result of that experiment was considered negative. Modern techniques using laser beams are many times more precise than the older experiments. The 1964 experiment of J aseja, Javin, and Townes was able to detect an “ether drift” less than 1/ 1000th of the velocity of the Earth, and none was found. A very recent experiment of A. Brillet and J. L. Hall (Physical Review Letters, Feb. 26, 1979) improved on the above accuracy by a factor of 4000. That is, the apparatus was capable of detecting a motion of the Earth relative to the “ether” 4,000,000 times smaller than the actual velocity of the earth around the sun. And none was found.

In modern terminology what this means is that the speed of light is found to be constant with a margin of error of about 2 parts in 1014. The Brillet-Hall experiment is one of the most precise experiments in the annals of physics.

It is necessary to understand how precise these experiments are, and how complete these experiments are, in order to recognize that when we say “the speed of light is a constant,” we are not just talking theory. We are talking about a measurement—a whole set of measurements that dovetail into a closely knit logical system of the most extraordinary precision.

Furthermore, the speed of light is unique. (Of course, when I talk about light I mean all electromagnetic waves.) Nothing traveling at any other speed has the property that its speed is the same to all observers. This is a very important statement, as we shall see.

Now, once we have established that the speed of light is a constant, then the rest of Einstein’s Special Theory of Relativity can be deduced. What I want to talk about for the rest of this article is just one consequence of the theory—the effect of relativity on the concept of time—especially on the concept of simultaneity.

2. Simultaneity and the Time Dilation.

What relativity does to time is the hardest part of the theory to understand. And usually, whenever a person gets into trouble with relativity, it is because he/she has not fully understood the time part of the theory.

Even an elementary concept such as simultaneity becomes very mysterious when we look at it from the relativity point of view. Relativity is a science that studies the relationship between events. We speak of an event as taking place at a certain point in space and at a certain instant of time. Two events are simultaneous when they occur at the same time.

Intuition tells us that if Richard Seaton sees two events happening simultaneously, then John Star will also see the same two events taking place simultaneously. However, Einstein proved that our intuition is wrong. In the immortal words of George Gershwin, “It ain’t necessarily so.” The remarkable thing that Einstein showed was that two events that are simultaneous to one observer are not necessarily simultaneous to another observer. And everybody’s ideas of time were knocked into a cocked hat.

We can demonstrate very simply how this strange state of affairs comes about. Consider three spaceships passing Earth at some high speed, spaced a few million kilometers apart. (See Fig. 1) The exact distance doesn’t matter.

Say that Kimball Kinnison is in Spaceship B. He has made spatial measurements so he knows spaceships A and C are equally distant from his ship. Now A and C each explode a bomb at the same instant of time. Kimball Kinnison knows that they both explode at the same time because he sees the light flashes reaching him at the same instant of time, and he knows he is halfway between A and C. So that’s how Kimball Kinnison defines simultaneity in his reference frame.

On the other hand, consider John Star on Earth. Spaceship B passed Earth just as the light flashes from the two bombs reach Earth. So John Star sees these two flashes at the same time Kimball Kinnison does. John Star sees the flashes simultaneously, but does he say that the two bombs exploded at the same time? Not if his reasoning is correct.

John Star starts out by saying: the light flashes from the explosions travel through space with the speed of light. That’s the one thing we know for sure. It’s going to take some time for the light to reach Earth. Therefore when the bombs explode, the three ships must be in the position shown in Fig. 2. We see that the light from bomb A has farther to travel than the light from bomb C. But if the two flashes reach Earth at the same time, then bomb A must have gone off before bomb C! (Remember both light flashes travel with the same speed.)

You see that as a result of the fact that the speed of light is constant, we find inexorably that Kimball Kinnison and John Star disagree about the timing of the bombs. One of them says they both went off at the same time. The other says bomb A went off before bomb C. Time has gone awry.

In the jargon of relativity, we speak of Kimball Kinnison being in one reference frame, while John Star is in another reference frame. The two frames are moving relative to each other. One of the chief functions of relativity is to see how things happening in one frame appear to the people in the other frame. What we have just shown is that two events that are simultaneous in one frame are not necessarily simultaneous in another, moving frame. (For the events to appear simultaneous in both frames, the two events would have to be located at the same point in space.)

Another distortion of time is demonstrated by a different experiment. Suppose Kimball Kinnison sets up a light source, a detector, and a mirror, as shown in Fig. 3.

He flashes the light and measures the time it takes for a short pulse to go from the source to the mirror and back. Let’s say the time is one microsecond. What does John Star see? He’s standing on Earth as Kimball Kinnison’s ship flashes by, and the path of the light pulse looks to him as shown in Fig. 4. The drawing shows, not three different ships, but the same ship as seen at three different times while it moves past the Earth.

Now the path of the light flash as it goes from source to mirror to detector is much longer than it appeared to K. K. standing in his ship. But! Remember that the light travels with the same speed, regardless of the observer. So if John Star sees it traveling over a longer path, it must be taking a longer time. But John Star and Kimball Kinnison are measuring the time interval between the same pair of events: emission of the light flash from the source, and arrival at the detector. We see, then, that the time between these two events depends on the motion of the observer relative to the events.

Kimball Kinnison says the light flash takes 1 microsecond to get from source to detector; John Star says it takes a longer time—let’s say 5 microseconds. This means John Star’s clock makes 5 ticks for every one tick of Kimball Kinnison’s clock. John Star says K. K.’s clock is running slow compared to his own. This effect is the famous time dilation—the slowing down of time in a moving reference frame. You see that the time dilation is a necessary consequence of the fact that the speed of light is a constant. (The formula for the time dilation can be derived from Fig. 4, using nothing more than the Pythagorean Theorem. See any good book on relativity.)

Now we are in a position to ask some interesting questions. Take our friend Kimball Kinnison scooting along at half the speed of light, engaging in a conversation with headquarters back on Earth, using the instantaneous communication powers of his lens. First of all, what does instantaneous communication mean? It means the signal is transmitted and received at the same instant of time. This means transmission and reception is simultaneous.

But we just showed that simultaneous is all in the eye of the beholder. What is simultaneous to K. K. will not be simultaneous to Earth. Communication that looks instantaneous in one frame will not be instantaneous in another.

So what does instantaneous communication mean?

We will come back to this question shortly.

3. The Geometry of Spacetime.

There is a set of equations that allows us to find out what is happening in one reference frame if we know what is happening in another. In other words, if we know the position and time of an event in K. K.’s ship, these equations give us the position and time of the same event as seen by John Star on Earth. These equations are known as the Lorentz transformations. Hendrik Antoon Lorentz was a Dutch physicist—one of the giants of 19th century physics. He discovered the equations that bear his name by considering the properties of electromagnetic Waves. These are the same equations that Einstein derived in developing the theory of relativity.

The equations are named after Lorentz because he did them first. The irony of the situation is that Lorentz never completely understood the equations. If he had, he would have been the inventor of relativity. But Lorentz never believed what the equations told him—that time could be different in two reference frames. He was stuck to classical ways of thinking, in which time is the same to all observers.

It was Einstein’s ability to break away from this classical thinking that was his peculiar genius. He was aided by the brilliant mathematician Hermann Minkowski, who originated the concept that Einstein’s theory could best be understood by thinking of space and time as a single entity—a space-time continuum. In other words, instead of describing the universe by three dimensions of space and a completely separate dimension of time, we now deal with a four-dimensional spacetime.

Time is now one of the four dimensions, on an equal footing with the three spatial dimensions. I emphasize that “equal footing” does not mean that time is the same as space. We merely mean that time is treated the same as space mathematically. (Incidentally, there are new theories which postulate three time-like dimensions to match the three space-like dimensions. I’ll let my son explain those.)

To show where events are located in this four-dimensional space, we use a spacetime diagram, such as in Fig. 5. The horizontal axis shows the distance (in light-years) away from the starting point, which in this case is Earth. The vertical axis is a time scale (in years). There can also be y and z axes, but these are left out in a two-dimensional drawing. Any point on this diagram represents the location of an event: where it is relative to Earth, and at what time.

In Fig. 5, we have located Earth on the vertical axis-at the point where X = 0. The time when all the clocks are set to zero is labeled t = 0. As time passes, the position of Earth advances upward on the time axis. Notice that the X axis is the location of all the places where t = 0 in this frame.

We also show Kimball Kinnison’s spaceship going away from Earth at half the speed of light, traveling along the trajectory so labeled. The ship has passed by Earth on zero time—that is, when t = 0. Its position is shown after 10 years (Earth time) has elapsed, and it has traveled 5 light-years through space. (In this article I am going to stick to ships traveling with constant speed, and will leave accelerating ships for another article.)

A beam of light projected from Earth at zero time will go a distance of one light-year in a time of one year, so it travels along a 45° path represented by the dashed line. A ship traveling faster than light would go along a trajectory lying below the light path. In this article we are not going to consider FTL spaceships, but whatever we say about signals going faster than light would also apply to any kind of object, spaceship or otherwise.

The diagram of Fig. 5 is the universe as seen from Earth; it is the Earth’s reference frame, and is an ordinary cartesian coordinate system, in which the axes are perpendicular to each other. Now let us see what the ship’s reference frame looks like. You must understand, of course, that the people in the ship think that they are standing still, and that the rest of the universe is moving. So space-time, to Kimball Kinnison and his crew, is also rectangular, just like Earth’s spacetime.

However, when the people on Earth look across to the moving ship, they see its spacetime grid altered. Fig. 6 shows what the ship’s coordinate system looks like at the instant the ship passes Earth, so that both Earth and ship are at the origin (x = 0 and t = 0).

The ship’s grid is distorted. Its x-axis is leaning up, and its t-axis is leaning to the right. The two axes are no longer perpendicular to each other. We call the ship’s axes x’ and t’.

Remember that the x-axis represents all the places where time is zero in the Earth frame. Likewise the x’-axis represents all the places where time is zero in the ship’s frame.

Now suppose we blow up a Klingon ship at point A along the x’-axis, some distance away from Kinnison’s ship. This explosion takes place at zero time according to the ship’s clock, but it is not zero time according to Earth clocks. We can calculate what the Earth time is by using the Lorentz transformation equations.

Let’s put in the following numbers: Kinnison’s ship is just passing Earth and traveling at half the speed of light. The Klingon ship is 10 light-years away from Earth when it is blown up (in Earth’s reference frame). But, as Kinnison sees it, the explosion is only 8.66 light-years away. And, as the Earth people see it, the explosion takes place 5 years after the starting time, rather than at time zero. (In technical terms, we say the coordinates of the explosion are x = 10 Ly and t = 5 y in the Earth frame, while x’ = 8.66 Ly and t’ = 0 in the ship’s frame.)

Notice that both space and time are transformed. Kimball Kinnison finds that the distance to the Klingon ship is less than the 10 light-years measured by the Earth-bound observers. This difference demonstrates the famous Lorentz-Fitzgerald contraction of space. It arises because Kinnison’s ship is moving relative to Earth. This story also illustrates what we were saying previously about simultaneity. All events happening along the line marked t = 0 (the x-axis) are simultaneous according to the Earth observers. But according to the people on the ship, it is the events happening along the line marked t’ = 0 that are simultaneous. And these are a different set of events. So the people on Earth and the people in the ship disagree about what is meant by the word simultaneous. To the people in the ship the blowing-up of the Klingon ship is simultaneous with the instant their clock hits zero. To the people on Earth, the explosion happens when their clock hits 5 years. (Notice that the people on Earth don’t actually see the explosion until the flash reaches them at 15 years.)

So precisely What do we mean when we talk about sending a message instantaneously? An instantaneous message is transmitted and received simultaneously. But if either the sender or the receiver is moving (or, to be exact, if one is moving relative to the other) then it is not possible for the message to be instantaneous to both the sender and the receiver. If it is instantaneous to one, it is not instantaneous to the other.

Immediately we are in trouble.

There is a way out. We can make the following rule: let the transmitter decide on the meaning of instantaneous (and simultaneous). Suppose, for example, we send a message through a wormhole from one part of space to another. The wormhole has to pass along some particular path in spacetime—some particular line on a spacetime diagram. The simplest way to do it is to say that the wormhole will travel along the x-axis in the reference frame of the transmitter. So a wormhole projected from Earth will go along the line t = 0, while a wormhole projected from the moving spaceship will go along the line t’ = 0. (Or along a line parallel to it, depending on where the ship is when it sends the message.)

Let us now see what consequences this assumption generates.

4. Consequences of Instantaneous Communication.

Consider the following scenario: Ten years (Earth time) have passed since Kimball Kinnison’s ship left the vicinity of Earth. Fig. 7 shows how things are arranged now.

Earth has moved up the time axis to the 10-year point. The ship has moved along its trajectory, and has traveled 5 Ly at half the speed of light, according to Earthly measurements. Of course, the people in the ship see things differently. They are of the opinion that they have gone a distance of 4.33 Ly in a time of 8.66 years.

Now, suppose the people on Earth project a wormhole out through space to the ship. And let us assume that messages can be transmitted by radio through this wormhole. The Wormhole, as we agreed in the last section, takes no time to get from one place to another. Or, let’s say, it tunnels through space, starting from the Earth’s position, and it comes out 5 light-years away at the same instant of time. So its path is represented by the arrow going from Earth to ship, parallel to the x-axis.

Just to make things specific, let’s assume that the ship passed Earth on Jan. 1, 2100. This is when all the clocks were set. The message leaves Earth 10 years later, on Jan. 1, 2110, and reaches the ship at the same time, according to the Earth point of view. But on the ship, the message is received at the 8.66-year point. If Earth is broadcasting news of New Year’s, A.D. 2110, the ship will receive that news in August, 2108, ship time. It is as though the message has gone backward in time while going from Earth to the ship.

Now what happens if the ship replies to this message from Earth? First, we have to decide how this message is going to travel. One way of doing it is simply to have the ship send its reply straight back through the Earth’s wormhole. After all, if the pipe has two ends, there’s no reason why it shouldn’t work equally well in both directions.

Or is there?

It turns out that there is a very powerful reason for thinking this scheme will not work, simple though it sounds. If we use the wormhole as a two-way tube, the message from Earth to ship travels toward the past—from January, 2110, to August, 2108, while the message from ship to Earth travels toward the future—from August, 2108 to January, 2110. There is a difference—an asymmetry—between the Earth and the ship.

Imagine what would happen if there were ten ships out there all going away from Earth. Earth sends wormholes out to all ten ships, and it knows its messages go toward the past to reach these ships. The ships, on the other hand, have to send their messages toward the future to reach Earth. The Earth can now say: I am unique, because I am the only one whose messages go toward the past. As a result Earth can claim that it is absolutely at rest, while it is the ships that are in motion.

But this violates the most fundamental postulate of relativity—the idea that there is no privileged reference frame—no frame that can be considered "absolutely at rest.” If we say a ship is in motion relative to Earth, we can equally well say Earth is moving relative to each ship. There should be no way to tell the difference.

Putting it another way: suppose an observer on a ship is monitoring radio waves coming from Earth (without wormhole). Due to the Doppler effect he finds the frequencies shifted downward. He can explain this by saying it’s because his ship is traveling away from earth. Or he can just as well say it’s because Earth is traveling away from the ship. It makes no difference. Furthermore, an observer on Earth, looking at the radio waves coming from the ship, will find them shifted downward also. All that counts is that Earth and ship are moving apart, and the Doppler effect shifts the frequencies downward, no matter who is doing the measurement.

And so it must be with the wormhole communication. If the message from Earth to ship goes toward the past, then the message from ship to Earth must also go toward the past. That makes the situation completely symmetrical, as required by the fundamental postulate of relativity.

On the other hand, we could turn the logic around. We could argue that if a wormhole allowing two-way conversations existed, then that would prove the fundamental postulate of relativity to be invalid. This conclusion would delight many people. But the proof of the pudding is in the eating. First you have to get a wormhole.

So now we go to another argument. We begin once more with the message sent via wormhole from Earth to ship, transmitted January, 2110 (Earth time), and received August, 2108 (ship time). The ship now sends a reply to Earth through its own wormhole—that is, a wormhole transmitted by the ship’s own generators. If we play the game according to consistent rules, the message must go instantaneously from ship to Earth, according to the ship’s clock—that is, in the ship’s reference frame.

That means the ship’s wormhole must lie along a line that represents t’ = 8.66 years on the diagram. This line will pass through the ship’s position and will be parallel to the line labeled t’ = 0. Since all points on this line represent the same time, I call this the ship’s Synchrony Line.

A message going along this line will reach Earth at the 7.5 year point (Earth time—that is, in July, 2107).

Now see what we have done. The original message left Earth in January, 2110; and the reply reached Earth in July, 2107, two and a half years before the original message was sent. Here we have all the ingredients for a time travel paradox. While the characters themselves have not traveled through time, sending messages into the past is good enough.

For this is the kind of thing that can happen. Sometime in 2109 a disaster happens—say the assassination of a president. In 2110 a message is sent to the spaceship telling them of this event. The ship immediately sends a message to Earth, informing them of the assassination. Since Earth receives the message before the assassination took place, the authorities are able to apprehend the assassin before he fires the shot. But then the assassination never takes place, so no message is sent to the ship. So no warning is received by Earth, and the president is killed. So a message is sent to the ship…

And so we go around and around.

This is a paradox. A real paradox.

The instantaneous communication allows us to set up a situation that has contradictory elements. If it happens, it doesn’t happen. And vice-versa.

Now I could use this argument to say: the existence of the paradox proves that instantaneous communication is impossible.

I will almost say it, but I’m going to leave one little loophole, one little hedge. In the last few years I have become very cautious about paradoxes. The reason is that I, myself, with my own hands, did an experiment whose results were paradoxical within the framework of our ordinary concepts. (See “On the Fundamental Mystery of Physics”, I.A.’sS.F. Magazine, September, 1979.) The only way to understand the experiment is to get a new set of concepts.

In a similar vein, I will say that if some means of instantaneous communication were found, then it would require us to invent a new set of concepts concerning the structure of spacetime. A set of concepts that allows the paradox to exist, that allows two contradictory events to take place. Something like an alternate-universe kind of theory, where the president is assassinated in one branch of the universe, and is warned against it in another branch.

But aside from that possibility, the existence of the paradoxes makes instantaneous communication very hard to swallow.

We can ask this question: what about communication just a little bit faster than the speed of light instead of instantaneously? It turns out that the conclusions reached in this article apply to any kind of message sent faster than light. The only thing different would be that the path of the message on the spacetime diagram would not lie along the synchrony line, but would have a different slope. But there would always be some range of velocities (both ship and signal) that would give a trajectory going into the past, and so would result in time-travel-type paradoxes. I have chosen to talk mainly about instantaneous communication because the arithmetic is easier to do and the diagrams are easier to draw.

Furthermore, everything we have said about transmitting signals faster than light also applies to solid objects traveling faster than light. A spaceship going faster than light could get into the same kind of paradoxes I’ve been describing. Therefore the arguments against FTL communication are also arguments against FTL travel.

5. Conclusions.

The trajectory of a signal is a straight line on a space-time diagram. We have seen that a line that represents instantaneous transmission of a message in the Earth’s reference frame cannot represent instantaneous transmission in the frame of a moving ship. Or, to put it another way, if the two ends of the transmission line are synchronous in one frame, they will not be synchronous in another frame. (By synchronous, I mean that they exist at the same time.) Therefore there is no meaning to the phrase “instantaneous transmission of information,” because the sender and receiver cannot agree on what is meant by that statement if one is moving relative to the other.

If we want to keep consistent with the laws of relativity, we can make the assumption that the transmission will be instantaneous in the reference frame of the transmitter. Then if Earth transmits to a spaceship moving away from Earth, the message goes toward the past. If the spaceship replies to Earth, the reply again goes towards the past, so the reply reaches Earth before the original message left, making possible a number of time-travel kinds of paradoxes.

There is also the possibility of making a fortune in stocks and commodities by having a confederate on the ship transmit to the past information about what prices are going to do in the future. But if you do it too much, your purchases will themselves have an effect on the market, so once more we get into a paradox.

You could, of course, avoid all such complications if you made sure that the sender and receiver were at rest relative to each other. (Or at least not moving very fast.) Then you could communicate between planets, but not between planets and ships. Such a scheme would require a very particular and peculiar kind of transmission, a communication system that fades out when the receiver, or transmitter, starts moving too fast.

So Kimball Kinnison is on his way to Capella, and before he picks up speed he can contact the Capellans through his lens, but once he gets past a certain minimum speed, the transmission fades out and he is now incommunicado.

I don’t know of any logical arguments that would rule out that kind of possibility, except that in physics we never deal with signals that can be detected only when you are at rest relative to the transmitter, and disappear when you are moving. I don’t know what that means.


The Lorentz transformations are equations that allow us to calculate the coordinates X and t of an event in one frame of reference if we know the coordinates x’ and t’ of the same event in another frame of reference (or vice versa). We will let X and t be the position and time of an event as seen by the Earth observer, while x’ and t’ are the position and time of the same event as seen by Kimball Kinnison, in his spaceship moving with velocity v relative to Earth. In the example We are going to consider, the spaceship is moving at half the speed of light, so v = 0.5c, or v/c = 0.5.

A common factor in these equations is the quantity

G = [1 - (v/c)2 ]1/2 ([x]1/2 means "square root of x")

which in this example has the value 1.155. Using this abbreviation, the transformation equations become:

t’ = G(t - vx/c2) (equation 1)
x’ = G(x - vt) (equation 2)

while in the other direction they are:

t = G(t’ + vx’/c2) (equation 3)
x = G(x’ + vt’) (equation 4)

In working with these equations we use years (y) for units of time, and light-years (Ly) for units of distance. The speed of light then becomes, conveniently, c = 1 Ly/y.

The ship is located at the origin of its own coordinate system, so the position of the ship is given by x’ = 0. Putting this value into Eqs. (3) and (4), we find, to no one’s surprise, that x/t = v, the velocity of the ship in the Earth frame. This equation represents the trajectory of the ship in the Earth’s frame, while on the spacetime diagram, the quantity

t/x = 1/v = 2y/Ly

is the slope of the trajectory line. (It is also the t’ axis, since it represents the set of points for which x’ = 0.)

Similarly, we get the x’ axis by setting t’ = 0 in Eqs. (3) and (4). After dividing (3) by (4) we then have

t/x = v/c2 = 0.5 y/Ly

This is the slope of the synchrony line—all the points in the ship’s frame that exist at the same time, as seen in the Earth’s frame.

In Fig. 6, we have an event that takes place on the ship’s synchrony line (t’ = 0), and 10 Ly away in the Earth frame. Setting t’ = 0 in Eq. (4), we find x’ = x/G = 10 Ly/1.155 = 8.66 Ly. The time t in the Earth frame can be found from Eq. (3) by putting in the above values of t’ and x’, to obtain t = 0.5 yr.

In Fig. 7 , the ship has been traveling for 10 years (Earth time) at half the speed of light, so in the Earth frame t = 10 y and x = 5 Ly. In the ship’s frame, x’ = 0, so from Eq. (3) we t’ = t/G = 10 y/1.155 = 8.66 y. The way it looks to the people in the ship, Earth has been going away from the ship at half the speed of light for a period of 8.66 years, so the distance to Earth is 4.33 Ly, instead of 5 Ly.

We want to find the time (t1) when the wormhole from the ship reaches Earth. Earth is at the point x = 0, and the wormhole leaves the ship and arrives at Earth at the time t’ = t/G, where t = 10 y. From Eq. (1) we have

t’ = Gt1 = t/G,


t1 = t/G2 = 10/1.1552 = 7.5 yrs.
From ON FASTER-THAN-LIGHT PARADOXES by Milton Rothman (1980)


     In the conventional interpretation of Special Relativity it is said that the Principle of Causality forbids physical influences from propagating faster than light. In this paper we demonstrate that physical ‘supra-luminal’ speeds need not violate causality, provided that certain less stringent conditions are met; it is suggested that causality can be preserved by a Lorentz-invariant ‘censor-field.‘ Consideration of General Relativity suggests that such a censor-field might be produced by mass-energy in a manner analogous to gravitation, perhaps derived directly from the metric tensor. Some philosophical and experimental implications are mentioned. We conclude that, despite long-standing dogma, the idea of faster-than-light travel or communication is not in conflict with either the Theory of Relativity or the Principle of Causality.


     Most textbooks on Special Relativity argue that it is impossible to go faster than light, giving various arguments in support of this claim; they usually point out that only physical objects or information are prohibited from propagating faster than light, whereas geometrical patterns or apparent motions are not limited in magnitude at all (cf “superluminal" radio sources). The arguments used fall into two classes: arguments from causality and arguments from physical effects. In this section we shall examine and dismiss the (naive) arguments from physical effects.

Because the mass of an object increases without limit as the velocity of light is approached it is necessary to provide an ever-increasing amount of energy to maintain its acceleration, and it would take an infinite amount of energy even just to reach the velocity of light. Therefore no object can travel faster than light.“

     This argument, as well as related ones using the divergence of time-rates, length-scales, etc. near light speed, has been demolished many times, notably by science-fiction writers (who like to be able to use fast starships in their stories). These writers usually observe that it is not necessary to go through the velocity of light in order to go faster than light (‘tachyon drives,’), or that it is not necessary to move through the intervening space in order to go from place to place (‘hyperspace drives' and ‘probability drives,‘).

     Another argument makes use of the law of addition of linear velocities:

“Because any velocity, however great, when added to the velocity of light, gives only the velocity of light, it is impossible to go faster than light."

     This is essentially the same as the ‘light-barrier’ argument. The relative velocity of two sub-luminal objects is indeed always sub-luminal, as is the relative velocity of two supra-luminal objects travelling in the same direction; whereas, the relative velocity of a sub-luminal object and a supra-luminal one is always supra-luminal. Physically this is reasonable and cannot be said to rule out FTL travel.

     Another argument makes use of the Lorentz factor:

“Since the Lorentz factor becomes imaginary for supra-lumlnal velocities, the results in that regime are physically meaningless. Therefore nothing can go faster than light."

     This is more subtle, but nonetheless invalid. There should be no objection to the occurrence of imaginary or complex factors in mathematical expressions in physics (indeed, they occur constantly). Only actual physical measurements need have real results. However, we must emphasise that great care must be taken when trying to interpret results for the supra-luminal regime.

     But these arguments and counter-arguments are of little importance; the important problem is the problem of causality.


     The argument from causality makes use of the fact that travel faster than light looks like travel backwards in time for some observers. With a bit of fast footwork a traveller could return before he set out — effect preceeding cause. Since this is obviously ridiculous, it is believed that travel faster than light is impossible. The argument is set out in more detail below, making use of space-time diagrams.

     First of all we note that a change of Lorentz frame is accomplished by rotating the t and z axes towards each other (Fig. 1). Note that the time-like worldline OW has a positive velocity in the original frame (dz/dt>0), but a negative velocity in the primed frame (dz'/dt'<0).

     Now consider a spacelike worldline viewed from two different frames (Fig. 2). Notice that OW, though apparently well-behaved in S, is travelling backwards in time in S'. Because we can draw a worldline that “goes back in time” we can set up a paradox.

     In Fig. 3 we have a spacelike worldline OW which in S' is going backwards in time; we add a similar worldline WV, which starts at the end-point of the first and goes in the opposite direction, crossing the time axis (in S') at negative t’. The cycle is completed by the timelike path VO.

     But this is absurd. For here O causes W, which causes V, which causes O itself, and so on ad infinitum. All observers in S and S' will agree that the traveller has gone into the absolute past of O; all observers everywhere will agree that the traveller has gone into his own absolute past on one or more legs of his journey; the traveller himself will conclude that he has followed a ‘closed timelike loop.’ This violates the Principle of Causality: effect could preceed cause, or be its own cause; A could equal NOT A (for example, the assertion “there is a traveller at O" could be at once both true and false). This is obviously nonsense; closed causal loops are impossible.

     Since we derived this absurdity simply by assuming that spacelike worldlines (supra-luminal velocities) could actually exist, we have proved that travel faster than light is impossible. Or have we?


     The previous section purported to show that the assumption of FTL travel automatically gives rise to causality violations. However, a hidden assumption was built into that argument, as we shall now attempt to demonstrate.

     For the first leg of the journey, OW, opinions differ as to whether the traveller is going forwards or backwards in time (Δt>0 but Δt'<0), but all agree that W is not in the absolute past of O (as seen from any frame like S or S'); so this stage of the journey is unobjectionable, even though carried out faster than light. It is true that in some frames (such as S') observers will see things happening the “wrong way round," but this is no more than an amusing illusion, and they will have no difficulty in sorting out what really happened. So far, so good.

     (The behaviour of tachyons, as observed via radar or emitted light, can appear very odd: Fig. 4 shows how a tachyon, moving past an observer, seems to appear out of nowhere at the point of closest approach and then move away in both directions; one image seems to go forward in time, the other backwards. If the tachyon accelerates (curved worldline) many images can be present simultaneously, "created" or “annihilated" in pairs. However, when the observer calculates the coordinates and trajectory of the images, in the usual manner, he will be able to assign the tachyon its worldline without ambiguity, and recognise the double images as optical illusions, similar to the sound images of supersonic aeroplanes. This phenomenon does not affect the validity of the space-time or Minkowski diagrams, or the nature of closed causal loops).

     As soon as we try to go from W to V for the second leg of the journey we run into trouble. For the worldline WV is in the absolute past of the worldline OW, as every observer will agree. This leg violates causality, then; it is certainly impossible.

     (The reader may object to the strength of the phrase “certainly impossible," which was indeed used with considerable reluctance; if so, he is invited to find a self-consistent (paradox free) description of a world in which such closed loops are allowed. It is not time travel per se which is forbidden, it is the returning to already visited events: “a man cannot step in the same river twice").

     So the legs VO (which is timelike) and OW (which is spacelike) are causally acceptable, whereas WV is not; the symmetry between OW and WV, which we implicitly claimed above, is broken. In other words, we need not mind if the traveller goes away faster than light, so long as he doesn't try to get back too quickly!


     How fast, then, can a traveller go — and which way? Consider the worldline OW in Fig. 5; it has a constant velocity βw>1 along the z-axis in frame S. The coordinates of W are (tw, zw).

     The dotted arrows indicate the “speed limits" in either direction; a worldline leaving W must keep within these limits if it is not to enter the absolute past of OW. By inspection:

     These limits transform into any Lorentz frame by using the usual formula for the addition of velocities:

βsum = (β1 + β2) / (1 + β1β2)     (5)

     (Here we are dealing with a logical limit on possible speeds, the only kind of limit that can ultimately be proven; this is of philosophical interest even if the physical limits appear to be more stringent; and whatever their physical status may be, the limits derived from the Principle of Causality will be far from arbitrary).

     Now clearly we cannot simply leave it up to the traveller to “obey” the speed limits; there will have to be some kind of ‘censor-field‘ which enforces obedience to appropriate speed limits at every point in space-time, and blocks any attempt to violate causality.

     A trivial example of such a censor is the scalar field of value unity (“maximum speed is everywhere c“); this is the choice that relativists usually make by default, but here we should like to find a less restrictive example.

     What properties should we demand of such a censor field? it should obey the Lorentz transformations, it should supply the "correct" speed limit in all directions (so that no particle can ever travel into the absolute past for any observer, including supra-luminal ones), and it should be smoothly differentiable (with the possible exception of a few “excised” singular points). it must also be generated or built into the metric without violating the Principle of Relativity (it must not define a ‘Universal Standard of Rest.’) Furthermore, to be consistent with known physics, it should not forbid the propogation of ‘tardyons‘ (sub-luminal particles) except, perhaps, under highly unusual conditions.

     (It should be emphasised that the imposition of a censor field is not ad hoc: the Principle of Causality requires that some mathematically defineable field exist, such that closed causal loops are forbidden; what relation (if any) this ‘censor-field‘ may have to actual physics can only be determined by experiment, but the logical limitations of causality and known physics certainly allow us to examine the requirements for a censor field without ad hoc invention. This is not to say that other descriptions (advanced potentials for example — see Ref. 13) are necessarily invalid, but that such descriptions must be mathematically equivalent to, or included in, a causal field description. It must also be pointed out that such alternative descriptions have not yet in fact succeeded in changing the general belief that FTL travel is impossible).


     Consider, as a censor-field, a sheaf of non-intersecting achronal slices through space-time, as shown in Fig. 6. An achronal slice is a surface (strictly, a hypersurface) in space-time which is everywhere spacelike (always “FTL"), but which is not necessarily a surface t=const; an example of a sheaf of achronal slices might be the surfaces t=t0+x/2c.

     At every point on the surface of a slice the limiting velocities are defined such that no worldline can pass through the surface. A maximally fast traveller could skate about upon the surface, but could not pass below it. In general a traveller would come up out of the surface. The achronal slice of the censor-field thus defines a (three dimensional) ‘surface of simultaneity.’

     It is important to realise that these surfaces of simultaneity are not in general the surfaces of constant time co-ordinates; indeed, they could only have t=const in at most one Lorentz frame. The surfaces of simultaneity are Lorentz invariant.

     In moving up out of the surface one is moving forwards in time, passing irreversibly through the sheaf of achronal surfaces. Thus, if events E+ and E- occur on slices respectively above and below the slice though the origin, then O can communicate with E+ but not with E-, whereas E- can communicate with O and E+, and E- can communicate with neither.

     The surfaces of simultaneity are smooth and can be defined by a unit normal vector at each point. They are allowed to undulate and change with time, but they must not intersect; at most they can approach one another infinitesimally closely.

     For the normal 4-vector we use censor (or c for short), such that c.c=-1, as shown in Fig. 7. Note that censor does not usually appear to be perpendicular to the surface of simultaneity; this is because the signature of space-time is (-+++), whereas the diagram can only treat the time dimension as if it were one of space.

     We have:

censor=censor (t, x, y, z)     (6)

     Allowable 4-velocities v obey the limit:

v.censor<0     (7)

     where the zero can be either imaginary or real, according as v and censor are, or are not, separated by the surface of null geodesics.

     It is apparent that this censor-field is Lorentz invariant, since censor is a 4-vector, and v.censor an invariant scalar. It is also smoothly differentiable. It defines a local standard of rest, that is, the frame in which c=( 1 , 0, 0, 0) locally, but not a universal one, since the local rest frame can vary with time and place. Because no worldline can pass back down through the surfaces of simultaneity, but must carry on up wards, closed loops are forbidden. Thus both the Principle of Relativity and the Principle of Causality are preserved by such a field.


     In the previous section an arbitrary set of non-intersecting achronal slices was considered. It is clear, however, that the surfaces of simuitaneity of the censor-field must be generated according to definite rules.

     In principle, it might be, I suppose, that this field was laid down by causes “outside” space-time and is unaffected by any event “within” space-time. This seems unlikely. We already know from General Relativity that the curvature of space-time is produced by matter, and in turn affects matter; it seems most reasonable to assume that the censor-field is bound up with the metric in a similar way.

     The censor-field, we assume, is generated by material objects and radiation; that is, by mass-energy.

     How might we expect this to work?

     We shouid expect that, in a sufficiently large region of homogeneous static matter, the surfaces of simultaneity would be flat and uniformly spaced, the censor-field at rest with respect to the matter. Clearly we can expect the induced gradients of the field to be proportional to the inducing mass (at least in the weak field approximation) and to be inversely proportional to its distance (or some power thereof).

     This is enough to show the qualitative form the surfaces of simultaneity must take. The trivial case of an infinite static homogeneous Universe is straightforward; the real Universe is similar, but expanding. Figure 8 shows the form of the surfaces of simultaneity for a homogeneous Universe with Hubble flow, and for a more realistic inhomogeneous one. The normal, censor, is simply the velocity of the Hubble flow (with small perturbations) and tends to unity slope at infinite redshift. The surfaces are also surfaces of constant proper age.

     The field of two equal masses in relative motion, as viewed in two suitable frames, is shown in Fig. 9. Here each mass is sufficiently concentrated to make the local rest frame closely approximate the proper frame of each mass. Notice how the masses make a “bump” in the surfaces of simultaneity, upwards for converging masses, downwards for diverging ones.

     Thus the censor-field can be seen to depend upon the distribution of mass-energy and momentum; that is, upon the stress-energy tensor that determines the structure of space-time.

     Tardyonic (slower than light) matter seems to be predominant throughout the Universe — no tachyons (FTL particles) have yet been conclusively observed. Nevertheless, we must also consider the effects of tachyons or imaginary mass upon the censor-field. It is clear that, in a region of space dominated by tachyonic matter, the 4-vector censor would also be tachyonic, and the surfaces of simuitaneity would become time-like (this would happen in TAUB-NUT space-time, for example). Of course, the tachyons would look at things the other way round: to them, we would be the tachyons (Fig. 10).


     In the conventional Big Bang theory of the origin of the Universe there is difficulty in explaining its observed isotropy. The microwave background radiation shows that the expansion rate and average mass density is the same in all directions to better than ~1 part per 1000.

     However, light has not yet had time to cross from one side of the sky to the other since the origin of the Big Bang; and the further back in time we consider, the less of the Universe could have been seen by any observer then.

     If signals cannot propogate faster than light, then only small regions of the early Universe could have been in causal contact. At earlier and earlier epochs, smaller and smaller fractions of the Universe could have been causally connected; and at the very beginning every particle would have been causally separate from every other.

     The problem is this: how could the causally unconnected regions of the Universe know how and when to expand?

     Not even infinitely precise ‘dead reckoning’ would suffice since quantum mechanical fluctuations would completely destroy this precision, The Universe would therefore expand in an infinitely disordered fashion, without even the topological simplicity of our own.

     That is, according to conventional interpretations of Relativity and the Big Bang, our Universe cannot exist. This is a problem.

     Various attempts have been made to modify the theory so as to avoid this difficulty; models in which the expansion pauses, to allow inhomogeneities to be damped out. possess some of the required properties. A recent model of this sort is the ‘new inflationary Universe‘, which is based upon considerations of Quantum Gravity and GUTS (Grand Unified field Theories): however, this model, and others like it, appear to disagree with observation.

     The problem hinges upon the issue of ‘Einstein Separability‘; that is, whether events are causally separate when their separation is spacelike. If Einstein Separability is rejected (as it must be if signals can propagate faster than light) then the difficulty vanishes: causal connectivity can be total even at the very beginning.

     A Big Bang scenario which includes tachyons and a censor-field would go something like this:

     In the beginning there was a singularity, which exploded. There were equal numbers of tardyons and tachyons, all in thermal equilibrium at an extremely-high temperature. The tachyons could thermalise the tardyons, and the tardyons the tachyons; across the whole Universe there was just one causally connected region. At this stage the surfaces of simultaneity would have been highly convoluted and topologically of very high connectivity. The labels "tardyon“ and “tachyon" are of course merely for convenience; there would have been complete symmetry and exchangeability between them.

     As the Universe cooled a process known as ‘spontaneous symmetry breaking‘ would occur: a preponderence of one claw of particle (thereafter called tardyons) would form, and most of the remaining tachyons would switch to being tardyons too. In the parlance of GUTS, a phase change from the symmetric to the asymmetric vacuum state would occur. The surfaces of simultaneity would now untangle themselves and merge into a smooth progression with the universal expansion.

     With so few tachyons now left, much of the Universe would now become effectively causally disconnected; but the expansion would by now be sufficiently advanced that its isotropy and homogeneity would not be lost. Hereafter, perturbations would have only a weak effect upon the later Universe.

     The scenario can then follow the standard model.

     Thus the censor-field interpretation of Relativity enables us to explain some otherwise highly puzzling features of the Big Bang; this is at least an indication that we may be on the right lines: the censor-field theory “predicts“ a moderately isotropic Universe, whereas Einstein Separability "predicts" a tangle. However, the evidential value of such “predictions,” which are really a posteriori explanations, is not generally considered to be high, because other explanations of the same facts may be conceivable.


A series of experiments founded on the ideas of Einstein, Podolsky and Rosen has recently brought into focus an important problem in Quantum Mechanics and Relativity, concerning the Reality of the physical world. The problem has been reviewed clearly in a Scientific American article. In brief, the problem is as follows (see Fig. 11).

     Quantum Mechanics predicts a strong correlation between certain kinds of distant events, a correlation which can be calculated and tested.

     Local Realistic Theories predict that the correlation between distant events must be less than a certain limiting value (the ‘Bell Inequality‘). Sometimes the correlation predicted by Quantum Mechanics can exceed that allowed by the Bell Inequality; and this can be tested too.

     Experimental tests have shown that the Bell Inequality can be violated, just as predicted by Quantum Mechanics.

     Therefore Local Realistic Theories are wrong.

     Therefore at least one of the premises of the local Realistic Theories must be incorrect.

     These are the three premises that together imply the Bell Inequality:

i) The doctrine of Realism; that observed phenomena are the result of some physical reality whose existence is independent of human observation.

ii) The validity of Inductive Inference; that inductive inference is a valid mode of reasoning, so that legitimate oonclusions may be drawn from consistent observations.

iii) The postulate of Einstein Separability; that no influence of any kind can propagate faster than light.

     Let us consider these premises in turn.

     First, Realism: this doctrine is at the root of scientific enquiry. We believe that there really is a world outside ourselves, that events have causes, that it makes sense to consider physical objects as having objective existence and properties. lt is not only Science that would be trivialised without Reality, but also all other human endeavours. I do not think that it is even possible for a man to deny reality consistently; however solipsistic his philosophy, in his behaviour he will adhere to realism.

     Second, Induction: this is even more fundamental to both Science and daily life than Realism; to all but the most sceptical of philosophers it is self-evident. Without inductive inference there could be ncither science nor philosophy. In particular, the very theory of Quantum Mechanics is built upon a foundation of Realism and Induction.

     Third, Einstein Separability: this has been held to be true on grounds of causality, but unlike the first two premises it has no immediate intuitive claim. In this paper we have seen that influences propagating faster than light need not violate the Principle of Causality; thus the grounds of this premise have been undercut and we need not scruple about dropping it.

     In summary we might claim that Realism, Induction and Causality are intuitively true, but that Einstein Separability is merely a hypothesis to be tested, and now found wanting.

     (Some readers may consider this claim excessive, preferring to deny Realism, Induction or Causality; if so, I invite them to consider which of the following seems intuitively more likely or aesthetically more pleasing:

i) It is incoherent to attempt objective description.

ii) It is incoherent to infer anything from anything.

iii) It is incoherent to talk about cause and effect.

iv) Signals can propagate faster than light).

     The grave problems caused by tests of the Bell Inequality can be resolved if a censor-field interpretation of Relativity is adopted, and Einstein Separability rejected. The way is also opened to a more realistic interpretation of Quantum Mechanics, a ‘statistical interpretation’ as opposed to the ‘Copenhagen interpretation,‘ as discussed in Ref. 19.


     So far only qualitative aspects of the censor-field have been considered. It is not immediately obvious what the precise form of censor should be, nor whether the solution will be unique. It seems reasonable to consider choices like:

summed over all bodies, for which the mass and distance are proper values, evaluated in their own rest frames. The ratio (m/r) is the Newtonian potential produced by each mass, and is the same term that is used for the ‘sum for inertia‘ when considering Mach's Principle.

     In a parameterised post-Newtonian (PPN) approximation of General Relativity one considers a frame which becomes Lorentzian at infinity; in the notation of MTW one obtains a metric;

In these terms the censor-field would be given by

When velocities and internal energies are small, this reduces to:

     where U is the Newtonian potential. Notice that transverse and radial velocities have slightly different effects in this expression, corresponding to the ‘dragging of inertial frames‘ in General Relativity.

     The question of the physical means by which such a censor-field might limit the speed of particles has not been addressed. Perhaps the simplest solution might be a coordinate singularity at the limit, leading to a 180° flip on the Minkowski diagram. Alternatively we may note that, if inertial effects propogate in a Machian fashion along the surfaces of simultaneity, then as an observer approaches the limiting speed he will interact “simultaneously” with the whole Universe and the inertial “drag” tend to infinity (I am indebted to the first referee of this paper for the idea behind this suggestion).

     It remains to find a generalised and completely covariant form for censor in the formalism of General Relativity, and to determine whether there is a natural unique solution or a range of possibilities (or whether such a field is not possible in General Relativity despite being consistent with Special Relativity).


     Let us consider what the effective maximum speed of an object or packet of energy may be, assurning a censor-field in form like that of Eq. (8).

     The effective ‘sum for inertia‘ throughout the Universe is perhaps m/r~0.1-1 ; this value depends strongly on strong field and high velocity integrals and the cosmological model chosen, and is therefore very uncertain. There is some reason to believe that for an open Universe it may even be infinite, in which case we might need to modify the fully relativistic form to give a finite integral, while retaining the weak-field or the Newtonian approximation.

     The self-potential, ~(m/r)self, is very much less than unity for most objects: for a proton it is ~10-40: for a man ~10-25; and for a 10,000 tonne/100 metre starship it would be ~10-22. Thus the self-effect on the censor-field will be much less than that of the background Universe; and a moving object will produce only a slight local gradient, ~(m/r)self / (m/r)universe, on the surfaces of simultaneity (Fig. 9).

     This will prevent the object from moving back and forth on a single surface of simultaneity, its maximum speed relative to the surface being the inverse of the gradient. Thus an elementary particle might travel at up to an effective ~1039c. In principle, a spaceship might fly out to the Hubble Distance (~3Gpc) and back in as little as a millisecond. If this speed is not infinite, it is certainly very fast.

     This calculation has perhaps been a little naive; it is not obvious that a supraluminal object will have the same effect as a similar object at rest would have. Moreover, as pointed out in the first section, we must not assume that an object has to cross the intervening space to go from place to place.


     We have not yet considered how the world would appear to a supra-luminal observer. Points to consider are these;

     How will he perceive our dimensions of space and time? Will they be reversed? How will he perceive the flow of time?

     Will the world of tachyons appear to him like our world of tardyons? Or will certain, apparently sub-luminal, motions be forbidden?

     Will he vanish from our sight? And can he ever reappear?

     How can the symmetry of the Lorentz transform be maintained? And what is the meaning of the imaginary factors that arise?

     It is not my intention to attempt to give a unified theory of tardyon-tachyon interactions, so little more will be done than to pose these questions for future consideration. Nevertheless, certain of the difficulties and certain possible routes for solution will be pointed out.

     One can soon convince oneself that the Lorentz transform leads to the existence of imaginary “observables” for the supra-luminal regime; and no simple mathematical trick, like multiplying by i, can remove them. The difficulty is the change of signature of spacetime from (-+++) for tardyons to (-+--) for tachyons, such that two dimensions of space behave like time; even if this can be accepted, it destroys the desired symmetry between the world of tardyons and the world of tachyons.

     A six-dimensional space-time would remove this difficulty since a symmetrical arrangement of three space and three time dimensions gives a signature (---+++). Any observer will see a conventional 4-D space-time, but on going supra-luminal two of his space dimensions will rotate out of his observable 4-plane, and the two previously unobservable dimensions will appear. Thus any observer is always in a space of the same signature (---+++).

     In such a scheme there would no longer be two distinct regimes (tardyons and tachyons), but a total of six regimes separated by null geodesics. Going from one to another involves rotation about one or more of the six orthogonal axes. This would mean that a supraluminal observer would be unable to observe events displaced sideways from his line of flight; instead, he would see part of “hyperspace."

     Whether this would imply innumerable parallel (or dissimilar) universes in the available sheafs of space-time is left for the reader to consider.

     Some aspects of six-dimensional relativity are examined in Refs. 22 and 23 which develop a real six-dimensional generalised form of the Lorentz Transformations.


     Let us be quite certain about what we have shown.

     We have NOT shown that faster-than-light travel is possible. We have NOT developed a scientific theory of the censor-field. We have not proved the existence of such a field. We have not even considered whether faster-than-light travel would be useful; still less have we examined its practicability.

     What we have done is to demolish the dogma that travel faster than light is necessarily impossible. We have shown that Special Relativity does not forbid it. We have shown that the Principle of Causality does not forbid it. We have pointed out a form of censor-field, consistent with known physics, that permits it. We have shown how such a field can solve some of the outstanding paradoxes in physics today; we have advanced this as speculative evidence of the propagation of certain signals faster than light.

     We can now answer the question posed in the title of this paper:

     Yes, faster-than-Light travel IS causally possible.


      Far away rose low hills, blurring into the sky, which was mottled and sallow like poor milk-glass. The intervening plain spread like rotten velvet, black-green and wrinkled, streaked with ocher and rust. A fountain of liquid rock jetted high in the air, branched out into black coral. In the middle distance a family of gray objects evolved with a sense of purposeful destiny: spheres melted into pyramids, became domes, tufts of white spires, sky-piercing poles; then, as a final tour de force, tesseracts.

     The Relict cared nothing for this; he needed food and out on the plain were plants. They would suffice in lieu of anything better. They grew in the ground, or sometimes on a floating lump of water, or surrounding a core of hard black gas. There were dank black flaps of leaf, clumps of haggard thorn, pale green bulbs, stalks with leaves and contorted flowers. There were no recognizable species, and the Relict had no means of knowing if the leaves and tendrils he had eaten yesterday would poison him today.

     He tested the surface of the plain with his foot. The glassy surface (though it likewise seemed a construction of red and gray-green pyramids) accepted his weight, then suddenly sucked at his leg. In a frenzy he tore himself free, jumped back, squatted on the temporarily solid rock.

     Hunger rasped at his stomach. He must eat. He contemplated the plain. Not too far away a pair of Organisms played—sliding, diving, dancing, striking flamboyant poses. Should they approach he would try to kill one of them. They resembled men, and so should make a good meal. He waited. A long time? A short time? It might have been either; duration had neither quantitative nor qualitative reality. The sun had vanished, and there was no standard cycle or recurrence. ‘Time’ was a word blank of meaning.

     Matters had not always been so. The Relict retained a few tattered recollections of the old days, before system and logic had been rendered obsolete. Man had dominated Earth by virtue of a single assumption: that an effect could be traced to a cause, itself the effect of a previous cause. Manipulation of this basic law yielded rich results; there seemed no need for any other tool or instrumentality. Man congratulated himself on his generalized structure. He could live on desert, on plain or ice, in forest or in city; Nature had not shaped him to a special environment.

     He was unaware of his vulnerability. Logic was the special environment; the brain was the special tool.

     Then came the terrible hour when Earth swam into a pocket of non-causality, and all the ordered tensions of cause-effect dissolved. The special tool was useless; it had no purchase on reality. From the two billions of men, only a few survived—the mad. They were now the Organisms, lords of the era, their discords so exactly equivalent to the vagaries of the land as to constitute a peculiar wild wisdom. Or perhaps the disorganized matter of the world, loose from the old organization, was peculiarly sensitive to psycho-kinesis.

     A handful of others, the Relicts, managed to exist, but only through a delicate set of circumstances. They were the ones most strongly charged with the old causal dynamic. It persisted sufficiently to control the metabolism of their bodies, but could extend no further. They were fast dying out, for sanity provided no leverage against the environment. Sometimes their own minds sputtered and jangled, and they would go raving and leaping out across the plain.

     The Organisms observed with neither surprise nor curiosity; how could surprise exist? The mad Relict might pause by an Organism, and try to duplicate the creature’s existence. The Organism ate a mouthful of plant; so did the Relict. The Organism rubbed his feet with crushed water; so did the Relict. Presently the Relict would die of poison or rent bowels or skin lesions, while the Organism relaxed in the dank black grass. Or the Organism might seek to eat the Relict; and the Relict would run off in terror, unable to abide any part of the world—running, bounding, breasting the thick air; eyes wide, mouth open, calling and gasping until finally he foundered in a pool of black iron or blundered into a vacuum pocket, to bat around like a fly in a bottle.

     The Relict valued their flesh as food; but the Organisms would eat him if opportunity offered. In the competition he was at a great disadvantage. Their random acts baffled him. If, seeking to escape, he ran, the worst terror would begin. The direction he set his face was seldom the direction the varying frictions of the ground let him move. But the Organisms were as random and uncommitted as the environment, and the double set of disorders sometimes compounded, sometimes canceled each other. In the latter case the Organism might catch him…It was inexplicable. But then, what was not? The word ‘explanation’ had no meaning.

     Alpha sank to his knees, lay flat on his back, arms and legs flung out at random, addressing the sky in a series of musical cries, sibilants, guttural groans. It was a personal language he had only now improvised, but Beta understood him well. “Observe the Relict on the hillside. In his blood is the whole of the old race—the narrow men with minds like cracks. He has exuded the intuition. Clumsy thing—a blunderer," said Alpha.

     “They are all dead, all of them,” said Beta. “Although three or four remain.” (When past, present and future are no more than ideas left over from another era, like boats on a dry lake—then the completion of a process can never be defined.) A rock, or perhaps a meteor, fell from the sky, struck into the surface of the pond. It left a circular hole which slowly closed. From another part of the pool a gout of fluid splashed into the air, floated away.

     “One moment! Look at the Organisms!”
     The women looked. The Organisms stood in a knot, staring at the sky.
     “Look at the sky!”
     The women looked; the frosted glass was cracking, breaking, curling aside.
     “The blue! The blue sky of old times!”
     A terribly bright light burnt down, seared their eyes. The rays warmed their naked backs.
     “The sun,” they said in awed voices. “The sun has come back to Earth.”
     The shrouded sky was gone; the sun rode proud and bright in a sea of blue. The ground below churned, cracked, heaved, solidified. They felt the obsidian harden under their feet; its color shifted to glossy black. The Earth, the sun, the galaxy, had departed the region of freedom; the other time with its restrictions and logic was once more with them.
     “This is Old Earth,”cried Finn. “We are Men of Old Earth! The land is once again ours!”
     “And what of the Organisms?”
     “If this is the Earth of old, then let the Organisms beware!”

     The Organisms stood on a low rise of ground beside a runnel of water that was rapidly becoming a river flowing out onto the plain.
     Alpha cried, “Here is my intuition! It is exactly as I knew. The freedom is gone; the tightness, the constriction are back!”
     “How will we defeat it?” asked another Organism.
     “Easily,” said a third. “Each must fight a part of the battle. I plan to hurl myself at the sun, and blot it from existence.” And he crouched, threw himself into the air. He fell on his back and broke his neck.
     “The fault,” said Alpha, “is in the air; because the air surrounds all things.”
     Six Organisms ran off in search of air, and stumbling into the river, drowned.
     “In any event,” said Alpha, “I am hungry.” He looked around for suitable food. He seized an insect which stung him. He dropped it. “My hunger remains.”
     He spied Finn and the two women descending from the crag. “I will eat one of the Relicts,” he said. “Come, let us all eat.”
     Three of them started off—as usual in random directions. By chance Alpha came face to face with Finn. He prepared to eat, but Finn picked up a rock. The rock remained a rock: hard, sharp, heavy. Finn swung it down, taking joy in the inertia. Alpha died with a crushed skull. One of the other Organisms attempted to step across a crevasse twenty feet wide and was engulfed; the other sat down, swallowed rocks to assuage his hunger, and presently went into convulsions.

     Finn pointed here and there around the fresh new land. “In that quarter, the new city, like that of the legends. Over here the farms, the cattle.”
     “We have none of these,” protested Gisa. “No,” said Finn.
     “Not now. But once more the sun rises and sets, once more rock has weight and air has none. Once more water falls as rain and flows to the sea.” He stepped forward over the fallen Organism. “Let us make plans.”

From THE MEN RETURN by Jack Vance (1957)

Time was slippery. The way Pirius understood it, it was only the speed of light that imposed causal sequences on events.

According to the venerable arguments of relativity there wasn't even a common "now" you could establish across significant distances. All that existed were events, points in space and time. If you had to travel slower than lightspeed from one event to the next, then everything was okay, for the events would be causally connected: you would see everything growing older in an orderly manner.

But with FTL travel, beyond the bounds of lightspeed, the orderly structure of space and time became irrelevant, leaving nothing but events, disconnected incidents floating in the dark. And with an FTL ship you could hop from one event to another arbitrarily, without regard to any putative cause-and-effect sequence.

In this war it wasn't remarkable to have dinged-up ships limping home from an engagement that hadn't happened yet; at Arches Base that occurred every day. And it wasn't unusual to have news from the future. In fact, sending messages to command posts back in the past was a deliberate combat tactic. The flow of information from future to past wasn't perfect; it all depended on complicated geometries of trajectories and FTL leaps. But it was good enough to allow the Commissaries, in their Academies on distant Earth, to compile libraries of possible futures, invaluable precognitive data that shaped strategies — even if decisions made in the present could wipe away many of those futures before they came to pass.

A war fought with FTL technology had to be like this.

Of course foreknowledge would have been a great advantage — if not for the fact that the other side had precisely the same capability. In an endless sequence of guesses and counterguesses, as history was tweaked by one side or the other, and then tweaked again in response, the timeline was endlessly redrafted. With both sides foreseeing engagements to come for decades, even centuries ahead, and each side able to counter the other's move even before it had been formulated, it was no wonder that the war had long settled down to a lethal stalemate, stalled in a static front that enveloped the Galaxy's heart.

(ed note: our heroes in the good ship Claw are being chased by a star-god Xeelee ship. They are trying to evade it by close passage to a flaring neutron star. But it will take hours of computer calculation to determine the precise course, and they only got seconds before the Xeelee destroys them.

Suddenly, their friend Dan in his ship appears out of nowhere. He transmits the precise course needed, along with a Virtual computer AI approximation of himself. Then his ship is destroyed.

Our heroes use the precise course supplied out of desperation, and amazingly it works. They skirt through the neutron star flare, while the Xeelee ship gets clobbered. Later they ask Dans's Virtual what the heck just happened.)

     “But what I can’t get my head around,” Pirius told Dans’s Virtual, “is how you appeared out of nowhere, and squirted down the right evasive maneuver for us, based on a knowledge of the flare’s evolution before it happened.”
     Dans said tinnily, “It was just an application of FTL technology. Remember, every FTL ship—”
     “Is a time machine.” Every child learned that before she got out of her first cadre.
     “I pulled away. Out of trouble, I watched the flare unfold, recorded it. I took my time to work out your optimal path—how you would have avoided destruction if you’d had the time to figure it out.”
     Pirius said, “But it was academic. You got the answer after we were already dead.”
     “And I had to watch you die,” said Dans wistfully. “When the action was over, the Xeelee out of the way, I used my sublight to ramp up to about a third lightspeed. Then I cut in the FTL.”
     Cohl understood; “You jumped back into the past—to the moment just before we hit the flare. And you fed us the maneuver you had worked out at leisure. You used time travel to gain the time you needed to plot the trajectory.”
     “And that’s the Brun maneuver,” Dans said with satisfaction.

     “It’s some computing technique,” Cohl mused. “With the right vectors you could solve an arbitrarily difficult problem in a finite time—break it into components, feed it back to the source…”
     Pirius was still trying to think it through. “Time paradoxes make my head ache,” he said. “In the original draft of the timeline, Claw was destroyed by the flare, and you flew away. In the second draft, you flew back in time to deliver your guidance, and then you—that copy of you—flew into the neutron star.”
     “Couldn’t be helped,” Dans said.
     He could see she was waiting for him to figure it out. “But that means, in this new draft of the timeline, we survived. And so you don’t need to come back in time to save us. We’re already saved.” He was confused. “Did I get that right?”
     Hope said, “But there would be a paradox. If she doesn’t go back in time, the information that future-Dans brought back would have come out of nowhere.”
     Cohl said, “Yes, it’s a paradox. But that happens all the time. A ship comes limping back from a lost battle. We change our strategy, the battle never happens—but the ship and its crew and their memories linger on, stranded without a past. History is resilient. It can stand a little tinkering, a few paradoxical relics from vanished futures, bits of information popping out of nowhere.” Cohl evidently had a robust view of time-travel paradoxes. As an FTL navigator, she needed one.

From EXULTANT by Stephen Baxter (2004)

She paused and smiled. "I have heard," she said conversationally, "the voice of the President of our Galaxy, in 3480, announcing the federation of the Milky Way and the Magellanic Clouds. I've heard the commander of a world-line cruiser, traveling from 8873 to 8704 along the world line of the planet Hathshepa, which circles a star on the rim of NGC 4725, calling for help across eleven million light-years — but what kind of help he was calling for, or will be calling for, is beyond my comprehension. And many other things.

From BEEP by James Blish (1954)

What Does It Look Like?

If the FTL drive is totally made up by the author, it looks like whatever the author damn well pleases.

If the FTL drive has an elaborate mechanism described in detail, the mechanism can suggest appearances. For instance, if the spacecraft travels from star to star through stargates, obviously one would expect to see a stargate involved. A ship that enters hyperspace might fade out and vanish. The Starship Enterprise streaks off with a rainbow contrail and vanishes in a flash. The Millennium Falcon just streaks off until it vanishes in the distance.

Regardless of that, it still looks like whatever the author damn well pleases. Or looks like whatever jazzy eye-candy scientifically-ridiculous ILM special effect which catches the movie director's fancy and is within the special effects budget.

But if the FTL drive somehow makes the starship move superluminal while still being visible in our mundane space-time continuum, that's when Newtonian and Einsteinian physics have a say in how it looks.


(ed note: about a hundred years ago Terra sent a slower-than-light colony ship to a habitable planet around Procyon. Terra had detected the signature of an alien FTL starship around Procyon, and was hoping the colony could discover the secret of the star-drive. Terra didn't hear from the colony for about a hundred years. Then one day they detected an FTL starship arriving from Procyon.)

     "We first began picking it up on the cosmic ray monitors at 16:12, shortly after the start of Second Watch. The monitors kept insisting that they had spotted a diffuse source of cosmic rays somewhere out beyond Neptune. We ran the usual maintenance checks and found nothing, so I ordered the neutrino scopes and X-ray equipment to take a look. They can see it, too."
      "What makes you think it's a ghost then?"
     "Because there isn't anything out there! Besides which, the source is moving."
     "Yes, sir. Moving fast. It appears to be traveling radially outward from the Sun."
     "Have you asked Aeneas to do a parallax measurement?"
     "Yes, sir. Two-and-a-half hours ago. I expect their reply momentarily." As though to punctuate Bartlett's comment, several readout screens chose that moment to begin displaying data. The half dozen people in the Operations Center turned to watch."
     "Well, I'll be damned!" Bartlett muttered incredulously a few seconds later. "They see it too."
     "Have you got a velocity vector yet?" Gruenmeier asked.
     The watch astronomer nodded, and then hesitated as he read the figures silently. He looked up at Gruenmeier and gulped. "It says here that the radiation source is moving directly away from the sun, toward Canis Minor, sir. The exact coordinates are: right ascension, 07h 39m; declination, plus 05° 18'. And get this. Whatever it is, it's moving at exactly the speed of light!" (which as you will read is actually an optical illusion. The ship is moving several orders of magnitude faster than light)
     Gruenmeier blinked. "It's moving away from the sun?"
     "Yes, sir."
     Gruenmeier turned to Chala Arnam. "Get me a top priority line to Earth. I will be sending a coded message to the Board of Trustees in about ten minutes.
     He turned back to Bartlett. "Get that data reduced fast. I want everything you can deduce about the source in the next five minutes. I will need it for my squirt to Earth. I also want every instrument we have focused on this contact. Aeneas, too. Understood?"
     Gruenmeier stopped, suddenly aware of the expressions of his subordinates. "What's the matter with you two? Hop to it!"
     Chala frowned. "What's the matter, Julius? What is it?"
     "Don't you see? We have a phantom source of high-energy particles moving away from the sun at 300,000 kps on a vector straight toward Procyon. That can mean only one thing."
     "They're back, damn it. They're back!"

     The younger man leaned forward, rested his arms on the table. "Earlier today, Kiral Papandreas approached Advisor Vischenko concerning a source of radiation SIAAO’s Achilles Observatory first observed some twelve hours ago. When first sighted, the source was on the outskirts of the solar system. Since that time, it has been moving outward from the sun in a straight line on a vector towards the star Procyon. The astronomers are convinced that we are seeing the wake of an object traveling faster than light."
     "You said the source was moving away from the sun?" Jutte Schumann asked.
     "Merely an optical illusion, Jutte," Kiral Papandreas said from across the table. He quickly reviewing the theory of superluminal shock waves, ending with: "So you see, as it travels through space, a starship will excite the interstellar medium quite vigorously. It will do so over vast distances in essentially zero time. Yet, the resulting radiation propagates only at the speed of light, taking a finite time to arrive where our instruments can observe it. Those particles with the shortest distance to travel arrive first, those from farthest away, last. Thus, it appears as though the source is receding from the observer at the speed of light."

(Meanwhile, on the colonist's FTL starship...)     "One minute to Breakout. Stand by." The voice belonged to Promise’s computer, a direct descendant of the original SURROGATE. After a short pause, the computer spoke again. "Thirty seconds. Shields going up."
     A series of wedge shaped sections rose from out of the metal hull at the perimeter of the viewdome and quickly converged at the apex to shut off the blackness overhead. All over the ship, similar shields were sliding into place.

     Like any other vehicle, Procyon’s Promise displaced the medium through which it traveled. In Promise’s case, that meant a vacuum thin mixture of hydrogen, cosmic dust, and primitive organic molecules. Had the ship been moving at less than superluminal velocity, its progress through the void would have been marked only by an undetectably small warming of its hull plates as it pushed the detritus of stellar evolution aside.
     However, once Promise cracked the light barrier, things changed markedly. At FTL velocities, each hydrogen atom became a significant obstruction. As the ship bored its narrow tunnel through space, the interstellar particles refused to be pushed. It was the classic case of the Irresistible Force meeting the Immovable Object. In a situation analogous to the supersonic flight of an atmospheric craft, the confrontation resulted in a shock wave of high energy Cherenkov radiation.
     Nor was Promise’s wake the friendly upwelling that follows any watercraft. It was a ravening storm intense enough to fry an unprotected human within seconds. Yet, the very speed that created the phenomenon also protected the starship from harm. Since the radiation of its wake was limited to the mere crawl that is light speed, Promise left its deadly wake far behind in the instant of its creation.
     There was a time, however, when Procyon’s Promise would lose its immunity to the titanic forces that its speed had unleashed. For, as soon as the ship slipped below light speed, the trailing wake would wash over it like a wave over a hapless surfer. In that instant, the starship would be engulfed in radiation equivalent to that encountered during a Class I solar flare.

     "Everyone ready for breakout?" Braedon asked over the command circuit. Around him, a dozen crewmen were monitoring the ship’s subsystems against the day when they might have to fly home without the computer’s assistance.
     "All ready, Captain," Calver Martin, Braedon’s executive officer answered from his console on the starboard side of the bridge.
     Braedon nodded. Several seconds later, the computer began the countdown. "Ten seconds ... five ... four ... three ... two ... one ... breakout!"
     Braedon felt a tiny lurch. That was all. There was a moment of silence, followed by two hundred voices cheering over the ship’s intercom system.
     "Breakout complete. Secure from breakout stations.

     "All Department Heads report status and damage." Braedon reached out and touched a control on his instrument panel. A green status light lit up immediately, and the voice that had so recently echoed from the annunciators spoke quietly in his ear.
     "Yes, Robert?"
     "We seem to have made it, PROM. What’s our status?"
     The computer answered almost before he had finished the question. "We are green across the board. I am still calculating a precise breakout point. Initial observations place us approximately six billion kilometers from Sol. We will need twelve hours to achieve intrasystem velocity."
     "How fast are you applying the brakes?"
     "I am holding deceleration at 7000 meters-per-second-squared. Do you wish to order a change?" Braedon hesitated momentarily. The figure cited was 650 times the force of gravity on Alpha. Should the internal compensators fail, two hundred crewmembers would be turned instantly to a thin red paste spread evenly over every interior surface facing Sol. Unfortunately, that was an unavoidable hazard. To back down from light-speed at one Alphan gravity would take most of a year.
     "No change in programmed deceleration," he said.
     "Understood," PROM answered.
     "Is it safe to unshutter?" Braedon asked one of the technicians seated directly in front of him.
     "The radiation storm peaked five seconds ago and is now declining as predicted, Captain," the man said without taking his gaze off his instruments. "Stand by..." There was a ten second period of silence, followed by: "It is now safe to unshutter."

From PROCYON'S PROMISE by Michael McCollum (1985)

I exchanged a bunch of emails a week or two ago with a journalist who was working on a story involving the possibility of faster-than-light travel. He wanted me to check some statements about the relationship between FTL and causality. FTL creates problems for causality, because if you have an object moving faster than light, there will be pairs of observers who see events involving the FTL object happening in different orders, which means somebody will see an effect happen before its cause.

I talk about this is How to Teach Relativity to Your Dog using the example of a stationary dog, a moving cat, and an alien zipping by at four times the speed of light. Here’s a figure showing how this appears to the dog:

In this “spacetime diagram,” the left-right axis indicates the position along the direction of the cat’s motion, while time marches upward into the future. Vertical lines are equally spaced position markers according to the dog, while horizontal lines are equally space instants of time according to the dog. The dashed red lines are rays of light sent out at the instant the cat and dog had the same position, and set the scale for everything.

The dog sees the cat moving left to right at half the speed of light. The alien comes in from the left, passes the dog first (event 1), and then the cat (event 2). Perfectly sensible, and the dog could, for example, hand the passing alien a water balloon which the alien could then use to soak that pesky cat.

This looks very different if you replace the dog’s grid of position and time markers with the cat’s, though. In that case, you get something that looks like this:

Both space and time look different to the cat, due to her high speed. Equally spaced position markers according to the cat have to tip to the right, parallel to the cat’s trajectory, while the cat’s time instants tip up. The regular squares of the dog’s grid become rhombuses in this representation.

According to the cat, then, the alien passes the cat, and only later passes the dog. Which makes the whole water balloon thing kind of problematic — the alien would appear to the cat to come in from the right empty-handed, soak the cat with a water balloon and then carry that balloon on to the left, and later on hand it to the dog. (this is how the Einsteinian FTL differs from the Newtonian FTL. It is because the cat is moving at relativistic velocity)

This reversal of ordering obviously screws up causality, and is one of the best reasons why FTL travel is impossible. It’s even possible to create paradoxes by using FTL communications, so sending information faster than the speed of light is ruled out.

My journalist friend had this basically correct, but we went back and forth a bit about a subtle issue of perception. This is always a tricky business in relativity, as it’s very tempting to attribute weird effects to the finite travel time for light to get from one place to another, and say things like “The events according to the cat appear to be in the opposite order.” That’s not what’s really going on, though — relativity isn’t about optical illusions. There is no measurement the cat can do that will tell her anything other than that the alien passed her first, and only later encountered the dog.

I think we got this cleared up — I don’t think the story has appeared yet, which is also why I’m being coy about the identity of the journalist, who is free to identify himself in comments. But it did raise the question in my mind of what this would actually look like from the point of view of the dog. That is, what would the dog see?

You see, the diagrams above are a sort of “God’s eye” view of the scenario, not the kind of thing any of the participants could directly record. The dog could draw this diagram of events, but only after the fact, after either compiling the records of lots of individual observers at the different position markers, or by looking at the light she sees, and working backwards to correct for the travel time of the light emitted by different objects.

So, what would the “dog’s eye” view of the scenario really look like? How would the dog perceive her interaction with the alien? Well, we can understand this by adding some extra events to the diagram:

Here, I’ve added events “a,” “b,” and “c,” so there are two events on either side — while the alien is approaching, and while the alien is heading away. To work out what the dog sees, we need to add lines corresponding to the light emitted by the alien as it passes each of these. Looking at the approaching side first, we see that things are a little weird:

The alien, moving at four times the speed of light, arrives well ahead of the light from earlier in its trajectory. Thus, the dog would have absolutely no warning of the alien’s approach — it would just suddenly be there. Then the light from nearby would arrive (event b), and then the light from farther away (event a) (it will act in the same way as the starship from Procyon).

If we add in the receding side, we have:

Again, the alien outraces its own light, so it’s gone just as suddenly as it appears. The light from its departure lags well behind the actual events, with nearby events appearing only after some delay (event c) and more distant events much later (event 2, the soaking of the cat).

So, the answer to the question “What does the dog see?” is “Some weird stuff.” Adding markers for the arrival of the light from each of the events gives you the idea:

From the dog’s point of view, the alien appears without warning (event 1), then seems to move away in both directions simultaneously– like two identical aliens headed in opposite directions. Light from a given distance on the approaching side will arrive a bit ahead of light from the receding side (event b is seen before event c, though they’re the same distance away), so it will look sort of like the alien zipping off to the left is heading away a bit faster than the one heading off to the right. The “dog’s eye” sequence of events is not the “a-b-1-c-2” sequence of the “God’s eye” view, but “1-b-c-a-2.” It’s only after the fact, when she’s had time to say “What the hell was that?” and do a bit of math that the dog can construct the global picture shown in the diagrams.

Common Handwaves

There are two main dodges. You may remember from Physics 101 that travel time = distance / rate of travel. For example, if you have to travel 100 miles, and you maintain a speed of 50 miles per hour in your automobile, the travel time will be two hours.

The laws of physics forbids any rate of travel faster than the speed of light. Since the distances between stars are so astronomically huge, this means the travel time will be measured in decades or centuries. This is unacceptable in a fast-paced science fiction novel.

Dodge #1 is to handwave some technobabble way of increasing the starship's rate of travel to faster than light. From the equation you can see this will reduce the travel time. In Geoffrey Landis' Canonical List of StarDrives, this includes Continuous Drives and Modifying the Universe: Modify the speed of light.

"Hyperdrives" often talk about the starship entering a magic dimension called "hyperspace" where that pesky speed limit does not apply. E.E. "Doc" Smith's interialess drive removes the inertia from the matter composing the ship and crew, so again the speed limit is side stepped (sort of). Also covered are FTL drives that convert the starship and crew into FTL tachyons, then convert back to ordinary matter at the destination.

Dodge #2a is to handwave some technobabble way of reducing the distance to the starship's destination. From the equation this also reduces the travel time. This includes "Space Warp Drives" that warp or fold space. There is a second kind of hyperspace in science fiction, one where the speed of light is the same as in our dimension, but distances are compressed by a factor of a billon or so. The 4.2 light-year distance to Alpha Centauri might therefore be only 40,000 kilometers in hyperspace. Pop into hyperspace, move 40k km in the Alpha-C direction, pop back into our dimension, and find yourself at our neighbor star.

Dodge #2b takes Dodge #2 distance reduction to extremes, the distance can be reduced to zero along with the travel time. These are "Jump" or teleportation drives where the ship vanishes at point A and instantly appears at point B. In the Landis list, this includes Discontinuous Drives and Modifying the Universe: Modify distance in space.

Sometimes a jump drive is a machine inside a starship, sometimes it is an external installation called a "jumpgate", "stargate", or "wormhole". Star Trek's "warp drive" was originally intended to use this method, but the method has sort of changed with each new generation of writers. Travel by wormholes also uses this technique.

Why do these dodges violate the laws of physics? Well, that is complicated, but there are two main problems: the Light-speed barrier and Causality. This is explained with some depth at Jason Hinson's authoritative "Relativity and FTL" website, so I'm just going to give a short summary. Refer to Hinson for details. And yes, wormholes violate causality as well.

It is unclear if reducing the distance is allowed or not, and nobody is sure how to warp space on a commercial level. Suggestions generally involve gravity fields of intensities only found around black holes and/or wormholes (aka Einstein-Rosen bridge). Warping the fabric of space would seem to require astronomical amounts of energy, and heaven help any solar systems that got wadded up in the warp.


To say that Non-space is “beside” the normal space-time universe is a weak analogy but better than none at all. Some had explained it this way: imagine two-dimensional universes stacked atop one another like sheets of paper, not quite, but almost touching; imagine further that the two-dimensional creatures, intelligences if you will, of one universe are unable to “see” the next universe beside theirs, though the actual three-dimensional space separation might be but centimeters; imagine now that they develop some means of passing across this space, of “jumping” through the intervening centimeters. Thus it was with mankind and his “three-dimensional” universe called “space-time” and that other continuum called, for want of a better name, Non-space.

And thus it was with the scanning device MAC-5 from the TF starship Douglas MacArthur. Spit violently from the three-dimensional macrocosm of mankind, it crossed the “four-(five) dimensional” space between and found itself in a second continuum.

The scanning device entered this suitcase cosmos, this matchbox universe that was, in size, a mere fraction of space-time. Non-space existed in its own right, independent of space-time, a complete universe, though lacking in the wealth of stars and dust that characterised space-time.

Imagine the two sheets of paper separated by centimeters. Imagine one sheet—call it “space-time”—as being large, and the other, “Non-space,” as being on a much smaller scale, a tenth the size of “space-time,” let us say.

Now, pick a spot on the sheet called “space-time” and pick a corresponding spot on the sheet called “Non-space.” Let us call them A and A1. Now, pick another spot on “space time” and call it B and the corresponding spot, to scale, on “Non-space,” B1.

The distance from A to B on “space-time” is, let us say, ten centimeters, but on the sheet called “Non-space,” the scale of A1 to B1 is but one centimeter. Moving from A to B at a fixed rate of speed, for example, one centimeter per hour, would take, of course, ten hours—but at the same speed, we can move from A1 to B1 in only one hour—and yet the two sets of points are spatially equivalent!

This again is a weak analogy, but the idea is there. From Sol to Altair at the speed of light—a 5.06 year trip in space-time; in Non-space, light would take only a little over an hour and a half!

From THE SKY IS FILLED WITH SHIPS by Richard C. Meredith (1969)

The Fourth Dimension

One of the classic faster-than-light dodges was for the starship to enter "another dimension" where the speed of light was faster or otherwise allowed the starship to violate Einstein's relativity with extreme prejudice. The standard name was "hyperspace."

Though considered somewhat passé now, in the 1940's hyperspace was a synonym for the dreaded "Fourth Dimension."

Yes, I know some call "time" the fourth dimension, this is talking about the fourth spatial dimension. Forwards/backwards, left/right, up/down, ana/kata (terms coined by Charles Hinton). The fourth dimension is a valid scientific concept, even though our puny three-dimensional intellects cannot truly comprehend it. It can be worked with using mathematics, and crudely visualized by using the magic of analogy.

0: A point has no dimensions. There is no width, there is no height, there is no thickness, there are zero dimensions.

1: If we take a point and move it in the X axis, the point becomes a line. It now has width. It still has no height or thickness, so it only has one dimension.

2: Take the line, and move it down in the Y axis (in a direction 90 degrees to the X axis). The line becomes a square. Now it has both width and height. No thickness so it only has two dimensions. There are four lines enclosing one square plane.

3: Take the square and move it towards you out of the plane of the computer monitor in the Z axis (in a direction 90 degrees to both the X axis and the Y axis). The square becomes a cube. It has width, height, and thickness, three dimension. There are six square planes enclosing one cubical volume

4: By analogy, take the cube and move it in the direction of the fourth dimension in the W axis (in a direction 90 degrees to the X, Y , and Z axes). The square becomes a tesseract or hypercube. It has width, height, thickness, and ana. There are eight cubes enclosing one hyper-cubical hyper-volume.

Your brain has started to hurt. It won't be the last time it hurts in this section.

The first major use of analogy to explain the fourth dimension was in the classic Flatland: A Romance of Many Dimensions, a 1884 satirical novella by the English schoolmaster Edwin Abbott Abbott. If you are interested in the fourth dimension, you should read it. There are quite a few free downloadable versions, but ensure that you get one that has the illustrations.

Mathematician Rudy Rucker wrote a slender textbook along the lines of Flatland with equations and everything, entitled Geometry, Relativity, and the Fourth Dimension. It is a bit dry. He later wrote a more popularized version with entertaining illustrations by David Povilaitis entitled The Fourth Dimension: A Guided Tour of the Higher Universes. Both are excellent.

If you want to delve more into the nitty-gritty details of the life and technology of two dimensional creatures, may I recommend The Planiverse by A. K. Dewdney? The appendix in the back has the details of various 2D items, such as a NOR logic gate where the wires do not cross, and a two dimensional steam engine.

In Flatland and The Fourth Dimension, a two-dimensional character named A. Square encounters dimensional weirdness when the 3D Sphere from the third dimension invades. The reader is then shown how by analogy the same thing can happen if they encounter the 4D Hypersphere invading from the fourth dimension.

Sometimes the 2D square character from the 2D flatland universe encounters the 1D line character living in the 1D "lineland" universe. A. Square is usually very annoyed at how the line character fails to comprehend two dimensional weirdness. In a case of the pot calling the kettle black, A. Square then finds himself incapable of comprehending three dimensional weirdness exhibited by the 3D sphere. The reader then squirms in their chair as they uncomfortably realize they would be just as incapable of comprehending four dimensional weirdness if the 4D hypersphere showed up and started messing with their mind.

One can imagine A Square to be like a square of paper on a tabletop. He can move around on the two dimensional table surface, but has no ability to move in the third dimension. He cannot even comprehend what direction that is. He knows all about north and sound, east and west. But an "up and down" at ninety degrees to the first two? Inconceivable.

In Flatland, A Square's adventures start when he dreams about encountering Lineland. The inhabitants are points and line segments, they can move east and west but not north or south. Nor can they comprehend what direction that is.

A Square tries communicating with the King of Lineland, but finds it to be quite frustrating. The king can hear A Square but his voice seems to be coming from nowhere. A Square's attempts to explain that he is "north" of the king (90 degrees to east-west) go nowhere. And A Square's visit to Lineland are weird. The king can only see that part of A Square which intersects Lineland. So when A Square passes through Lineland, as far as the king is concerned he just sees a line segment pop out of nowhere, exists for a while, then vanishes. A Square tries to explain that his body is composed of a series of line segments stacked in the second dimension, which is total gibberish to the king.

Now it is time for A Square to be flummoxed.

A Square is in his locked two-dimensional house with his wife when the Sphere from the third dimension comes to call. Just like the king of lineland, A Square thinks the Sphere's voice is coming from nowhere. The Sphere's attempt to explain that he is "above" A Square (90 degrees to north-south and east-west) goes nowhere. And the Sphere's visit to Flatland is weird. A Square can only see the part of the Sphere that intersects Flatland. So when the Sphere passes through Flatland, as far as A Square is concerned he just sees a dot pop out of nowhere, becoming an expanding circle, then contracting back down to a dot, then vanishing. The Sphere tries to explain that his body is composed of a series of circles stacked in the third dimension, which is total gibberish to A. Square.

The reader sits there smugly feeling superior to the stupid King of Lineland and A. Square. Then they receive a visit from the Hypersphere from the fourth dimension.

Just like A Square, the reader thinks the Hypersphere's voice is coming from nowhere. The Hypersphere's attempt to explain that he is "ana" the reader (90 degrees to north-south, east-west, up-down) goes nowhere. And the Hypersphere's visit to the third dimension is weird. The reader can only see the part of the Hypersphere that intersects the third dimension. So when the Hypersphere passes through, as far as the reader is concerned they just sees a dot pop out of nowhere, becoming an expanding sphere, then contracting back down to a dot, then vanishing. The Hypersphere tries to explain that his body is composed of a series of spheres stacked in the fourth dimension, which is total gibberish to the reader.

A Square's mind was blown by a simple sphere from the fourth dimension. Just imagine if a irregularly shaped human being came for a visit! A Square would probably see several apparently separate blobs, the intersections of your torso, arms and legs. If you tried to explain that they were all connected in the third dimension, A Square would tell you that now you were just makin' stuff up. He would also have difficulty understanding how your parts keep changing shape and texture.

And of course if the reader was visited by some living being from the fourth dimension, it would also be just as disjointed and terrifying.

Imagine that flatland was the surface of a lake. A Square floats on the surface, but can only see the outline of where your body pierces the surface of the water. If you tried to grab A Square, you'd stick your fingers into the water. A Square would see five apparently separate irregular circles appear out of nowhere, which converge on him. By analogy if a large hyper-person in the fourth dimension tried to grab you, you would see five apparently separate irregular flesh-colored spheres appear out of nowhere, which converge on you.


And there he saw his first Palainian.

Or, strictly speaking, he saw part of his first Palainian; for no three-dimensional creature has ever seen or ever will see in entirety any member of any of the frigid-blooded, poison-breathing races. Since life as we know it—organic, three-dimensional life—is based upon liquid water and gaseous oxygen, such life did not and could not develop upon planets whose temperatures are only a few degrees above absolute zero. Many, perhaps most, of these ultra-frigid planets have an atmosphere of sorts; some have no atmosphere at all. Nevertheless, with or without atmosphere and completely without oxygen and water; life—highly intelligent life—did develop upon millions and millions of such worlds. That life is not, however, strictly three-dimensional. Of necessity, even in the lowest forms, it possesses an extension into the hyper-dimension; and it is this metabolic extension alone which makes it possible for life to exist under such extreme conditions.

The extension makes it impossible for any human being to see anything of a Palainian except the fluid, amorphous, ever-changing thing which is his three-dimensional aspect of the moment; makes any attempt at description or portraiture completely futile.

Virgil Samms stared at the Palainian; tried to see what it looked like. He could not tell whether it had eyes or antennae; legs, arms, or tentacles, teeth or beaks, talons or claws or feet; skin, scales, or feathers. It did not even remotely resemble anything that the Lensman had ever seen, sensed, or imagined. He gave up; sent out an exploring thought.

She tried; but demonstration, too, was useless; for to Samms the Palainian’s movements were pointless indeed. The peculiarly flowing subtly changing thing darted back and forth, rose and fell, appeared and disappeared; undergoing the while-cyclic changes in shape and form and size, in aspect and texture. It was now spiny, now tentacular, now scaly, now covered with peculiarly repellent feather-like fronds, each oozing a crimson slime. But it apparently did not do anything whatever. The net result of all its activity was, apparently, zero.

From FIRST LENSMAN by E. E. "Doc" Smith (1950)

Remember that when the Sphere from the third dimension visited A Square in Flatland, it appeared inside A Square's locked house. How did it manage that? Because even though the house was closed in the second dimension, it was quite open in the third.

If you are constrained to stay in two dimensional Flatland, there is no way to move into the house without first encountering the walls of the house. But if you can enter the third dimension, you can "hop" over the wall and enter the house anyway. By analogy, locking yourself inside your home will not prevent the Hypersphere from entering the fourth dimension and "hopping" over the walls and thus entering your locked home.

This also means that your space dreadnought coated in adamantium armor and guarded by impenetrable force fields will be quite defenseless to an enemy warship in the fourth dimension. They can fire all their weapons over the armor and force fields, and gut your dreadnought from the inside.

And "walls" do not just apply to houses, they apply to an organism's skin as well. Pictured below is a two dimensional being from the Planiverse. Remember that 2D creatures can only see things in the 2D plane they exist in. So when they look at another inhabitant, they see their skin.

But a 3D observer is "looking down" at the 2D creature. So they see the 2D creature's internal organs. In the same way, a hyper-observer looking at you would mostly see all your internal organs. And they could reach inside you and touch said organs without breaking your skin first.


     “What did you see?”
     “The box did not simply vanish. The process was not quite instantaneous but lasted some measurable fraction of a second. From where I am sitting it appeared to shrink very, very rapidly, as if it were disappearing into the far distance. But it did not go outside the room, for I could see it right up to the instant it disappeared.”
     “But where did it go?”
     “That is all I can report.”

     The cameras were Mitchell servos; the projector was a Yashinon tabletop tank, with an adapter to permit it to receive Land Solid-Sight-Sound 4 mm. film. Shortly they were listening to and watching the events leading up to the disappearance of the empty brandy case.
     Jubal watched the box being thrown at his head, saw it wink out in midair. “That’s enough,” he said. “Anne will be pleased to know that the cameras back her up. Duke, let’s repeat that last bit in slow motion.”
     “Okay.” Duke spooled back, then announced, “This is ten-to-one.”
     The scene was the same but the slowed-down sound was useless; Duke switched it off. The box floated slowly from Jill’s hands toward Jubal’s head, then quite suddenly ceased to be. But it did not simply wink out; under slow-motion projection it could be seen shrinking, smaller and smaller until it was no longer there.
     Jubal nodded thoughtfully. “Duke, can you slow it down still more?”
     “Just a sec. Something is fouled up with the stereo.”
     “Darned if I can figure it out. It looked all right on the fast run. But when I slowed it down, the depth effect was reversed. You saw it. That box went away from us fast, mighty fast — but it always looked closer than the wall. Swapped parallax, of course. But I never took that cartridge off the spindle. Gremlins.”
     “Oh. Hold it, Duke. Run the film from the other camera.”
     “Unh … oh, I see, That’ll give us a ninety-degree cross on it and we’ll see properly even if I did jimmy this film somehow.” Duke changed cartridges. “Zip through the first part, okay? Then undercranked ten-to-one on the part that counts.”
     “Go ahead.”
     The scene was the same save for angle. When the image of Jill grabbed the box, Duke slowed down the show and again they watched the box go away.
     Duke cursed. “Something was fouled up with the second camera too.”
     “Of course. It was looking at it around from the side so the box should have gone out of the frame to one side or the other. Instead it went straight away from us again. Well, didn’t it? You saw it. Straight away from us.”
     “Yes,” agreed Jubal. “‘Straight away from us.’”
     “Out it can’t — not from both angles.”
     “What do you mean, it can’t? It already did.” Harshaw added, “If we I had used doppler-radar in place of each of those cameras, I wonder what they would have shown?”
     “How should I know? I’m going to take both these cameras apart.”
     “Don’t bother.”
     “But — ”
     “Don’t waste your time, Duke; the cameras are all right. What is exactly ninety degrees from everything else?”
     “I’m no good at riddles.”
     “It’s not a riddle and I meant it seriously. I could refer you to Mr. A. Square from Flatland, but I’ll answer it myself."

(ed note: what is exactly ninety degrees from everything else is of course the fourth dimension)

From STRANGER IN A STRANGE LAND by Robert Heinlein (1961)

“But even if we decide to try the fourth dimension, how could you do it? Surely that dimension is merely a mathematical concept, with no actual existence in nature?”

“No; it’s actual enough, I think—nature’s a big field, you know, and contains a lot of unexplored territory. Remember how casually that Eight thing out there discussed it? It isn’t how to get there that’s biting me; it’s only that those intellectuals can stand a lot more grief than we can, and conditions in the region of the fourth dimension probably wouldn’t suit us any too well.

“However, we wouldn’t have to be there for more than a hundred thousandth of a second to dodge this gang, and we could stand almost anything that long, I imagine. As to how to do it—rotation. Three pairs of rotating, high-amperage currents, at mutual right angles, converging upon a point. Remembering that any rotating current exerts its force at a right angle, what would happen?”

“It might, at that,” Crane conceded, after minutes of narrow-eyed concentration; then, Crane-wise, began to muster objections. “But it would not so affect this vessel. She is altogether too large, is of the wrong shape, and—”

“And you can’t pull yourself up by your own boot straps,” Seaton interrupted. “Right—you’ve got to have something to work from, something to anchor your forces to. We’d make the trip in little old Skylark Two. She’s small, she’s spherical and she has so little mass compared to Three that rotating her out of space would be easy—it wouldn’t even shift Three’s reference planes.”

Six mighty rotating currents of electricity impinged simultaneously upon the spherical hull of Skylark Two and she disappeared utterly. No exit had been opened and the walls remained solid, but where the forty-foot globe of arenak had rested in her cradle an instant before there was nothing. Pushed against by six balancing and gigantic forces, twisted cruelly by six couples of angular force of unthinkable magnitude, the immensely strong arenak shell of the vessel had held and, following the path of least resistance—the only path in which she could escape from those irresistible forces—she had shot out of space as we know it and into the impossible reality of that hyperspace which Seaton’s vast mathematical knowledge had enabled him so dimly to perceive.

As those forces smote his vessel, Seaton felt himself compressed. He was being driven together irresistibly in all three dimensions, and in those dimensions at the same time he was as irresistibly being twisted—was being corkscrewed in a monstrously obscure fashion which permitted him neither to move from his place nor to remain in it. He hung poised there for interminable hours, even though he knew that the time required for that current to build up to its inconceivable value was to be measured only in fractional millionths of a single second. Yet he waited strainingly while that force increased at an all but imperceptible rate, until at last the vessel and all its contents were squeezed out of space, in a manner somewhat comparable to that in which an orange pip is forced out from between pressing thumb and resisting finger. At the same time Seaton felt a painless, but unutterably horrible, transformation of his entire body—a rearrangement, a writhing, crawling distortion; a hideously revolting and incomprehensibly impossible extrusion of his bodily substance as every molecule, every atom, every ultimate particle of his physical structure was compelled to extend itself into that unknown new dimension.

“You aren’t talking—haven’t you discovered that yet? You are thinking, and we are getting your thoughts as speech; that’s all. Don’t believe it? All right; there’s your tongue. right there—or better, take your heart. It’s that funny-looking object right there—see it? It isn’t beating—that is, it would seem to us to take weeks, or possibly months, to beat. Take hold of it—feel it for yourself.”

“Take hold of it? My own heart? Why, it’s inside me, between my ribs—I couldn’t possibly!”

“Sure you can! That’s your intellect talking now, not your brain. You’re four-dimensional now, remember, and what you used to call your body is nothing but the three-dimensional hypersurface of your new hyperbody. You can take hold of your heart or your gizzard just as easily as you used to pat yourself on the nose with a powder puff.”

“Well, I won’t, then—why, I wouldn’t touch that thing for a million dollars!”

“All right; watch me feel mine, then. See, it’s perfectly motionless, and my tongue is, too. And there’s something else that I never expected to look at—my appendix. Good thing you’re in good shape, old vermiform, or I’d take a pair of scissors and snick you off while I’ve got such a good chance to do it without …”

“Dick!” shrieked Dorothy. “For the love of Heaven …”

“Calm down, Dottie, calm down. I’m just trying to get you used to this mess—I’ll try something else. Here, you know what this is—a new can of tobacco, with the lid soldered on tight. In three dimensions there’s no way of getting into it without breaking metal—you’ve opened lots of them. But out here I simply reach past the metal of the container, like this, see, and put it into my pipe, thus. The can is still soldered tight, no holes in it anywhere, but the tobacco is out, nevertheless. Inexplicable in three-dimensional space, impossible for us really to understand mentally, but physically perfectly simple and perfectly natural after you get used to it. That’ll straighten you out some, perhaps.”

"However, there is another matter which I think is of more immediate concern. It occurred to me, when I saw you take that pinch of tobacco without opening the tin, that everywhere we have gone, even in intergalactic space, we have found life, some friendly, some inimical. There is no real reason to suppose that hyperspace is devoid of animate and intelligent life.”

“Oh, Martin!” Margaret shuddered. “Life! Here? In this horrible, this utterly impossible place?”

“Certainly, dearest,” he replied gravely. “It all goes back to the conversation we had long ago, during the first trip of the old Skylark. Remember? Life need not be comprehensible to us to exist—compared to what we do not know and what we can never either know or understand, our knowledge is infinitesimal.”

She did not reply and he spoke again to Seaton: “It would seem to be almost a certainty that four-dimensional life does in fact exist. Postulating its existence, the possibility of an encounter cannot be denied. Such beings could of course enter this vessel as easily as your fingers entered that tobacco can. The point of these remarks is this would we not be at a serious disadvantage? Would they not have fourth-dimensional shields or walls about which we three-dimensional intelligences would know nothing?”

“Sweet spirits of niter!” Seaton exclaimed. “Never thought of that at all, Mart. Don’t see how they could—and yet it does stand to reason that they’d have some way of locking up their horses so they couldn’t run away, or so that nobody else could steal them.

"I think I can explain it, too, by analogy. Imagine a two-dimensional man, one centimeter wide and ten or twelve centimeters long; the typical flatlander of the classical dimensional explanations. There he is, in a plane, happy as a clam and perfectly at home. Then some force takes him by one end and rolls him up into a spiral, or sort of semisolid cylinder, one centimeter long. He won’t know what to make of it, but in reality he’ll be a two-dimensional man occupying three-dimensional space."

From SKYLARK OF VALERON by E. E. "Doc" Smith (1934)

Finally getting to the point, the fourth dimension might be used as a method of faster-than-light travel. The basic idea is that our 3D space might be crumpled up in the fourth dimension without us being aware of it. So points that were far apart in 3D space might be adjacent if one could only make a little hop in the fourth dimension.

If of course we are lucky enough that our space is all crumpled up in the fourth dimension. Or if our FTL drive is powerful enough to crumple up light-years of space all by itself. That could be dangerous, some passing cosmic four dimensional being might inadvertently have its lower left tentacle suddenly pleated into painful Origami, with unfortunate consequences. And any advanced 4D civilization might take exception to having their entire solar system wadded up like piece of used facial tissue.

Nelson Brown

     Hmmm. As much as a like hard SF, there are times I ponder inventing completely imaginary physics with the caveat that they are mathematical and self-consistent. That's difficult to accomplish, but I think readers/watchers/players are happy with consistency and are willing to compromise on realism for good imagination.
     In that way, I sometimes imagine adding a W-direction to XYZ+T spacetime. Specialized ships can leave the "horizontal volume" we all know, giving the impression that they have disappeared as a cloaking device would do.
     However, the W direction is fraught with peril, because the further you go "below" the more difficult it becomes to return. Even small depths are hostile to our technology because «insert imagined reasons here».
     Perhaps the positive W direction works in an inverse way. Ships are easy to detect, move fast, have very little mass, and if they fail they return abruptly to the W=0 volume.

Winchell Chung

     Yes, decades ago I toyed with the same idea. Except I assumed that W=0 level (our mundane Euclidean dimension) had gravity. Meaning that if an object was at, say W= 10, gravity will force it to "fall" until it reached W=0.
     The justification was to explain why we didn't see natural objects vanishing off into the fifth dimension.
     A hyperspace submarine starship could accelerate into the +W direction, and could perhaps angle the ship so it could look "down" at mundane reality.
     Let me explain: imagine a two dimensional "flatlander", like the one described in Edwin Abbott's book. The flatlander can only look along the x-y dimension, it cannot turn its gaze into the z dimension at all. Unless a 3D entity (like you), picked the flatlander up into the Z direction, and rotated the flatlander so that its local x-y sensory plane intersected its flatland x-y dimension. You turned it so it can look "down".
     In the same way a hyperspace sub high in the W direction could rotate in a hyperspace way so that it could look "down" into our mundane 3D universe.
     Whats more, the sub could move so it was "over" an enemy spacecraft, and dump a bomb out its airlock. The "gravity" would drag the bomb down until it hit the enemy and exploded.
     As far as the enemy ship is concerned, the bomb materialized out of nowhere.
     Until one fine day the enemy learned how to rotate electromagnetic radiation into the W direction. Then its telescopes and radar could see the dastardly hyperspace subs. And shoot at it with rotated laser beams.

Nelson Brown

     Yes. I'd like to continue toying with that idea. Maybe the "looking" has to be some novel kind of sensor. Passive sensors barely work, and using active scans immediately announce the presence of the scanner.
     Perhaps there's some naturally occurring stuff out in the W direction (possibly a form of dark matter?) The natural hazards are coarsely mapped and difficult to detect.
     Another thought… perhaps the energy required to leave the W=0 volume increases greatly at close proximity to a gravity well. So if a hyperspace sub is near a star or a planet, it is forced back to shallow W distances.

Winchell Chung

     There are certainly lots of interesting lines of speculation.
     A star or planet with a W+ coordinate would appear in our xyz universe as a place with gravitational attraction but no object in the center.
     The math for distances is easy, just add a fourth term to the true distance equation.

     Distance = sqrt( (x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2 + (w1-w2)^2 )

Ian Borchardt

     In my old 4X space campaign stealth ships (aka submarines) had to anchor to reality with a "periscope" or be lost forever in their own quantum universe. Worked well. Especially since the "periscope" tended to be fairly vulnerable to attacks.

Isaac Kuo

     You might like my pet idea for convenient magical physics FTL - ballooning in hyperspace. As per Winchell Chung's idea, there is a W dimension, but without magical hyperspace drive everything falls onto W=0. But the layers aren't fixed with respect to each other, they are sliding past each other at FTL speeds, like fast horizontal winds.
     So, the FTL drive works by adjust hyperspace "altitude" up and down to reach an altitude where the "wind" is in the desired direction. Usually, this restricts motion to a wide cone, and but it might only be possible to go in one direction between two systems. Even if it's possible to go in both directions, the speeds may be radically different.
     I didn't really think of this scheme as "stealthy", though...not any more "stealthy" than any other FTL propulsion system. A spacecraft operating its hyperspace drive will inevitably have some sort of exhaust...propellant, or waste heat photons, or whatever. These immediately fall into real space, possibly acquiring a lot of thermal kinetic energy in the process. Either way, it leaves a visible trail of evidence.

From a thread on Google+ (2015)

      But he had not eyes for it. To the west where avenue and buildings ended was the field and on it space ships, stretching away for miles — fast little military darts, stubby Moon shuttles, winged ships that served the satellite stations, robot freighters, graceless and powerful. But directly in front of the gate hardly half a mile away was a great ship that he knew at once, the starship Asgard. He knew her history, Uncle Chet had served in her. A hundred years earlier she had been built out in space as a space-to-space rocket ship; she was then the Prince of Wales. Years passed, her tubes were ripped out and a mass-conversion torch was kindled in her; she became the Einstein. More years passed, for nearly twenty she swung empty around Luna, a lifeless, outmoded hulk. Now in place of the torch she had Horst-Conrad impellers that clutched at the fabric of space itself; thanks to them she was now able to touch Mother Terra. To commemorate her rebirth she had been dubbed Asgard, heavenly home of the gods.
     Her massive, pear-shaped body was poised on its smaller end, steadied by an invisible scaffolding of thrust beams. Max knew where they must be, for there was a ring of barricades spotted around her to keep the careless from wandering into the deadly loci.

     "Mmm . . . you seem to know about such things. Could you tell me just what it is we do? I heard the Astrogator talking about it at the table but I couldn't make head nor tail. We sort of duck into a space warp; isn't that right?"
     "Oh no, not a space warp. That's a silly term—space doesn't 'warp' except in places where pi isn't exactly three point one four one five nine two six five three five eight nine seven nine three two three eight four six two six four three three eight three two seven, and so forth—like inside a nucleus. But we're heading out to a place where space is really flat, not just mildly curved the way it is near a star. Anomalies are always flat, otherwise they couldn't fit together—be congruent."
     She looked puzzled. "Come again?"
     "Look, Eldreth, how far did you go in mathematics?"
     "Me? I flunked improper fractions. Miss Mimsey was very vexed with me."
     "Miss Mimsey?"
     "Miss Mimsey's School for Young Ladies, so you see I can listen with an open mind." She made a face. "But you told me that all you went to was a country high school and didn't get to finish at that. Huh?"
     "Yes, but I learned from my uncle. He was a great mathematician. Well, he didn't have any theorems named after him—but a great one just the same, I think." He paused. "I don't know exactly how to tell you; it takes equations. Say! Could you lend me that scarf you're wearing for a minute?"
     "Huh? Why, sure." She removed it from her neck.
     It was a photoprint showing a stylized picture of the solar system, a souvenir of Solar Union Day. In the middle of the square of cloth was the conventional sunburst surrounded by circles representing orbits of solar planets, with a few comets thrown in. The scale was badly distorted and it was useless as a structural picture of the home system, but it sufficed. Max took it and said, "Here's Mars."
     Eldreth said, "You read it. That's cheating."
     "Hush a moment. Here's Jupiter. To go from Mars to Jupiter you have to go from here to here, don't you?"
     "But suppose I fold it so that Mars is on top of Jupiter? What's to prevent just stepping across?"

     "Nothing, I guess. Except that what works for that scarf wouldn't work very well in practice. Would it?"
     "No, not that near to a star. But it works fine after you back away from a star quite a distance. You see, that's just what an anomaly is, a place where space is folded back on itself, turning a long distance into no distance at all."
     "Then space is warped."
     "No, no, no! Look, I just folded your scarf. I didn't stretch it out of shape! I didn't even wrinkle it. Space is the same way; it's crumpled like a piece of waste paper—but it's not warped, just crumpled. Through some extra dimensions, of course."
     "I don't see any 'of course' about it."
     "The math of it is simple, but it's hard to talk about because you can't see it. Space—our space—may be crumpled up small enough to stuff into a coffee cup, all hundreds of thousands of light-years of it. A four-dimensional coffee cup, of course."
     She sighed. "I don't see how a four-dimensional coffee cup could even hold coffee, much less a whole galaxy."
     "No trouble at all. You could stuff this sheer scarf into a thimble. Same principle. But let me finish. They used to think that nothing could go faster than light. Well, that was both right and wrong. It . . ."
     "How can it be both?"
     "That's one of the Horst anomalies. You can't go faster than light, not in our space. If you do, you burst out of it. But if you do it where space is folded back and congruent, you pop right back into our own space again—but a long way off. How far off depends on how it's folded. And that depends on the mass in the space, in a complicated fashion that can't be described in words but can be calculated."
     "But suppose you do it just anywhere?"
     "That's what happened to the first ones who tried it. They didn't come back. And that's why surveys are dangerous; survey ships go poking through anomalies that have been calculated but never tried. That's also why astrogators get paid so much. They have to head the ship for a place you can't see and they have to put the ship there just under the speed of light and they have to give it the gun at just the right world point. Drop a decimal point or use a short cut that covers up an indeterminancy and it's just too bad. Now we've been gunning at twenty-four gee ever since we left the atmosphere. We don't feel it of course because we are carried inside a discontinuity field at an artificial one gravity—that's another of the anomalies. But we're getting up close to the speed of light, up against the Einstein Wall; pretty soon we'll be squeezed through like a watermelon seed between your finger and thumb and we'll come out near Theta Centauri fifty-eight light-years away. Simple, if you look at it right."
     She shivered. "If we come out, you mean."
     "Well . . . I suppose so. But it's not as dangerous as helicopters. And look at it this way: if it weren't for the anomalies, there never would have been any way for us to reach the stars; the distances are too great. But looking back, it is obvious that all that emptiness couldn't be real—there had to be the anomalies. That's what my uncle used to say."

From STARMAN JONES by Robert A. Heinlein (1953)

      "Well, then, someone just tell me how we got here!" Calvin's voice was still angry and his freckles seemed to stand out on his face. "Even traveling at the speed of light it would take us years and years to get here."
     "Oh, we don't travel at the speed of anything," Mrs. Whatsit explained earnestly. "We tesser. Or you might say, we wrinkle."
     "But we will not do it all at once," Mrs. Whatsit comforted them. "We will do it in short stages." She looked at Meg. "Now we will tesser, we will wrinkle again. Do you understand?"
     "No," Meg said flatly.

     Mrs. Whatsit sighed. "Explanations are not easy when they are about things for which your civilization still has no words. Calvin talked about traveling at the speed of light. You understand that, little Meg?"
     "Yes," Meg nodded.
     "That, of course, is the impractical, long way around. We have learned to take short cuts wherever possible."
     "Sort of like in math?" Meg asked.
     "Like in math." Mrs. Whatsit looked over at Mrs. Who. "Take your skirt and show them."
     "La experiencia es la madre de la ciencia. Spanish, my dears. Cervantes. Experience is the mother of knowledge." Mrs. Who took a portion of her white robe in her hands and held it tight.
     "You see," Mrs. Whatsit said, "if a very small insect were to move from the section of skirt in Mrs. Who's right hand to that in her left, it would be quite a long walk for him if he had to walk straight across."
     Swiftly Mrs. Who brought her hands, still holding the skirt, together.
     "Now, you see," Mrs. Whatsit said, "he would be there, without that long trip. That is how we travel."

     Charles Wallace accepted the explanation serenely. Even Calvin did not seem perturbed. "Oh, dear," Meg sighed. "I guess I am a moron. I just don't get it."
     "That is because you think of space only in three dimensions," Mrs. Whatsit told her. "We travel in the fifth dimension. This is something you can understand, Meg. Don't be afraid to try. Was your mother able to explain a tesseract to you?"
     "Well, she never did," Meg said. "She got so upset about it Why, Mrs. Whatsit? She said it had something to do with her and Father."
     "It was a concept they were playing with," Mrs. Whatsit said, "going beyond the fourth dimension to the fifth. Did your mother explain it to you, Charles?"

     "Well, yes." Charles looked a little embarrassed. "Please don't be hurt, Meg. I just kept at her while you were at school till I got it out of her."
     Meg sighed. "Just explain it to me."
     "Okay," Charles said. "What is the first dimension?"
     "Well—a line."
     "Okay. And the second dimension?"
     "Well, you'd square the line. A flat square would be in the second dimension."
     "And the third?"
     "Well, you'd square the second dimension. Then the square wouldn't be flat any more. It would have a bottom, and sides, and a top."
     "And the fourth?"
     "Well, I guess if you want to put it into mathematical terms you'd square the square.
But you can't take a pencil and draw it the way you can the first three. I know it's got something to do with Einstein and time. I guess maybe you could call the fourth dimension Time."
     "That's right," Charles said. "Good girl. Okay, then, for the fifth dimension you'd square the fourth, wouldn't you?"
     "I guess so."
     "Well, the fifth dimension's a tesseract. You add that to the other four dimensions and you can travel through space without having to go the long way around. In other words, to put it into Euclid, or old-fashioned plane geometry, a straight line is not the shortest distance between two points."

     For a brief, illuminating second Meg's face had the listening, probing expression that was so often seen on Charles's. "I see!" she cried. "I got it! For just a moment I got it! I can't possibly explain it now, but there for a second I saw it!"

From A WRINKLE IN TIME by Madelein L'Engle (1962)

Ivo took his stance before the blackboard he had set up. "A conception of cosmology," he said, assuming the manner of a lecturer. "The evidence available indicates that our universe is in a state of continual expansion. Calculations suggest that there is a finite limit to such expansion, governed by variables too complex to discuss at this time. For convenience we shall think of the present universe as that four-dimensional volume beyond which our three-dimensional physical space and matter cannot expand: the cosmic limitation. We shall further consider these four dimensions to be spatial in nature, though in fact the universe is a complex of n dimensions, few of which are spatial and many of which interact with spatial planes deviously. Do you understand?"

"Which other dimensions are you thinking of?"

"Time, mass, intensity, probability — any measurable or theoretically measurable quality." She nodded, and he saw that he had her interest. "Now assume that the 3-space cosmos we perceive can be represented by a derivative: a one-dimensional line." He drew a line on the board. "If you prefer, you may think of this line as a cord or section of pipe, in itself embracing three dimensions, but finite and flexible." He amplified his drawing:

"Quite clear," she said. "A pipe of macroscopic diameter represented by a line."

"Our fourth spatial dimension is now illustrated by a two-space figure: a circle." He erased the pipe-section and drew a circle on the board. "Within this circle is our line. Let's say it extends from point A to point B on the perimeter." He set it up:

"The ends of the universe," she agreed.

"Call this 3-space line within this 4-space circle the universe at, or soon after, its inception."

"The fabled big bang."

"Yes. Now in what manner would our fixed circle accommodate our variable line — if that line lengthened? Say the line AB expanded to a length of 2 AB?"

"It would have to wrinkle," she said immediately.

"Precisely." He erased his figure and drew another with a bending line:

"Now our universe has been expanding for some time," he continued. "How would you represent a hundredfold extension?"

She stood up, came to the board, accepted the chalk from him, and drew a more involved figure in place of his last:

"Very good," he said. "Now how about a thousandfold? A millionfold?"

"The convolutions would develop convolutions," she said, "assuming that your line is infinitely flexible. May I draw a detail subsection?"

"You may."

Carefully she rendered it:

compacted line

"This would be shaped into larger loops," she explained, "and the small ones could be subdivided similarly, until your circle is an impacted mass of threads. The diameter and flexibility of your line would be the only limitation of the process."

"Excellent," he said.

"Now assuming that this is an accurate cosmology," he lectured, "note certain features." He pointed with the chalk. "Our line touches itself at many points, both in the small loops and large ones. Suppose it were possible to pass across those connections, instead of traveling down the length of our line in normal fashion?"

"Down the line being traveled from one area to another in space? As from Earth to Neptune?" He nodded. "Why — " She hesitated, seeing the possibilities. "If Earth and Neptune happened to be in adjacent loops, you might jump from one to the other in — well, virtually, no time."

"Let's say that this is the case, and that those adjacent subloops are here." He pointed to the top of the first major loop. "Assume that arrangements and preparations make the effective duration of any single jump a matter of a few hours. How long would it take to reach Alpha Centauri from Earth?"

"That depends on its position and the configuration. It might be possible in a single hop, or it might require several months of jumping. By the same token, it might be as easy to traverse the entire galaxy — if this representation of the nature of space is accurate."

"The macroscope suggests this is the case."

She caught on rapidly. "So the destroyer origin is theoretically within reach?"


From MACROSCOPE by Piers Anthony (1969)


"What does that look like to you, Dr. Benedict?"

Benedict studied the ball, put a finger into the notch that McEvoy had cut, and looked up, frowning. "It looks to me like a tennis ball somebody turned inside out."

McEvoy nodded. "Right. And how would you go about turning a tennis ball inside out?"

"I don't think I could, without cutting a hole in it to turn it inside out through." The psychologist tossed the ball back onto the desk. "Which, I gather, you did not do. What can I do for you, Dr. McEvoy?"

"Fine. Things were going along very well until one of my men devised a radically new refrigerating pump that worked far better than anybody dreamed it could. We got our test material—a block of tungsten supported on an insulated tripod in the refrigerating vault—down closer to absolute zero than we'd ever hoped for. Maybe we hit absolute and dropped below it…I don't even know that for sure."

The phychologist blinked. "I don't follow. From absolute zero, just where can the temperature drop to?"

"A good question," McEvoy said. "I can't answer it. Below absolute zero you might speculate on some kind of negative molecular motion. Maybe that's what we did get. Certainly something changed. The test block simply evaporated. Vanished. The tripod vanished, and so did the temperature-recording device. All we could see in the vault was a small, glowing hole in the center of the room where the block had been. Nothing in it, nothing. Just a pale, blue, glowing area about six inches across that looked to some of us very strangely like a hypercube."

"A hypercube?"

"A three-dimensional picture of a four-dimensional object; just as you can draw a picture of a cube in perspective on a flat two-dimensional surface like a piece of paper. It looks like a cube when you look at it, but it doesn't actually have any depth. This glowing area was in three dimensions—cubical—but the lines were distorted as if there were more than one cube in the same space. In fact, it looked very suspiciously like a four-dimensional hole in our three-dimensional space, as if the energy we had been applying had inadvertently cut through a corner or an edge of some…some other universe constructed in four spatial dimensions instead of three."

Ed Benedict was silent for a moment, staring at the tennis ball. "So you investigated," he said finally.

"We investigated…and you know from the doctor what happened."

(ed note, the people who looked inside the hypercube died of fright)

"What about this?" Benedict pointed to the ball.

"That's one of the characteristics of this thing we are able to investigate. That was an ordinary, normal tennis ball until we dropped it into the area of this hypercube. It came out the other side looking like this. I stuck a pencil into the area and it came out with a thin layer of graphite around a solid wooden core. A light bulb we pushed in just exploded and vaporized."

That was her anchor, then. Her mind narrowed on that single thought. She was here, and this unbelievable place was here, too. There was nothing she could comprehend, but at least she was surviving. All about her she was aware of lines, angles, circles, but none of them were right, the way they should be. Three perfectly parallel lines which met each other at ninety-degree angles to form a perfect square with seven triangular sides…

It couldn't be!

But it was. Right here, all around her. And she was here. It has to be so, she told herself. Adjust to it! She sensed that in crossing the threshold into this universe she had turned a corner, an odd corner, not like any corner she had ever seen before, but her own universe was just inches away, back around that same corner. And, even more strange, she realized that she could get back through to her own universe again any time she wanted to just by turning back through the same strange angle, now that she knew it was there.

Like a desk with a secret drawer, she thought suddenly. Hidden, concealed from view, nobody could get in without knowing where the release spring was. Once you knew that, you could open and close it at will. Of course, you might discover the secret drawer by accident if you were sawing a corner off the desk, but even so, you wouldn't be able to work it without knowing about the hidden release.

What was it McEvoy had said? "We think it may be a three-dimensional slice through a fourth dimension." And he was right. They had found the secret drawer by sawing the corner off the desk. Quite by accident the stresses they had been using on that tungsten block had inadvertently twisted a segment of three-dimensional space and torn a hole through into this place. Accidentally, they had thrown open a door, and nothing they had found inside had been comprehensible to anyone who had crossed through. A door into Nowhere…no wonder they had died of fright! With no training, no experience to fall back on. It was only her own individual experience, her own incredibly high ability to adapt that was shielding her now, and for all her skill her own mind was now reeling to maintain control.

From THE UNIVERSE BETWEEN by Alan E. Nourse (1965)


This is nothing more than amusing handwavium invented in 1930 by E. E. "Doc" Smith. However, so many authors have copied this over the years that I thought I'd better explain it to you. So you'll understand when you stub your toe on the concept while reading. Sometimes the alternative term "fifth-order wave" is used.

Some 17th century scientists figured that light was a wave. Due to their lack of imagination they figured that if it was a wave, it had to be a wave in some medium. They postulated some insubstantial gas called the Luminiferous Aether which filled the universe. Light and other electromagnetic radiation were vibrations in the aether. They were "etheric vibrations".

As science progressed, the aether became harder and harder to justify. The required mechanical qualities of the aether had become more and more magical: it had to be a fluid in order to fill space, but one that was millions of times more rigid than steel in order to support the high frequencies of light waves. It also had to be massless and without viscosity, otherwise it would visibly affect the orbits of planets. Additionally it appeared it had to be completely transparent, non-dispersive, incompressible, and continuous at a very small scale. Aether theory was becoming less and less viable.

But it wasn't killed dead until Einstein's relativity pounded a stake through its heart.

Anyway, back in 1930 the legendary E. E. "Doc" Smith was writing "Skylark Three," the sequel to his space opera series. He needed a totally imaginary, but logical, theory to make energy beams that traveled faster than light. He started with the luminiferous aether and postulated that it was a fluid composed of etheric particles. Now, it was well known that atoms are not the smallest particles in physics. There were smaller particles that composed atoms: electrons and protons (neutrons were not discovered until 1932). These were called "sub-atomic" particles, because they were smaller than atoms.

So what if there were units of aether that were smaller than etheric particles? Well, they would be "sub-etheric" particles, would they not?

Doc Smith gleefully handwaved further, that vibrations in the sub-ether would manifest as beams of radiation which moved faster than vibrations in the grosser ether. Instant FTL energy beams. Logically this makes no sense, but hey, we're hand waving. Move along, nothing to see here.

As a digression, Doc Smith also postulated a type of force field that would freeze etheric particles in place at a given distance from the force field generator. This would stop any hostile etheric weapon beams dead in their tracks: frozen etheric particles cannot vibrate so cannot propagate etheric vibrations.

But if one was very clever, a weapon beam of sub-etheric vibrations would go sailing right through the barrier of frozen etheric particles, since the weapon beams are vibrations in the un-frozen sub-etheric particles.

A related term is "sub-space" found in Star Trek, but arguably that was invented by some author tired of using the term "hyperspace" and trying to invent the logical opposite just to be contrary.

Since Doc Smith invented sub-etheric radiation, it has been used by many science fiction authors.

  • E. E. "Doc" Smith SKYLARK THREE (1930)
  • Eando Binder STATIC 1936
  • Jack Williamson THE LEGION OF TIME (1938)
  • George O. Smith BEAM PIRATE (1944)
  • J. Sheldon YOU ARE FORBIDDEN (1947)
  • R. Rocklynne DISTRESS SIGNAL (1947)
  • Isaac Asimov THE TALKING STONE (1955) and later stories
  • Diane Duane SPOCK'S WORLD (1989)

...and many others that I have missed


(ed note: our heros Richard Seaton and Martin Crain, plus their spouses, have returned to Terra from their adventures in the previous novel. Richard has discovered how to make a remarkable force field, the "zone of force", but is frustrated because it renders the user almost helpless.)

      ‘Mart, we’re stuck – stopped dead. If my head wasn’t made of solid blue mush I’d’ve had a way figured out of this thing before now, but I can’t. With that zone of force the Skylark would have everything imaginable – without it, we’re exactly where we were before. That zone is immense, man – terrific – its possibilities are unthinkable – and I’m so damned dumb that I can’t find out how to use it intelligently – can’t use it at all, for that matter. By its very nature it is impenetrable to any form of matter, however applied; and this calc here,’ shaking the sheaf of papers viciously, ‘shows that it must also be opaque to any wave whatever, propagated through air or through ether, clear down to cosmic rays. Behind it we would be blind and helpless, so we can’t use it at all. It drives me frantic! Think of a barrier of pure force, impalpable, immaterial, and exerted along a geometrical surface of no thickness whatever – and yet actual enough to stop a radiation that travels a hundred million light-years and then goes through twenty-seven feet of solid lead just like it was so much vacuum! That’s what we’re up against! However, I’m going to try out that model, Mart, right now. Let’s go!’

     ‘You are getting idiotic again, Dick,’ Crane rejoined calmly, without moving. ‘You know, even better than I do, that you are playing with the most concentrated essence of energy that the world has ever seen. That zone of force probably can be generated—’

     ‘Probably, nothing!’ barked Seaton. ‘It’s just as evident a fact as that stool,’ kicking the unoffending bit of furniture halfway across the room as he spoke. ‘If you’d’ve let me I’d’ve shown it to you yesterday.’

     ‘Undoubtedly, then. Grant that it is impenetrable to all matter and to all known wave-lengths. Suppose that it should prove impenetrable also to gravitation and to magnetism? Those phenomena probably depend upon the ether, but we know nothing fundamental of their nature, nor of that of the ether. Therefore your calculations, comprehensive though they are, cannot predict the effect upon them of your zone of force. Suppose that that zone actually does set up a barrier in the ether, so that it nullifies gravitation, magnetism, and all allied phenomena; so that the power-bars, the attractors, and repellors, cannot work through it? Then what? As well as showing me the zone of force, you might well have shown me yourself flying off into space, unable to use your power and helpless if you released the zone. No, we must know more of the fundamentals before you try even a small-scale experiment.’

     ‘Oh, bugs! You’re carrying caution to extremes, Mart. What can happen? Even if gravitation should be nullified, I would rise only slowly, heading south the angle of our latitude – that’s thirty-nine degrees – away from the perpendicular. I couldn’t shoot off on a tangent, as some of these hop-heads have been claiming. Inertia would make me keep pace, approximately, with the Earth in its rotation. I would rise slowly – only as fast as the tangent departs from the curvature of the Earth’s surface. I haven’t figured out how fast that is, but it must be pretty slow.’

     ‘Pretty slow?’ Crane smiled. ‘Figure it out.’

     ‘All right – but I’ll bet it’s slower than the rise of a toy balloon.’ Seaton threw down the papers and picked up his slide rule, a twenty-inch deci-trig duplex. ‘You’ll concede that it is allowable to neglect the radial component of the orbital velocity of the Earth, for a first approximation, won’t you – or shall I figure that in too?’

     ‘You may neglect that factor.’

     ‘All right – let’s see. Radius of rotation here in Washington would be cosine latitude times equatorial radius, approximately – call it thirty-two hundred miles. Angular velocity, fifteen degrees an hour. I want secant fifteen less one times thirty-two hundred. Right? Secant equals one over cosine – um-m-m-m – one point oh three five. Then point oh three five times thirty-two hundred. Hundred and twelve miles first hour. Velocity constant with respect to sun, accelerated respecting point of departure. Ouch! You win, Mart – I’d step out! Well, how about this, then? I’ll put on a suit and carry rations. Harness outside, with the same equipment I used in the test flights before we built Skylark One – plus the new stuff. Then throw on the zone, and see what happens. There can’t be any jar in taking off, and with that outfit I can get back O.K. if I go clear to Jupiter!’

     Crane sat in silence, his keen mind considering every aspect of the motions possible, of velocity, of acceleration, of inertia. He already knew well Seaton’s resourcefulness in crises and his physical and mental strength. ‘As far as I can see, that might be safe,’ he admitted finally, ‘and we really should know something about it besides the theory.’

     The two men stepped out of the ‘testing shed’ – the huge structure that housed their Osnomian-built space-cruiser, Skylark Two. Seaton waddled clumsily, wearing as he did a Crane space-suit which, built of fur, canvas, metal, and transparent silica, braced by steel netting, and equipped with air-tanks and heaters, rendered its wearer independent of outside conditions of temperature and pressure. Outside this suit he wore a heavy harness of leather, buckled about his body, shoulders, and legs, attached to which were numerous knobs, switches, dials, bakelite cases, and other pieces of apparatus. Carried by a strong aluminum framework which was in turn supported by the harness, the universal bearing of a small power-bar rose directly above his grotesque-looking helmet.

     ‘What do you think you’re going to do in that thing, Dickie?’ Dorothy called. Then, thinking that he could not hear her voice, she turned to Crane. ‘What are you letting that precious husband of mine do now, Martin? He looks like he’s up to something.’

     While she was speaking, Seaton had snapped the release of his face-plate. ‘Nothing much, Dottie. Just going to show you-all the zone of force. Martin wouldn’t let me turn it on unless I got all cocked and primed for a year’s journey into space.’

     ‘Dot, what is that zone of force, anyway?’ asked Margaret.

     ‘Oh, it’s something Dick got into his head during that awful fight they had on Osnome. He hasn’t thought of anything else since we got back. You know how the attractors and repellors work? (yes, Doc Smith invented tractor beams as well) Well, he found out something funny about the way everything acted while the Mardonalians were bombarding them with a certain kind of a wave-length. He finally figured out the exact vibration that did it, and found out that if it is made strong enough, it acts as if a repellor and attractor were working together – only so much stronger that nothing can get through the boundary, either way – in fact, it’s so strong that it cuts anything in two that’s in the way. And the funny thing is that there’s nothing there at all, really; but Dick says that the forces meeting there, or something, make it act as though something really important were there. See?’

     ‘Uh-huh,’ assented Margaret, doubtfully, just as Crane finished the final adjustments and moved toward them. A safe distance away from Seaton, he turned and waved his hand.

     Instantly Seaton disappeared from view, and around the place where he had stood there appeared a shimmering globe some twenty feet in diameter – a globe apparently a perfect spherical mirror, which darted upward and toward the south. After a moment the globe disappeared and Seaton was again seen. He was now standing upon a hemispherical mass of earth. He darted back toward the group upon the ground, while the mass of earth fell with a crash a quarter of a mile away. High above their heads the mirror again encompassed Seaton, and again shot upward and southward. Five times this maneuver was repeated before Seaton came down, landing easily in front of them and opening his helmet.

     ‘It’s just what we thought it was, only worse,’ he reported tersely. ‘Can’t do a thing with it. Gravitation won’t work through it – bars won’t – nothing will. And dark? DARK! Folks, you never saw real darkness, nor heard real silence. It scared me stiff!’
     ‘Poor little boy – afraid of the dark!’ exclaimed Dorothy. ‘We saw absolute blackness in space.’
     ‘Not like this, you didn’t. I just saw absolute darkness and heard absolute silence for the first time in my life. I never imagined anything like it – come on up with me and I’ll show it to you.’
     ‘No you won’t!’ his wife shrieked as she retreated toward Crane. ‘Some other time, perhaps.’

     Seaton removed the harness and glanced at the spot from which he had taken off, where now appeared appeared a hemispherical hole in the ground. ‘Let’s see what kind of tracks I left, Mart,’ and the two men bent over the depression. They saw with astonishment that the cut surface was perfectly smooth, with not even the slightest roughness or irregularity visible. Even the smallest grains of sand had been sheared in two along a mathematically exact hemispherical surface by the inconceivable force of the disintegrating copper bar.

(ed note: After further adventures, they discover a race of evil aliens called the Fenachrone who are in the process of conquering the galaxy. Our heroes barely escape with their lives, by unexpected use of the zone of force. The aliens are going to send a dreadnought to blow Terra into smithereens. Seaton has to discover how to work through the zone of force before then. He travels to an area of space where is suspected to exist a highly advanced benevolent race who will teach them. He is contacted by Orlon of Norlamin, a member of that race.)

      ‘How many families are working on rays – just one?’

     ‘One upon each kind of rays. That is, each of the ray families knows a great deal about all kinds of vibrations of the ether, but is specializing upon one narrow field. Take, for instance, the rays you are most interested in; those able to penetrate a zone of force. From my own slight and general knowledge I know that it would of necessity be a ray of the fifth order. These rays are very new – they have been under investigation only a few thousands of years – and the Rovol is the only student who would be at all well informed upon them. Shall I explain the orders of rays more fully than I did by means of the educator?’

     ‘Please. You assumed that we knew more than we do, so a little explanation would help.’

     ‘All ordinary vibrations – that is, all molecular and material ones, such as light, heat, electricity, radio, and the like – were arbitrarily called waves of the first order, in order to distinguish them from waves of the second order, which are given off by particles of the second order, which you know as protons and electrons, in their combination to form atoms. Your scientist Millikan discovered these rays for you, and in your language they are known as Millikan, or Cosmic, rays.

     (the following is pure handwavium) ‘Some time later, when sub-electrons of the first and second levels were identified, the energies given off by their combinations or disruptions were called rays of the third and fourth orders. These rays are most interesting and most useful; in fact, they do all our mechanical work. They as a class are called protelectricity, and bear the same relation to ordinary electricity that electricity does to torque – both are pure energy, and they are interconvertible. Unlike electricity, however, it may be converted into many different forms by fields of force, in a way comparable to that in which white light is resolved into colors by a prism – or rather, more like the way alternating current is changed to direct current by a motor-generator set, with attendant changes in properties. There are two complete spectra, of about five hundred and fifteen hundred bands, respectively, each as different from the others as red is different from green. Thus, the power that propels your space-vessel, your attractors, your repellors, your object-compass, your zone of force – all these things are simply a few of the fifteen hundred wave-bands of the fourth order, all of which you doubtless would have worked out for yourselves in time. Since I know practically nothing of the fifththe first sub-ethereal level – and since that order is to be your prime interest, I will leave it entirely to Rovol.’

     ‘If I knew a fraction of your “practically nothing” I’d think I knew a lot. But about this fifth order – is that as far as they go?’

     ‘My knowledge is slight and very general; only such as I must have in order to understand my own subject. The fifth order certainly is not the end – it is probably scarcely a beginning. We think now that the orders extend to infinite smallness, just as the galaxies are grouped into larger aggregations, which are probably in their turn only tiny units in a scheme infinitely large. ‘Over six thousand years ago the last fourth order rays were worked out; and certain peculiarities in their behavior led the then Rovol to suspect the existence of the fifth order. Successive generations of the Rovol proved their existence, determined the conditions of their liberation, and found that this metal of power was the only catalyst able to liberate them in usable quantity. This metal, which was called Rovolon after the Rovol, was first described upon theoretical grounds and later was found, by spectroscopy, in certain stars, notably in one star only eight light-years away; and a few micrograms have been obtained from meteorites. Enough for study, and to perform a few tests, but not enough to be of any practical use.’

     ‘Neither your rocket-ships nor projections could get you any Rovolon?’

     ‘Except for the minute quantities already mentioned, no. Every hundred years or so someone develops a new type of rocket that he thinks may stand a slight chance of making the journey to that Rovolon-bearing solar system, but not one of those venturesome youths has as yet returned. Either that sun has no planets or else the rocket-ships have failed. Our projections are useless, as they can be driven only a very short distance upon our present carrier wave. With a carrier of the fifth order we could drive a projection to any point in the galaxy, since its velocity would be millions of times that of light and the power necessary would be reduced accordingly – but as I said before, such waves cannot be generated without the metal Rovolon.

     ‘Now about those fifth-order rays, which will penetrate a zone of force. I am told that they are not ether waves at all?’

     ‘They are not ether waves. The fourth-order rays are the shortest vibrations that can be propagated through the ether; for the ether itself is not a continuous medium. We do not know its nature exactly, but it is an actual substance, and is composed of discrete particles of the fourth order. Now the zone of force, which is itself a fourth-order phenomenon, sets up a condition of stasis in the particles composing the ether. These particles are relatively so coarse that rays and particles of the fifth order will pass through the fixed zone without retardation. Therefore, if there is anything between the particles of the ether – this matter is being debated hotly among us at the present time – it must be a sub-ether, if I may use that term. We have never been able to investigate any of these things at all fully, not even such a relatively coarse aggregation as is the ether; but now, having Rovolon, it will not be many thousands of years until we shall have extended our knowledge many orders farther, in both directions.’

     ‘Just how will Rovolon help you?’

     ‘It will enable us to generate an energy of the ninth magnitude – that much power is necessary to work effectively with that which you have so aptly named a zone of force – and will give us a source of fifth, and probably higher orders of vibrations which, if they are generated in space at all, are beyond our present reach. The zone of force is necessary to shield certain items of equipment from ether vibrations; as any such vibration inside the controlling fields of force renders observation or control of the higher orders of rays impossible.’

     ‘Hm … m. I see – I’m learning something,’ Seaton replied, cordially. ‘Just as the higher-powered a radio set is, the more perfect must be its shielding?’

     ‘Yes. Just as a trace of gas will destroy the usefulness of your most sensitive vacuum tubes, and just as imperfect shielding will allow interfering waves to enter sensitive electrical apparatus – in that same fashion will even the slightest ether vibration interfere with the operation of the extremely sensitive fields and lenses of force which must be used in controlling forces of the higher orders.’

     ‘Orlon told me that you had the fifth order pretty well worked out.’

     ‘We know exactly what the forces are, how to liberate and control them, and how to use them. In fact, in the work which we are to begin today, we shall use but little of our ordinary power: almost all our work will be done by energies liberated from copper by means of the Rovolon you have given me. But here we are at my laboratory. You already know that the best way to learn is by doing, and we shall begin at once.’

From SKYLARK THREE by E. E. "Doc" Smith (1930)

      "With this introduction I can get down to fundamentals. Molecules are particles of the first order, and vibrations of the first order include sound, light, heat, electricity, radio, and so on. Second order, atoms—extremely short vibrations, such as hard X-rays. Third order, electrons and protons, with their accompanying Millikan, or cosmic, rays. Fourth order, sub-electrons and sub-protons. These, in the material aspect, are supposed to be the particles of the fourth order, and in the energy aspect they are known as Roeser's Rays. That is, these fourth-order rays and particles seem to partake of the nature of both energy and matter. Following me?"

     "Right behind you," she assured him. She had been listening intently, her wide-spaced brown eyes fastened upon his face.

     "Since these Roeser's Rays, or particles or rays of the fourth order, seem to be both matter and energy, and since the rays can be converted into what is supposed to be the particles, they have been thought to be the things from which both electrons and protons were built. Therefore, everybody except Norman Brandon has supposed them the ultimate units of creation, so that it would be useless to try to go any further...."

     "Why, we were taught that they are the ultimate units!" she protested.

     "I know you were—but we really don't know anything, except what we have learned empirically, even about our driving forces. What is called the fourth-order particle is absolutely unknown, since nobody has been able to detect it, to say nothing of determining its velocity or other properties. It has been assumed to have the velocity of light only because that hypothesis does not conflict with observational data. I'm going to give you the generally accepted idea, since we have nothing definite to offer in its place, but I warn you that that idea is very probably wrong. There's a lot of deep stuff down there hasn't been dug up yet. In fact, Brandon thinks that the product of conversion isn't what we think it is, at all—that the actual fundamental unit and the primary mechanism of the transformation lie somewhere below the fourth order, and possibly even below the level of the ether—but we haven't been able to find a point of attack yet that will let us get in anywhere.

     "However, I'm getting 'way ahead of our subject. To get back to it, energy can be converted into something that acts like matter through Roeser's Rays, and that is the empirical fact underlying the drive of our space-ships, as well as that of almost all other vehicles on all three planets. Power is generated by the great waterfalls of Tellus and Venus—water's mighty scarce on Mars, of course, so most of our plants there use fuel—and is transmitted on light beams, by means of powerful fields of force to the receptors, wherever they may be. The individual transmitting fields and receptors are really simply matched-frequency units, each matching the electrical characteristics of some particular and unique beam of force. This beam is composed of Roeser's Rays, in their energy aspect. It took a long time to work out this tight-beam transmission of power, but it was fairly simple after they got it.

"From the accumulators, then, the power is fed to the converters, each of which is backed by a projector. The converters simply change the aspect of the rays, from the energy aspect to the material aspect. As soon as this is done, the highly-charged particles—or whatever they are—thus formed are repelled by the terrific stationary force maintained in the projector backing the converter. Each particle departs with a velocity supposed to be that of light, and the recoil upon the projector drives the vessel, or car, or whatever it is attached to. Still with me?"

From SPACEHOUNDS OF IPC by E. E. "Doc" Smith (1931)


Sub-Etha is an interstellar faster-than-light telecommunications network used by hitchhikers to flag down passing spaceships. The primary hitcher's tool is known as the Electronic Thumb, a short black rod that can be used to contact passing ships and ask to be let on board. Ford also carries a Sens-O-Matic, a device for monitoring ships' Sub-Etha signals, and learns from it that the Vogons are on their way to demolish the Earth.

Sub-Etha is used throughout the Milky Way for any kind of data transmission, such as listening to the news or updating the Hitchhiker's Guide to the Galaxy itself. (ed note: sort of like an intergalactic Kindle, using intergalactic Wifi)

The name is a reference to the ether, which was once believed to be a medium filling the universe.

FTL That Ain't

There are a few science fiction interstellar transport methods that look like Faster Than Light, but are not actually Faster Than Light.



First off is boring old relativistic time dilation. You've probably seen it a million times before. The advantage is it's solidly hard-science, no science fiction here.

What it boils down to is a starship moving at an outrageous velocity near the speed of light, time moves slower for the crew as compared to the rate of time expereinced by everybody staying at home on Terra. For example, if the starship is heading from Terra to Alpha Centauri at 0.9999 c, the crew of the ship will think the trip took 23 days. But the people on Terra watching the starship through a telescope will think the trip took four years and 4.5 months.

An unbelievably naive starship crew would figure "Oh boy! Our ship can travel seventy times faster than light!"

But the people on Terra would say "Not so fast, morons. Your ship did not go FTL at all. It's just that you crew were living in slow motion. If you turned around and came back you'd find that almost nine years has gone by on good ol' Terra."

There are more details here.


The good ship FTL OR BUST is going to travel from Terra to Alpha Centauri (4.37 light-years, or 1,595 light-days) at a velocity of 99.99% the speed of light (0.9999 c).

Calculate the gamma factor. Either do the equation found here, or look it up in the table to the left. V/c is the factor of c, which in this case is 0.9999. The gamma factor γ is 70.712446, round to 70.7.

The trip time according to the stay-at-homes on Terra is 4.27 * 0.9999, or pretty much 4.27 years.

The trip time according to the crew is 1,595 / 70.7 or 23 days.

The biggest drawback is it takes hideously huge amounts of energy to accelerate a starship up to near lightspeed, then braking to a halt at the destination.

Between the Strokes of Night

In Charles Sheffield's BETWEEN THE STROKES OF NIGHT (1985) they use a system with many of the advantages and disadvantages of relativistic time dialation, EXCEPT without the hideously huge energy requirements.

In the novel, scientists discover a handwaving drug and physiological protocol that will switch a person into what they call the "S-state". In that state, people perceive time in slow motion. Even if the ship is standing still. The slow down is a whopping 1/2,000 of normal (a gamma similar to if their starship was traveling at 0.99999987499999 c).

It is also possible to switch a person in S-state back to normal state.

So if a person in S-state experiences one second, it seems like half an hour to a person in normal state. If an average life-span is 80 years, an S-state person will think that normal-state people only live 15 days. Due to further hand-waving reasons, a person in S-state ages more slowy than normal.

What does this mean? Say you had a putt-putt starship that could barely get up to a velocity of 0.1 c (10% light speed) and brake down to a halt. If a normal state person used this to travel to Alpha Centauri they would think the trip would take a bit more than forty freaking years. But to an S-state person the same trip would appear to take only eight days. Wow! Two-hundred times faster than light.

There are a few drawbacks, obviously.

Accelerations involve the square of the time—distance per second per second. Which means if you change the perception of a second, you change the perception of the acceleration. By the square of the time change. This means to an S-space person, an acceleration of a millionth of a gravity would be perceived as four gravities of acceleration! A four-millionth of a gravity would seem like a 1 g field.

To a normal state person, a four-millionth of a gravity would be so close to free fall as to make little difference.

Normal state people see S-state people as being immobile, since they are moving 1/2,000 times as slow. On the flip side, S-state people cannot even see normal state people because they move in the wink of an eye.


In Karl Schroeder's LOCKSTEP (2014) the science is hard, but the situation is tightly choreographed. Mr. Schroeder has found a way to have a Star Wars like spaceopera universe of tens of thousands of worlds, but utilizing only slower than light starships.

Mr. Schroeder figured the problem was how to allow a person to travel to a star, return home, and still find the same home that they left. But within the laws of physics.

  • Slower-than-light low velocity starships do not violate the laws of physics. But the traveler will return home to a planet that has aged decades or even hundreds of years. Not the same home. This assumes the traveler has not died of old age during the trip.

  • Slower-than-light near c starships do not violate the laws of physics. This will help prevent the traveler from dying of old age, but do nothing to prevent home from aging centuries in the interim.

  • Faster-than-light starships prevents the traveler from dying of old age, and home does not age appreciably. What a pity that it violates the laws of physics.

Mr. Schroeder took a close look and figured that science fiction authors were attempting to solve the wrong problem. The idea was to allow a Star Wars like interstellar empire. But the authors were trying create it by solving the ship velocity problem.

What if you tried solving the problem of duration instead?

Everybody in the Cicada corporation empire uses the Cicada lockstep protocol. All the planets and all the starships are inhabited by people who sleep in suspended animation for 360 months. Then in unison, they all wake up and spend one month awake. Then they all go to sleep for another 360 months. In other words: they are awake for one month every 30 years.

This means that any slower-than-light trip which takes less than thirty years can be scheduled so it takes place seemingly overnight.

Mr. Schroeder fine-tunes the concept a bit. The Cicada empire is actually about three light-years in diameter, composed of 70,000 rogue planets. The ships travel at 0.03 c using garden variety solid-core NTR or fission fragment engines. In practice a science fiction author could scale this up to as many light-years as they wanted, by increasing the time span that the people spent in suspended animation.

This allows private starships, explorers and despots and rogues. There are evil realtimers, who prey on locksteppers as they sleep. The locksteppers employ countermeasures to protect themselves.

Lockstep allows marginal worlds to be colonized. Robots have thirty years to farm and stockpile one month of food for the planet's population. A planet with zero hydrogen can use Bussard ramscoops to harvest the thin gruel of one hydrogen molecule per cubic centimeter, they have thirty years to scoop up enough to supply the population for one month.

It is a very clever solution to the scifi author's problem.

The Depths of Time

Roger MacBride Allen's THE DEPTHS OF TIME (2000) has an interesting drive that is sort of in between FTL and STL.

Now, technically if one can lay their hands on a traversable wormhole, it is possible to transform the little monster into a time machine by methods that do not violate the laws of physics. And believe me, physcists have done their darnedest to prove such things are impossible, since they hate time machines with the white hot intensity of a thousand suns.

In the novel, such a time machine is called a "timeshaft wormhole."

In this example, there is a colony at the Home System (at distance zero), and the Destination system (at distance 10 light-years). Starships can travel at 0.1 c (one-tenth lightspeed). As with all major trade routes, thoughtfully located at the mid-point (at distance 5 light-years) is a timehsaft wormhole that will transport the starship into the past a number of years equal to the total transit time (in this case 10 / 0.1 = 100 years).

A spacecraft sits at home system, when an order arrives from destination system for thirty crates of turbo-encabulator.

  1. In the year 5,000 CE the captain loads his spacecraft with the ordered turbo-encabulators. Spacecraft departs home system, bound for destination system, ten light-years away. Crew enters suspended animation for duration of the voyage.

  2. Spacecraft travels for fifty years at one-tenth lightspeed, thus traveling fifty years "uptime" and a distance of five light years.

  3. Spacecraft reaches timeshaft wormhole, midway between home system and destination system, in the year 5050 CE. Captain is revived briefly to pilot ship through time shaft.

  4. Oh, I almost forgot. Each wormhole time machine has a battlefleet of the Chronological Patrol. Who have orders to "shoot to kill" without warning any unauthorized ship who tries to use the time machine to damage causality, change history, or otherwise mess with time. Their basic job is to prevent information from the future from entering the past.

  5. Spacecraft drops through timeshaft and is propelled one hundred years downtime, into the past.

  6. Spacecraft emerges from wormhole in the year 4950 CE, fifty years before its departure from its home system and one hundred years before it enters the wormhole. Captain returns to suspended animation.

  7. Spacecraft once again travels for fifty years at one-tenth lightspeed, again traveling fifty years uptime and five more light-years.

  8. After traveling for one hundred years shipboard time, spacecraft arrives at target system in 5,000 CE, a few days or weeks after departure in objective time. Crew is revived from one hundred years of suspended animation to find that less than one month has passed.

From the point of view of the people at the destination system, the delivery took less than a month.

On the other hand, from the point of view of the captain, the ship, and the load of turbo-encabulators; they are all 100 years older.

All the Bridges Rusting

(ed note: This is a faster than light drive that ain't. The ships travel at lightspeed. But when a ship enters a matter transmitter and becomes encoded as a transition particle, time stops for the ship. When it travels from Terra to Alpha Centauri the ship materializes at the receiver 4.3 years later. However, for the crew, zero time has elapsed. Which is a huge savings on life support consumables. Not to mention wear and tear on the crew.)

      Take a point in space.
     Take a specific point near the star system Alpha Centaurus, on the line linking the center of mass of that system with Sol. Follow it as it moves toward Sol system at lightspeed. We presume a particle in this point.
     Men who deal in the physics of teleportation would speak of it as a “transition particle.” But think of it as a kind of superneutrino. Clearly it must have a rest mass of zero, like a neutrino. Like a neutrino, it must be fearfully difficult to find or stop. Despite several decades in which teleportation has been in common use, nobody has ever directly demonstrated the existence of a “transition particle.” It must be taken on faith.
     Its internal structure would be fearfully complex in terms of energy states. Its relativistic mass would be twelve thousand two hundred tons.
     One more property can be postulated. Its location in space is uncertain: a probability density, thousands of miles across as it passes Proxima Centauri, and spreading. The mass of the tiny red dwarf does not bend its path significantly. As it approaches the solar system the particle may be found anywhere within a vaguely bounded wave front several hundred thousand miles across. This vagueness of position is part of what makes teleportation work. One’s aim need not be so accurate.
     Near Pluto the particle changes state.
     Its relativistic mass converts to rest mass within the receiver cage of a drop ship (a spaceship with a teleportation receiver with the back end open). Its structure is still fearfully complex for an elementary particle: a twelve-thousand-two-hundred-ton spacecraft (the good ship Phoenix), loaded with instruments, its hull windowless and very smoothly contoured. Its presence here is the only evidence that a transition particle ever existed. Within the control cabin, the pilot’s finger is still on the TRANSMIT button.

     But she (captain Karin Sagan) remembered the shock of relief when the heat struck. She had pushed the TRANSMIT button a light-month out from Alpha Centaurus B. An instant later sweat was running from every pore of her body.
     There had been no guarantee. The probability density that physicists called a transition particle could have gone past the drop ship and out into the universe at large, beyond rescue forever. Or … a lot could happen in nine years. The station might have been wrecked or abandoned.
     But the heat meant that they had made it. Phoenix had lost potential energy entering Sol’s gravitational field and had gained it back in heat. The cabin felt like a furnace, but it was their body temperature that had jumped from 98.6° to 102°, all in an instant.

(ed note: the Phoenix is self-teleporting, but there has to be a drop ship with a receiver cage in the path of the transition particle. Or the Phoenix transition particle will just sail off to the far side of the universe, and never change back into the ship and crew.)

(ed note: captain Karin Sagan has an interview on live TV)

     Q: What about the Centaurus planets? Are they habitable?
     “No.” It hurt to say that. She saw the disappointment around her.
     Q: Neither of them checked out?
     “That’s right. There are six known planets circling Alpha Centaurus B. We may have missed a couple that were too small or too far out. We had to do all our looking from a light-month away. We had good hopes for B-2 and B-3 — remember, we knew they were there before we set out — but B-2 turns out to be a Venus-type with too much atmosphere, and B-3’s got a reducing atmosphere, something like Earth’s atmosphere three billion years ago.”
     Q: The colonists aren’t going to like that, are they?
     “I don’t expect they will. We messaged the (uncrewed) drop ship Lazarus II to turn off its JumpShift unit for a year. That means that the colony ships won’t convert to rest mass when they reach the receiver. They’ll be reflected back to the solar system. They should appear in the Pluto, drop ship about a month from now.”
     Q: Having lost nine years.
     “That’s right. Just like me and the rest of the crew of Phoenix.”

From ALL THE BRIDGES RUSTING by Larry Niven (1973)

Establishing Limits

Since FTL drives are ruled more or less impossible by current science, you have to invent your own. In such cases, the best way to start is to focus on effects instead of causes (as well as the rest of the rules of inventing handwavium).

An example of an effect is "The star drive can move the ship at ten light-years per hour".

An example of a cause is "The Mason Field is generated by the amplification of the interaction of the Alpha and Omega sub-particles contained in the Xanthe crystal when bombarded by pseudo electron valients in a charged hydrogen field."

In other words causes are technobabble fluff that the science fiction writer could get away with eliminating entirely. If anybody asks the writer how do the star drives work, the writer can reply "Splendidly." I mean, in a thriller novel when the protagonist gets on a passenger jet, do they suddenly stop and start explaining how a turbojet engine works?

Effects are basically the limits the writer puts on their science fiction star drives.

Effects help you avoid unintended consequences, and define the practical implications of your drive. If your star drive moves at ten light-years per hour, you can easily calculate that it will take about 28 minutes to travel to Alpha Centauri, and about two and one-quarter years to travel the width of the Milky Way galaxy. Which implies the former trip is akin to a corner store dash for a carton of milk, while the latter is more akin to Magellan circumnavigating the globe. Good practical facts an author can use to plot their novel.

Here are a few examples:

  • How much faster than light is the ship? (that's the one effect you have to establish.)
  • How big a ship can be moved?
  • Does it require large intricate starships, or can you just mount it in a submarine?
  • Does it require huge amounts of energy?
  • Does it require the ship to be outside any planetary or solar gravity wells?
  • Can the ship only enter FTL flight at special locations ? ("jump points")
  • Does each FTL "jump" require days of tedious mathematical calculations?
  • Can a ship in FTL flight be detected by another ship also in FTL flight?
  • Can a ship in FTL flight be detected by another ship or base not in FTL flight?
  • Does FTL flight make the crew vomit, hallucinate, have epileptic fits?
  • Is the supply of FTL drive units limited due to a tight monopoly on their manufacture, or due to the fact that they can no longer be manufactured at all?
  • Is a required component a rare sort of person with some kind of mystical psionic power?
  • Do the drive units require rare and hard to get materials in the drive's construction? (the Traveller RPG required Lanthanum, H. Beam Pipers' ships required Gadolinium, Captain Future's ship required a ring of Terbium. All of these are rare earth elements, emphasis on the "rare")
  • Does the drive units require exotic and uncommon fuel, or do they only need something common like hydrogen that is more or less available everywhere? Meaning how hard is it to refuel your ship?
  • Does the drive units require huge quantities of fuel or do they have fantastic fuel economy? In other words: can your ship travel the entire galaxy for months on one tank of gas or is all the fuel consumed in a single trip to the next-door star system?

These are just off the top of my head, you can find more by reading SF novels, or from your imagination.


The effects have implications in the SF universe you are creating:

If your ship is twice as fast as the speed of light, it can go 100 light years in a mere 50 years. Therefore most of the action in your universe will take place close to Sol, if the average interstellar journey is two years. On the other hand if your ship is 36,500,000 times as fast as the speed of light, your ship can cross the Galaxy the long way in about one single day. The action in this universe will therefore be galactic in scope.

If the only ships that can be moved are ones smaller than a Greyhound Bus, one implication is that you will not have titanic ships the size of Star Wars Imperial Star Destroyers, much less any Death Stars.

If there are only large intricate starships, they will be few in number and crewed by the cream of the crop. If any fool can build an FTL drive from plans downloaded from the internet and convert a septic tank into a starship, there will be zillions of starships crewed by a wide range of eccentric people.

If ships require huge amounts of energy for their FTL drives, you have to decide upon the source of said energy. Antimatter fuel implies antimatter factories or antimatter "mining." There is also the unintended consequences of a given starship containing enough energy to, say, vaporize Greenland. The further implication is that starship captains will be on a very short leash (John's Law). If on the other hand a starship can run on one AAA battery, you start having problems with FTL missiles the size of bullets.

A very common limit is that the FTL drive can only be entered if the ship is "not too deep in a gravity well", that is, farther than a certain distance from either a planet or the primary star. Again keep in mind that if ships can only enter or leave FTL at about Pluto's orbit, the ships will either require unreasonably powerful normal-space rocket drives that run afoul of Jon's Law, or the ships will take years to travel between Terra and the FTL take-off point. The New Horizons space probe took about 9.4 years to travel from Terra to Pluto.

Or if you are doing several jumps in a series, the travel time in normal space going from one jump point to another within a given solar system will add to the total trip time. Even if doing each FTL-jump takes zero time.


  1. First leg of the trip is from Terra in the Sol solar system to Sol jump point 5 (JP5) via normal space travel within the Sol solar system
  2. Next leg is from Sol JP5 to Alpha Centauri JP3 via FTL jump
  3. Next leg is from Alpha Centauri JP3 to Alpha Centauri JP9 via normal space travel within the Alpha C solar system
  4. Next leg is from Alpha Centauri JP9 to Tau Ceti JP2 via FTL jump
  5. Final leg is from Tau Ceti JP2 to planet Tau Ceti III

Even if the two FTL jumps take zero time, the three normal space travel legs will take either years or the services of torchship engines.

In Jerry Pournelle's Alderson Drive, the average distance of a jump point from the primary star is proportional to a star's mass. Therefore the total normal-space travel time will be shorter for a chain of jumps between spectral class M stars than it will for a chain of spectral class F stars. Class F stars have an average mass of 1.50 solar masses, while class M stars have an average mass of 0.50 solar masses. Of course Jerry Pournell's starships all have torchship drives so that is more an inconvenience than a show-stopper.

In the boardgame Attack Vector: Tactical, Ken Burnside avoided this problem by specifying that jump points orbit a star at about the orbit of Mercury.

Ships that can only enter/exit FTL flight at special locations make those locations into military choke points. Ships that can exit FTL flight anywhere coupled with ships that cannot be detected while FTL will open the possibility to genocidal interstellar wars that last all of five minutes.

In John Maddox Roberts novels Space Angel and Spacer: Window of the Mind, the "Whoopee Drive" makes the crew suffer projectile vomiting, violent diarrhea, and hallucinations. Before each jump they have to attach a barf bag over their mouth, strap themselves on to a toilet, and try to ignore the paisley Peter Max metal termites eating the hull. Naturally this made troop ships a nightmare. In Gordon Dickson's The Genetic General, closely spaced FTL jumps made without a recovery period in between would rapidly incapacitate the crew.

In David Lynch's movie adaptation of Frank Herbert's novel DUNE, mutated Guild Steersmen move starships between stars with their psychic abilities. Thus the Spacing Guild has a monopoly on starships, and the total number of starships was limited to the available supply of mutated Guild Steersmen. The same general situation occurs in SPI's StarForce and SPI's Universe RPG. Other stardrives have to be controlled by a human being, they cannot be automated or computer controlled. For more details go here

In John Brunnner's Interstellar Empire and Frederik Pohl's Heechee novels (Gateway et al) the starships are artifacts from some long lost alien race, humans can fly them but cannot construct them.

In SPI's game Freedom in the Galaxy all stardrives are manufactured by the Empire, and contain a thermonuclear booby-trap to discourage attempts at reverse-engineering. The empire takes its monopoly on stardrives very seriously.

And there are one or two short little shocker scifi stories that use FTL as an off-beat explanation for the Fermi Paradox. It seems that using an FTL drive in a solar system causes the primary star to go nova. So any space-going civilization will incinerate themselves upon testing their first FTL prototype. An example is Randall Garrett's Time Fuze


      "No—never!" she exclaimed. "I didn't mean it that way at all. I'm going to have this full dance with you, and enjoy every second of it And later I'm going to pack this dance card—which I hope you will sign for me—away in lavender, so it will go down in history that in my youth I really did dance with Gray Lensman Kinnison. Perhaps I've recovered enough now to talk and dance at the same time. Do you mind if I ask you some silly questions about space?"
     "Go ahead. They won't be silly, if I'm any judge. Elementary, perhaps, but not silly."

     "I hope so, but I think you're being charitable again. Like most of the girls here, I suppose, I've never been out in deep space at all. Besides a few hops to the moon. I've taken only two flits, and they were both only interplanetary—one to Mars and one to Venus. I never could see how you deep-space men can really understand what you're doing—either the frightful speeds at which you travel, the distances you cover, or the way your communicators work. In fact, according to the professors, no human mind can understand figures of those magnitudes at all. But you must understand them, I should think… or, perhaps…"
     "Or maybe the guy isn't human?" Kinnison laughed deeply, infectiously. "No, the professors are right. We can't understand the figures, but we don't have to—all we have to do is to work with 'em. And, now that it has just percolated through my skull who you really are, that you are Gladys Forrester, it's quite clear that you and I are in the same boat."
     "Me? How?" she exclaimed.
     "The human mind cannot really understand a million of anything. Yet your father, an immensely wealthy man, gave you clear title to a million credits in cash, to train you in finance in the only way that really produces results—the hard way of actual experience. You lost a lot of it at first, of course; but at last accounts you had got it all back, and some besides, in spite of all the smart guys trying to take it away from you. The fact that your brain can't envisage a million credits hasn't interferred with your manipulation of that amount, has it?"

     "No, but that's entirely different!" she protested.
     "Not in any essential feature," he countered. "I can explain it best, perhaps, by analogy. You can't visualize, mentally, the size of North America, either, yet that fact doesn't bother you in the least while you're driving around on it in an automobile. What do you drive? On the ground, I mean, not in the air?"
     "A DeKhotinsky sporter."
     "Um. Top speed a hundred and forty miles an hour, and I suppose you cruise between ninety and a hundred. We'll have to pretend that you drive a Crownover sedan, or some other big, slow jalopy, so that you tour at about sixty and have an absolute top of ninety. Also, you have a radio. On the broadcast bands you can hear a program from three or four thousand miles away; or, on short wave, from anywhere on Tellus…"
     "I can get tight-beam short-wave programs from the moon," the girl broke in. "I've heard them lots of times."
     "Yes," Kinnison assented dryly, "at such times as there didn't happen to be any interference."
     "Static is pretty bad, lots of times," the heiress agreed.
     "Well, change 'miles' to 'parsecs' and you've got the picture of deep-space speeds and operations," Kinnison informed her. "Our speed varies, of course, with the density of matter in space; but on the average—say one atom of substance per ten cubic centimeters of space—we tour at about sixty parsecs an hour, and full blast is about ninety. And our ultra-wave communicators, working below the level of the ether, in the sub-ether…"

     "Whatever that is," she interrupted.
     "That's as good a definition of it as any," he grinned at her. "We don't know what even the ether is, or whether or not it exists as an objective reality; to say nothing of what we so nonchalantly call the sub-ether. We can't understand gravity, even though we make it to order. Nobody yet has been able to say how it is propagated, or even whether or not it is propagated—no one has been able to devise any kind of an apparatus or meter or method by which its nature, period, or velocity can be determined. Neither do we know anything about time or space. In fact, fundamentally, we don't really know much of anything at all," he concluded.

     "Says you… but that makes me feel better, anyway," she confided, snuggling a little closer. "Go on about the communicators."
     "Ultra-waves are faster than ordinary radio waves, which of course travel through the ether with the velocity of light, in just about the same ratio as that of the speed of our ships to the speed of slow automobiles—that is, the ratio of a parsec to a mile. Roughly nineteen billion to one. Range, of course, is proportional to the square of the speed."
     "Nineteen billion!" she exclaimed. "And you just said that nobody could understand even a million!"
     "That's the point exactly," he went on, undisturbed. "You don't have to understand or visualize it. All you have to know is that deep-space vessels and communicators cover distances in parsecs at practically the same rate that Tellurian automobiles and radios cover miles. So, when some space-flea talks to you about parsecs, just think of miles in terms of an automobile and a teleset and you'll know as much as he does—maybe more."

     "I never heard it explained that way before—it does make it ever so much simpler. Will you sign this, please?"
     "Just one more point." The music had ceased and he was signing her card, preparatory to escorting her back to her place. "Like your supposedly tight-beam Luna-Tellus hookups, our long-range, equally tight-beam communicators are very sensitive to interference, either natural or artificial. So, while under perfect conditions we can communicate clear across the galaxy, there are times—particularly when the pirates are scrambling the channels—that we can't drive a beam from here to Alpha Centauri…. Thanks a lot for the dance."

(ed note: the point being that the author Doc Smith set up his FTL ships and FTL radio speeds to be analogous to familiar automobiles and radios. Which helps both the author and the reader understand what is going on)

From GRAY LENSMAN by E.E. "Doc" Smith (1951)

Matching Intrinsic Velocity

This concept dates all the way back to the 1930s, with E. E. "Doc" Smith's LENSMAN series. Say Lensman Kimball Kinnison's starship is moving seven kilometers per second towards Galactic North. When Kim turns on his ship's FTL inertialess drive, he can fly all over the place in any direction at a speed of 90 parsecs per hour, or even become perfectly stationary. But when Kim turns off the inertialess drive, the starship reverts back to moving 7 km/sec towards Galactic North. Doc Smith calls this the starship's "intrinsic" velocity.

The point being that even though Kim's ship can travel from Sol to Alpha Centauri in 52 seconds, when he gets there he will have to use normal space thrusters to match the ship's intrinsic velocity to the ship (or solar system) that is his destination.

This can be a real problem if the target ship is moving relativistically, or the solar system is around a runaway star. Or worse, a hypervelocity star. You are going to need a huge amount of reaction mass, or a reactionless drive (plus the threat of RocketCat's Atomic Wedgie).

Doc Smith takes this to an extreme, because inertialess drives can be made small enough for a person to wear on their belt. So if starship Alfa and person Bravo are both currently inertialess and both have moderate differences in intrinsic velocity, they can match velocity by using the spring room. Person Bravo enters the ship, goes to the spring room, enters the padded leather form fitting coffin which is attached to all the walls with huge strong springs, and both the person and the ship turns off their inertialess drives. The person in the coffin jolts around the room until the velocity is matched.

Larry Niven gets around the problem with a handwaving gizmo called a Gravity Drag. It uses zero reaction mass and very low amounts of power. The handwaving is that it somehow converts a ship’s momentum relative to the "nearest powerful mass" into heat. So all you need is a large heat radiator. If the intrinsic velocity difference is too great one might have to bleed off the momentum in stages. You bleed off all the momentum you can until you are too close to the destination planet. Then you use your hyperdrive to move further away from the planet, reenter normal space, and use the gravity drag to bleed off some more.

Poul Anderson turned the problem of no reactionless drives into a plot point. In The Bitter Bread there are starships with an FTL drive with the intrinsic velocity problem of Doc Smith's drive. One exploration starship is investigating a pair of massive stars in close orbit with each other. Oh noes! The FTL drive malfunctions while the ship is too close. Such star pairs can be used as a gravitational catapult. It grabs the starship and gives it near relativistic intrinsic velocity. More to the point, too much intrinsic velocity for the ship to get rid of with its on board reaction mass, by several orders of magnitude. So they are trapped. They fly back to Terra, but nobody can leave the ship (or their intrinsic velocity will sent them out of the solar system at a large percentage of lightspeed), and they cannot load more reaction mass to slow down (since intrinsic velocity can only be shed with the stardrive turned off, and the instant you do that the newly loaded reaction mass will shoot off at near lightspeed and destroy the ship).


(ed note: "Free" means with the inertialess drive turned on, and the intrinsic velocity is held in abeyance. "Inert" means you turn off the inertialess drive, you revert to normal conditions, and the intrinsic velocity suddenly reappears.)

Armored, he strode out into the landing field across the paved way. There awaiting him were two armored figures, the two top-bracket pilots. There were the doctor and the nurse. He barely saw—or, rather, he saw without noticing—a saucy white cap atop a riot of red-bronze-auburn curls, a symmetrical young body in its spotless white. He did not notice the face at all. What he saw was that there was a neutralizer strapped snugly into the curve of her back, that it was fitted properly, and that it was not yet functioning.

For this that faced them was no ordinary job. The speedster would land free. Worse, the admiral feared—and rightly—that Kinnison would also be free, but independently, with an intrinsic velocity different from that of his ship. They must enter the speedster, take her out into space, and inert her. Kinnison must be taken out of the speedster, inerted, his velocity matched to that of the flier, and brought back aboard.

Then and only then could doctor and nurse begin to work on him. Then they would have to land as fast as a landing could be made—the boy should have been in hospital long ago.

And during all these evolutions and until their return to ground the rescuers themselves would remain inertialess. Ordinarily such visitors left the ship, inerted themselves, and came back to it inert, under their own power. But now there was no time for that. They had to get Kinnison to the hospital, and besides, the doctor and the nurse—particularly the nurse—could not be expected to be space-suit navigators. They would all take it in the net, and that was another reason for haste. For while they were gone their intrinsic velocity would remain unchanged, while that of their present surroundings would be changing constantly (because the planet is rotating). The longer they were gone the greater would become the discrepancy. Hence the net.

The net—a leather-and-canvas sack, lined with sponge-rubber-padded coiled steel, anchored to ceiling and to walls and to floor through every shock-absorbing artifice of beryllium-copper springs and of rubber and nylon cable that the mind of man had been able to devise. It takes something to absorb and to dissipate the kinetic energy which may reside within a human body when its intrinsic velocity does not match the intrinsic velocity of its surroundings—that is, if that body is not to be mashed to a pulp. It takes something, also, to enable any human being to face without flinching the prospect of going into that net, especially in ignorance of exactly how much kinetic energy will have to be dissipated. Haynes cogitated, studying the erect, supple young back, then spoke.

“Maybe we’d better cancel the nurse, Lacy, or get her a suit…”

“Time is too important,” the girl herself put in, crisply. “Don’t worry about me, Port Admiral, I’ve been in the net before.”

The crash-wagon and its crew were waiting, and as Kinnison was rushed to the hospital the others hurried to the net room. Doctor Lacy first, of course, then the nurse, and, to Haynes’ approving surprise, she took it like a veteran. Hardly had the surgeon let himself out of the “cocoon” than she was in it, and hardly had the terrific surges and recoils of her own not inconsiderable one hundred and forty-five pounds of mass abated than she herself was out and sprinting across the sward toward the hospital.

From GALACTIC PATROL by E. E. "Doc" Smith (1937)

(ed note: the good guys are the League of Planets, an interstellar coalition very much like Star Trek's Federation. The Guardians are a thoroughly nasty group of ultranational bastards mostly composed of the the Ku Klux Klan, The New John Birchers, and the remnants of Afkrikaaners in Exile. A century ago the group that was to become the Guardians stole a starship and vanished into uncharted space.

The Guardians settled a planet, made it their capital of a future galactic empire, and build a war fleet to attack the League. The important point is the Guardians know the locations of all the League planets, but the League has no idea where the Guardian planet is.

Mac of the Legion is given the task of sending out scoutships to try and discover the location of the Guardian planet.)

      In the meantime, Mac wanted to get his frigates out toward their first targets. He spent days studying the star charts, playing with a dozen variables in his head, trying to figure which were the most likely stars to harbor Capital. Distance from Earth, distance to suspected hijack points, the limits of space technology at the time the Guards had left Earth—he even dug up the specs on their colony ship, the Oswald Mosley.

     And thinking about history brought up something he had almost dozed through in lecture, years before, a factor that hadn’t been considered before: With the C-squared drive, it wasn’t the distance between stars that mattered so much, but their velocity, relative to each other as they moved through space. A century before, with far less powerful and less efficient ship's engines, and with ships that tended to have much more mass than modern designs, that had mattered a great deal more than it did now. Crudely put, the Mosley couldn’t go very fast, and so couldn’t catch up with a star system that was moving more than about one hundred twenty kilometers a second, relative to Earth.

     Mac had never actually believed that those History of Astronautics classes would have the slightest practical application, but he was beginning to appreciate the benefits of a well-rounded liberal education. He did the velocity calculations, which led him to throw out four of the target systems altogether—the Mosley couldn’t possibly have matched velocity with them. However, it also pulled five new systems out of Randall and George’s “lower probability” list and into the prime running. Now he had thirty-two target systems.

     Finally, he had sifted the data and made as many hunches and badly-educated guesses as he could. It was time to send some ships out.

     Three hundred fifty hours after Pete had brought news of the Imp, the first frigates headed out across the sky.

From ROGUE POWERS by Roger MacBride Allen (1986)

(ed note: in this novel, starships which are occupying hyperspace can move faster than light. Or they can stay stationary. However, when they re-enter normal space, their intrinsic velocity reappears.

In this quote, the mothership is carrying a flotilla of "climbers", which are raider ships with cloaking devices. The mother has to transport the climbers to "fuel point", a top-secret rendezvous in deep space where the climbers will be refueled with antimatter. However, the enemy fleet is doing its darnedest to intercept the mothership and its escorts. Failing that, the enemy wants to follow the mother to fuel point and wreck havok)

      “Why are we holding hyper?” Seems to me a quick getaway is in order.
     “Waiting for the other firm. They have ships in hyper waiting to ambush us. We won’t take till they drop and show us their inherent velocities and vectors. Can’t just go charging off, you know. Got to give them the slip. If we don’t, they’ll dog us to Fuel Point and all hell will break loose.”
     I crane and look at the display tank. The mother is the focus there. Neither side looks inclined to start anything. Each is hoping the other will screw up.

     While the butterflies float, the mother keeps increasing her rate of acceleration. The relay talker says, “Coming up on time Lima Kilo Zero.” ("Lima" is NATO Phonetic Alphabet for "L", which is Roman Numeral 50. "Kilo" is SI prefix for 1,000, and slang for "kilometers" or "klicks")
     “What does that mean?”
     Yanevich is passing. “The point when we hit fifty klicks per second relative to TerVeen. When we throw a rock in the pond to see which way the frogs jump. We’re following a basal plan preprogrammed after an analysis of everything that’s been done before.” He pats my shoulder. “Things are going to start happening.”

     “Bogey Niner accelerating.”
     We’ve got nine of them now? My eyes may be open, but my brain has been sleeping.
     I watch the tank instead of trying to follow the ascensions, declinations, azimuths, and relative velocities and range rates the talker chirrups. The nearest enemy vessel, which has been tagging along slightly to relative nadir, has begun hauling ass, pushing four gravities, apparently intent on coming abreast of us at the same declination.
     “They do their analyses, too,” Yanevich says.
     His remark becomes clear when a new green blip materializes in the tank. A pair of little green arrows part from it and course toward the point where bogey Nine would’ve been had she not accelerated. The friendly blip winks out again. Little red arrows were racing toward it from the repositioned enemy.
     “That was a Climber from Training Group. Seems he was expected.”
     The two missile flights begin seeking targets. Briefly, they chase one another like puppies chasing their tails. Then their dull brains realize that that isn’t their mission. They fling apart, searching again. The greenies locate the bogey, surge toward her.
     She takes hyper, dances a hundred thousand klicks sunward, and ceases worrying about missiles. She begins crawling up on the mother’s opposite quarter.
     “A victory of sorts,” Yanevich observes. “Made them stand back for a minute.”
     By evading rather than risking engaging the Climber’s missiles, our pursuer has complicated her inherent velocity vector with respect to her quarry. We can take hyper now and shake her easily. Unfortunately, she has a lot of friends.
     The enemy missiles head our way. We’re the biggest moving target visible. The mother’s energy batteries splatter them.

     This is a complex game, played in all the accessible dimensions and levels of reality. The Training Climbers give the home team an edge. Each of their appearances scrapes another hunter off the mother’s trail, making her escorts more formidable against any attack.
     “We’re almost clear,” Yanevich says. “Won’t be long before we do a few false hyper takes to see what shakes.”
     The first of those comes up a half-hour later. It lasts only four seconds. The mother jumps a scant four light-seconds. Her pursuers try to stay with her, but time lags taking and dropping hyper distort their formation. While they’re trying to adjust, the mother skips twice more, in a random program generated beforehand and made available to our escort.
     They’re not dummies over there. They react quickly and well. They have one grand advantage over us. They have instantaneous interstellar communications gear, or instel. All their ships are equipped. We only have a handful scattered throughout the Fleet. Our normal communications are limited to the velocity of light.

     Yanevich says, “Now a test fly to see if they’ve been holding anything back. And they are. They always are.”
     This time there’s a half-hour interval between the take and drop hyper alarms. In the interim the opposition throws in a pair of singleships. They bust in out of deep space almost too fast for detection. For a few seconds a lot of firepower flashes around. No one gets hurt. The singleships bounce off the escort screen.

     “Now a lot of stutter steps and mixing so they lose track of which ship is which. We hope.” The mother’s maneuvers have gained her a margin in which she can commence grander maneuvers.
     Alarms jangle almost continuously while the flotilla mixes its trails. I await the final maneuver, which I assume will be a flower, with every ship screaming off in a different direction, getting gone before the other firm decides which to chase.
     I guess right. “What now?”
     “We have lead time now,” Yanevich assures me. “Next stop, Fuel Point.”

From PASSAGE AT ARMS by Glen Cook (1985)

      In the middle of that majestic chaos, two things which have been suns whirl crazily about each other. One, hardly bigger than Earth although more massive than Sol, has no light of its own, but flings back the fury of its huge companion’s death. There are no words to tell of this. And yet the image is a ghost, a mathematical construct. Men who looked straight upon the reality would die before they knew they had been blinded.
     Narrator: “Here crews have stood watch and watch for a score of years, ever since astronomers predicted that the blue giant would soon explode. Here was our chance to observe a supernova close at hand."
     The tone cools: “Now that the last of the trio has erupted, the system is indeed breaking apart. Losing immense quantities of mass, the supernova must spiral away from the neutron star, and vice versa, to conserve angular momentum. But friction, again, hinders this retreat. It had scarcely begun when (starship) Uriel arrived, to relieve Zophiel on the regular three-month rotation plan.
     “Certain persons question the sense of traveling a light-millennium, weeks at top quasi-speed, for so short a season of duty. But we have no choice. The radiation around a recent supernova is too intense. Even under superdrive, a ship gets some of it, and a percentage of that comes through the heaviest shielding. Nor can the crew make accurate studies, entirely while moving faster than light. Much of their work must be done in normal state, at true velocity. Of course, then they extend magnetohydrodynamic fields well beyond the hull, control a plasma cloud, and enjoy quite effective protection. But no protection is perfect. In view of propable cumulative dosage, the rule has been that three months is the maximum safe exposure time.

     “In Uriel’s case, the period was greatly lessened.”

     More drawings and narration explain: “…conservation of energy. A ship about to enter superdrive has a certain definite velocity—speed and direction—with respect to any other given object in the universe, including its destination. Crossing space with inertia nullified does not change that velocity, nor do gravitational wells affect it significantly … as a rule. In ordinary procedure, we try to match this so-called intrinsic to the intrinsic of the target, as closely as feasible, before staring the nonrelativistic part of our journey. Else we might have to spend too much fuel at the far end of the trip, where it can’t readily be replaced. Not even the tanks of a fusion engine can carry enough for more than about five thousand kilometers per second of delta-V—that is, total velocity changes, both speedups and slowdowns, added together in the course of a mission …” Old hat.

     The little fleet glides on superdrive to the initial goal. The three which will wait there, making different observations as they free-float in normal state, are sufficiently distant from the core—a quarter lightyear—that their hulls and low-intensity MHD fields guard personnel from harm. Fading fast as it expands, today the burst sun gives them hardly more heat and X-rays than they would get in the orbit of Venus; the blast of leptons has already gone past this region, the baryons and ions have not yet reached it, the thin light-haze around is mainly due to excited interstellar gas.
     Briefly back under superdrive, Uriel slips close, close to the inferno before reverting to normal state, visibility, vulnerability. From protector nozzles gushes a cloud of plasma, which a heightened field wraps around the hull like a faintly shimmering cocoon. This will ward off not only the hurricane of charged particles, but the lethal photons … most of them. Should the dose aboard approach a safe limit, the ship will flee, faster than light.

     These events must be shown in reconstruction. No outside lens, were any that close, could have spied a work of man against the nebular blaze. No message beam, were any receiver that close, could have pierced the wild electricity around. What we see is an impressionistic view, the craft large till it suddenly whirls off, dwindles to sight, vanishes amidst fire. Next, as if given the eyes of angels, we see the greater globe white-hot and still collapsing, the lesser burnt-out and compressed though now ashimmer, whipping in seconds through their orbit. And we see a dot which images Uriel. That dot plunges in.
     Narrator: “Without warning, power failed. Engineers Smith and Polleard could barely squeeze out the ergs to maintain radiation shielding. Nothing could be spared for either thrust or superdrive. The collapse of the MHD field for half an instant would mean death. There was nothing to do but work—find the cause of the trouble and make repairs—while Uriel, helpless, was hauled in like a comet by the gravity of two suns both heavier than Sol itself.
     “The orbit had been established beforehand, to swing safely wide of the hot companion, slightly nearer the cold. Nobody had expected to continue in the path for long—certainly not till it almost grazed the sun-clinker. But this is what happened.”

     A scarlet thread grows behind the dot, marking its track through space. At first, time on the screen is compressed. Uriel had a high intrinsic in the direction of the double, whose mass accelerated it ever more furiously. Nevertheless the ship took days, terrible days to reach apastron.
     Later, time is necessarily stretched. For close in, speed increases, increases, increases, dizzily beyond what the simple attraction of matter for matter can wreak. Uriel sweeps around the side of the neutron star opposite the late supernova, a moment in shadow which saves the men, since radiation is forcing itself past their screens in such amounts that every danger signal shrills. Acceleration climbs to better than half a million gees, five hundred kilometers per second per second. Thus the ship departs spaceward in the wink of a quantum, too swiftly for its re-exposure to the starblast to kill. The acceleration tumbles down again; but by then, Uriel is coursing on the heels of light.

     Narrator: “Bodies as massive as these two, spinning as fast, generate forces according to the laws of general relativity which act like a kind of negative gravity. That is what seized our unhappy men. They felt no drag, no pressure; they were in free fall throughout, and did not come within the effective tidal action zone. But their intrinsic mounted to more than fifty times what their thrust drive could possibly shed before fuel was exhausted. They were, they are trapped in the speed they have gained.

     Afterward they resume stations, start the superdrive; automatic optical compensators give them an illusion of being back in a familiar universe; they run toward rendezvous with their fellows.
     Narrator: “In the inertialess condition, a difference of intrinsic does not manifest itself. Taking due precautions, crews from the spared vessels boarded Uriel, offered consolation, taped messages to bring home.”

     Maybe you, archeologist, wonder why. In your ultra sophisticated astronautics what could be simpler than to lay alongside, both vessels in superdrive, and transfer cargo? Why, you may know how to kill such speed and let its victims rejoin the human race.
     But we—well, Uriel already had systems for recycling air and water. However, they were not completely adequate. Nobody had expected them to be in continuous use for half a century. They would degrade, poisonous organics would accumulate, unless we added refinements and ancillaries. And we couldn’t simply plug in the new stuff. We had to do considerable rebuilding. Likewise, the ship had carried six months’ worth of food. We would install closed-ecology units that would feed the men indefinitely, indeed yield a large surplus. But this too we couldn’t merely dump aboard. It must be integrated with everything else. For a single example of our needful planning, remember that health and sanity required we leave the crew reasonable elbow room.
     And while we labored, we must take elaborate precautions to assure no substantial number of atoms from Uriel got aboard our own ship. A few nanograms would destroy us, the moment we reverted to normal state and they took off at their light-like intrinsic velocity. There wouldn’t be an explosion unless the mass was really gross, up in the milligrams or whatever. But from end to end of our hull would go a fatal wave of radiation.

     Obviously, Uriel can never leave the inertialess state. It must always keep moving at a quasi-speed which outruns light—a modern incarnation of that eerie ancient legend, the Flying Dutchman. Even if we invented a means to slow it, it would first have to enter normal state—would it not?—and our gift of supplies and machinery would annihilate it in a brief burst that might rival a nova.
     Fortunately, fuel is no problem. The demands of life support are modest, those of keeping an inertialess body moving are less. Tanks topped off by us ought to serve for more years of exploration than those men have left in their bodies.

     You may not believe me, but fools have actually asked why Uriel didn’t backtrack, once its superdrive was operational again, and let the double star undo what was wrought. Evidently, for them the narration was futile when explaining that a velocity is a direction as well as a speed. And, to be sure, Asklund calculated that at the rate yon companions are moving apart, already then they could no longer accelerate an infalling object in anything near the fashion they handled him.
     Less crackpot was the suggestion that the ship find a safe, solitary and cold neutron star, go normal near its surface, and let gravity act as a brake, repeating this process until the intrinsic was down to a reasonable figure. This would work, but only corpses would be aboard at the end of it. The difficulty is that every such star known to us is surrounded by too much gas—whether left over from its death throes or drawn in later from the interstellar medium—through too vast a volume. Deceleration would necessarily be at a low rate, especially at first. During the time required, more hard synchrotron radiation would be generated by the passage of the vessel’s own shielding fields, and leak through, than life can tolerate.
     Another double of precisely the right characteristics, or any of several more exotic and hypothetical things, could reverse the effect, yes. While we have not publicized the fact, Uriel spent what months were possible on minimum rations, before reserves got hopelessly low, seeking just such a deliverance. The hunt was foredoomed, of course. Recall the sheer size of space, and guess at the probabilities.

     Further search is pointless. The equipment of survival, which we have given our comrades, has a differential intrinsic of almost three hundred thousand kilometers per second: to the best of our present-day knowledge and imagination, irrevocable.

From THE BITTER BREAD by Poul Anderson (1975)

Little Lost Starship

For reasons that are unclear to me, I've seen more than one science fiction universe where starships were detectable at a distance of many parseces as long as they were moving faster than light, but are practically invisible once they turn off their FTL drive. Or when the drive shuts off due to a malfunction or something.

This tends to appear in order to support one of two possible story plots:

  1. The protagonist's starship is being hotly pursued by an enemy starship with too many guns, so the protagonist turns off the stardrive hoping to become a microscopic needle hiding inside an astronomically sized haystack.

  2. The protagonist's starship is off on a jaunt somewhere, suffers a drive malfunction and becomes dead in the water, and the rescue ships have to try and find them before the oxygen runs out.

Locating Yourself

A vaguely related plot is where the starship is suffers some sort of faster-than-light accident, and it materializes in some unknown location in space. The ship is lost in space (dunt-Da-DUHHHHH!). The drive still works, but the astrogator has no idea where the ship is or where the destination is. The captain will be breathing down the astrogator's neck until they figure where the heck in the galaxy the ship is, so a course can be plotted to the destination.

The astrogator will use triangulation.

The astrogator will repair to the astrodome and pick three bright guide stars. Each guide star will have its spectrogram taken, and with any luck the guide star can be identfied by looking up its fingerprint in the star catalog. The catalog will give the guide star's location coordinates. By measuring the angular separation between the three guide stars with a sextant, the starship's location can be calculated by triangulation. The captain will relax as the astrogator plots a course to the original destination.

If the stars are not in the star catalog, it probably means the starship has materialized far outside known space. The stars in the vicinity have not been cataloged by the Galactic Survey. The astrogator will start to sweat, put away the star catalog, and pick up a catalog of nearby galaxies. Determining the identity of galaxies is a bit more difficult, since they do not have a clear-cut spectral fingerprint. Luckily they are large enough that details such as spiral arms can be seen, that will help with identification.

If the galaxies are not in the galaxy catalog, the crew is up doo-doo pulsar with no gravity generator. They are probably in some unknown galaxy a gazillion megaparsecs from home. The only thing that can be done is start a quick exploration of the nearby stars to find a habitable planet suitable for an emergency base. Assuming there are nearby stars, if they are in intergalactic space the closest galaxy will have to be determined.


      “Very good,” Braedon replied, his tone carefully neutral as he heaved a mental sigh of relief. The entire fleet was now accounted for. All twelve ships had successfully crossed the interstellar vastness between Earth and Sanctuary.

     Considerable genius had been poured into the problem of what to do if a starship were to suffer a breakdown en route. Even a relatively benign malfunction could lead to catastrophic consequences in the long, dark light-years between Earth and Sanctuary. The first line of defense lay in the design of the ships themselves. Engineers had provided the starships with triple and quintuple redundancy in critical subsystems. However, as an ancient philosopher named Murphy once pointed out: if anything can possibly go wrong, it will, and at the worst possible moment. Therefore, each ship had been provided with enough spare parts to practically rebuild the stardrive if necessary (excluding the main field coils which were an integral part of the ships themselves).

     In a bit of belt-and-suspenders logic, each ship carried within its hangar bay a single FTL cutter. Any ship that found itself marooned among the stars could dispatch the cutter to summon rescue. That, at least, was the theory.

     Unfortunately, summoning rescue might well prove to be impractical. A captain in interstellar space never knows precisely where he is. Even the most meticulous analysis based on course and speed is rarely accurate to within better than a few tenths-percent of the total distance traveled. Cumulative inaccuracies in astrogation could easily result in a ship being two light-years off course at the end of the flight from Earth.

     Nor would star sightings after breakout be of much assistance. Astronomy has always been a science that is extremely good at measuring the angular positions of stars in the sky, but not their distances. Without knowing the exact location of the stars in three dimensions, it would be impossible for a ship’s captain to pinpoint his own position with sufficient precision to allow a rescuer find him in the blackness of space.


The problem of locating something lost is a problem in two dimensions today—even a lost airplane. For a lost airplane is presumed to be down. And even in two dimensions, a search for something missing is a tremendous task, covering huge areas of the earth which must be combed in a definite pattern. Picture this search expanded to three dimensions in space. Picture all distances extended from miles to light years. Picture the smallest degree of error and how great it becomes when run out to a distance of several light years. And try to imagine the difficulties of a search for a tiny ship lost in space.

—The Editor

           "Your undivided attention, please! This is urgent! You have eleven minutes from the end of this announcement to follow these directions. There has been a partial failure of the warp-generator. If this failure becomes complete, and the space field collapses, the effect will be that of precipitating intrinsic mass into the real Universe while traveling at some high multiple of the velocity of light. The spacecraft then will drop instantly below the speed of light but in doing so will radiate all the energy-mass equivalent to those multi-light speeds, according to the Einstein equation of mass and energy. It is therefore expedient that you repair to the lifeship locks and prepare to debark. The partial failure may or may not continue. If not, there will be no more danger. But in case of continued breakdown—”
     The recorded announcement stopped abruptly as a louder alarm bell rang briefly. Then another voice from the squawk-box shouted:
     “The warp-generator is failing! You have—
     A third voice came in automatically saying, “Eleven minutes,” after which the second voice continued neatly, “to make your way to a lifeship and debark. Please do not panic. You have plenty of time.”

     UNDER the temporary command of Commodore Theodore Wilson the space squadron sped out into the uncharted wastes of the sky on the true line toward Castor. Slowly, as the squadron flew, its component spacecraft diverged in a narrow cone so that the volume of space to be covered would fall within the scope of the detection equipment aboard each ship. Computers flicked complex functions in variables of the laws of probability, and came up with a long series of “and-or-if” results.
     Toby Manning, Master Computer for the squadron, sympathized when Wilson showed the latest sheaf.
     Wilson grunted, “This is no damn good at all. It sort of says that the lifeships will be wherever we find them.”
     Manning nodded. “Like the problem of catching a lion on the Sahara Desert. You get a lion cage with an open door, electronically triggered to close at the press of a distant button. Then the laws, of probability state that at any instant there exists a mathematical probability the lion is in the region of the cage. At this instant you shut the door. The lion lies within the cage, trapped.”
     “Stop goofing off. This is no picnic. Have you any idea of how many square light years we have to comb?”
     “Cubic light, years. Commodore Wilson.”
     “Cubic. So I’m sloppy in my speech, too? Look, Manning, all we really want from you is the overall conic volume in which the lifeships must lie. You know the course of Flight Seventy-nine. You know the standard take-off velocity of a lifeship. The forward motion plus the sidewise, escape velocity, produces a vector angle which falls in the volume of a cone because we don’t know which escape angle they may have used. We can pinpoint the place of escape fairly close.”
     “Yeah, within a light year. Maybe two.”
     “And we know that the lifeship will reduce its velocity below light as soon as possible.”
     “So somewhere on that vector cone, or within it, is a lifeship—two lifeships—traveling on some unknown course at some velocity considerably lower than the speed of light.”
     “We’ve located ’em before. We’ll locate ’em again.”
     Wilson shook his head worriedly. “That’s a lot of vacant space out there. Even admitting that we have the place pinpointed, the pinpoint is a couple of light years in diameter, and will grow larger as time and the lifeship course continues. Or,” he added crisply, “shall we take a certain volume of space and assert that a definite mathematical probability exists that the survivors lie within that volume?”
     “Sorry, Commodore. I didn’t mean to be scornful.”
     “Well, then, you’d better set up your space grid in the coordinate tank and we’ll start combing it cube by cube.”
     “Correct,” said Toby Manning.
     The “tank” was not really a tank. It was a stereo projection against a flat glass wall at one end of the big Information Center. Room below the bridge section of the flagship. Wilson went there some time later to watch the bustle as the tank was set up to cover the segment of space they intended to comb.
     Even looking at the thing required some training. The plotters and watchers wore Polaroid glasses to provide the stereo effect. Through the special glasses, the tank looked like a small scale model of this section of the sky. Castor and Pollux and other nearby stars were no longer pinpoints on a flat black surface, but tiny points of light that seemed to hang in space, some in front of and some behind the position of the screen itself.
     Behind the glass screen, a technician was carefully laying a curve down on a drawing table with a pantagraph instrument. As he moved the pencil point along the curve, a thin green line appeared in stereo, starting close by and abruptly, and leading towards the dot labeled Castor.
     The loudspeaker said, “This green line is the computed course of Spaceflight Seventy-nine.”
     A RED KNOT was placed on the line.
     “This is the approximate point of explosion.”
     Wilson asked, “Is that nominal or is that placed on the minus side?”
     “The spot is placed to give the maximum factor of safety.”
     “Now, after considering the probable velocity of escape from Seventy-nine, which would be a lifeship leaving the mother vessel at a ninety-degree relative course at full lifeship speed, we find a vector combination of velocities and courses that diverge from the main course.”
     From the red knot another line went out at a small angle to the original course, thin and red.
     “But because we have no way of knowing what the axial attitude of Seventynine was at the moment of escape, the volume of probability now becomes a cone.”
     The angled red line revolved about a green course line describing a thin cone, its base pointed toward the star. Castor. As the line revolved about the axis of the cone, it left a faint residue behind it, which became a thin, transparent cone.
     Manning said, “Our field of operations lies within this cone.”
     Someone running the projector went to work. The scene expanded until the thin red cone filled the screen and seemed to project deep into the room, its apex almost at the eyes of the watchers. Then a polar pattern appeared across the cone near the apex, a circular grid marked off in thin white lines, each line numbered, each area or segment, marked with a letter.
     Down the room where the cone was larger, another grid appeared similarly marked.
     Manning went on, “We cannot tell, of course, at what point in the collapse the survivors made their escape. We know that the automatic circuits begin deceleration as soon as the warp-generator shows signs of failure, the hope being that the spacecraft will fall to a safe velocity before the field collapses completely. Therefore escape could be made at any velocity between forty parsecs per hour, if they escaped before the deceleration began, or at normal underlight velocity, which might take place if the spacecraft had succeeded in dropping to safety before the field collapsed. However, in that case, there would have been no explosion and our space wreck victims would have remained in the spacecraft, or returned to it as soon as they saw it was safe. Therefore, integrating the probabilities outlines here, the survivors must lie between the planes of maxima and minima, representing escape at maximum forward velocity and minimum forward velocity. Here, gentlemen, is your search grid.”
     The rest of the stereo field went out, leaving the white lines of the grids. Lateral lines now appeared to connect intersections of the fore grip with the corresponding intersection of the aft grid.
     “We are here.”
     Tiny discs of purple dotted space before the small end grid. The discs were flat-on to the grid and represented the maximum distance for space detection of matter.
     Wilson felt something touch him on the arm. He turned. A tech-operator standing there had a bewildered look on his face.
     “Yes?” said Wilson.
     “I'm puzzled. Commodore. Suppose we don’t find them in a long time. Won’t that far grid have to be pushed back?”
     “No,” Wilson explained wearily. “The function of a lifeship is to get its occupants down below the velocity of light and then coast. Since that grid represents a total distance of about ten light years, they’d have to be floating for ten years at the velocity of light to make it. Any normal speed, over a period of weeks, would hardly appear long enough to cover the thickness of one of the grid lines.”
     “Ten light years!”
     Wilson nodded and repeated. “This is no picnic.” He turned from the tech-operator to the planning table. “Unless someone has a better suggestion, we’ll set up a hexagonal flight pattern with a safe detector overlap and start by cutting a hole down through this grid volume along the prime axis. Anybody got any other suggestions?”
     Space Captain Frank Edwards shook his head. “Not unless someone has improved on the Manual of Flight Procedures,” he said.
     “Okay then. Here we go.”

     POISED in space, Wilson and his squadron waited. While they waited, the astro-techs made star sightings and the computer mulled over their readings and delivered opinions of several probable enclosures of position. These volumes were horribly vast compared with the mote of a spacecraft. They were spherical, indicating the margin of error in precision-pinpointing their position in deep space. And as the astrotechs delivered more and more angle sightings on the known stars, the computer delivered smaller and smaller enclosures as their true position.
     The problem was a matter of parallax, a matter of angular measurement against the more distant, or “fixed” stars. Now, it may seem an easy job to measure the angle of a star with respect to another star. But it must be remembered that the parallax of the nearer stars, as measured across the orbit of the earth, is a matter of seconds of arc.
     Parallax is not measured directly with a protractor. It is measured by comparing the position of the star on a plate against a similar photograph taken six months ago, using the fixed stars as the frame of reference.
     In deep space, position is pinpointed by solid triangulation. This can be represented by a pyramid suspended in space, the corners of which end at the fixed stars. Take a pyramid of certain solid angles, depended by points in space, and the apex can be satisfied for only one spacial position. Repeat these solidangle measurements and there are several pyramids pointing their apexes toward the true position.
     But if the orbit of the Earth produces only a second or so of parallax-arc, any error in angular measurement of such magnitude produces an error of a thousand light seconds. And the greater the error in measurement, the larger is the volume of uncertain position.
     This, then, was their problem. To cover, like a blanket, a volume of space so vast as completely to defy description. All that can be said of it is in comparison with a number of cubic light years. And who can grasp the fathomless distance of a light year? It is just a meaningless statement.
     Eventually the second squadron came up and the ships milled around until a larger space pattern was formed. Then the two squadrons began to return along the search grid, on a line overlapping that area covered in the first pass along the computed line of flight…

From SPACEMEN LOST by George O. Smith (1954)

(ed note: in the prior novel, our heroes are testing a new type of starship. Through an accident, the ship gets thrown into a different space-time continuum. There they meet human being on the planet Magyan around the star Anrel. These humans are descendants of space explorers from Terra who suffered the same type of accident, 30,000 years ago. Those humans originally came from the lost continent of Mu, but that's a long story. Anyway they give our heroes data they need to return to our space-time continuum.)

      "We ready?" asked Aarn Munro looking at Carlisle and then at Spencer. The engineer nodded, half eagerly, half regretfully. The three turned toward the great metal bulk of the Magyan Battleship Tharoon Yal. A tiny figure in a microscopic port in the mighty wall waved a farewell.
     "Here's hoping," exclaimed Aarn.
     "Here's hopping—from one space to another!" Spencer grinned a trifle shakily.

     The giant spaceship was suddenly expanding, growing tremendously—they must be rushing toward it. Instinctively their hands tightened on their grips, then relaxed, for the ship was suddenly impossibly huge. It seemed tenuous, ghostly-ghostly motionless figures became visible inside, then vanished in cloudy smoke and a darkening pall. Space was black; the wonderful gleaming suns that shone blazing in the strange space of Magya and her sun Anrel, the stars that had made that space a never-darkened curtain, were gone. Slowly, slowly, pinpoints of misty light began to materialize, stars, gigantic, cloudy things, growing then shrinking—and the change was complete.

     "We're here!" Carlisle whispered. Munro turned the Sunbeam slowly around, revealing every angle of space. Only occasional stars were visible now. They had changed spaces.
     "Where?" asked Aarn quizzically. "I don't see old Sol anywhere."
     "Is this the right space?" Spencer demanded.
     "Having eyes, you can see as much as I," suggested Aarn.
     "Not having your knowledge, I can't," replied Spencer. 'Engineering's mine. I built the apparatus you asked for, with the help of those Magyan engineers. It's your job to know where we are."

     Aarn grinned good-naturedly. The grin looked at home on his extremely broad face over his short thick body. "I'm worried too, so let's not get snappy. But I think this is the right space. Remember: Magya is in a four-dimensional space separated from our own space by a fifth-dimensional inter-space where we can't exist. We were first sent out of ours by the accident when we hit that asteroid, and our various forces started fighting the collision. That opened a path and kicked us out. Magya's space was the easiest to enter, and due to Magya's perfectly enormous sun and its gravitational attraction, we broke into their space at that point, as the Magyans had done before us.
     "Now in getting back we've got to lift ourselves out of Magya's space, and bore ourselves into another space. That's harder to do—takes a lot of power. Also—there's no way to choose one space or another to fall into, except by our mathematics based on those ancient Magyan Data Plates and the analysis of our own space as we knew it from data gained while on Earth. But unless there is another space with exactly the same characteristics as those of our own space, we had to go to our own. The chances that there are two identical spaces is pretty remote. I think we hit the right space—but not at the right point. Remember, those calculations we were working from were nearly 30,000 years old to the Magyans. How many Earth-years?" Aarn shrugged. "Who knows? But I believe we're home—in the right space. And an indeterminable distance from Earth. We were lost in spaces. Now we're lost in space. The inter-space is so vast it contains thousands of spaces—but just the same even one rather unimportant minor space like ours is several hundreds of millions of light years in diameter. I think we are still in the same galaxy."
     "Good Lord!" gasped Spencer. "We're as bad off as ever."

     "How do we determine where we are?" asked Carlisle simultaneously.
     "I've been thinking. Let's assume for the time that we're in the right galaxy. We're in some galaxy, because we can see so many stars. You'll notice there's a Milky Way effect only on one side. That means we're out toward the edge of the galaxy, since if we were deep in it the Milky Way would be a circle around us. We're probably somewhere near where the proper motion of Anrel during the last 30,000 years would take you from where the sun was thirty thousand years ago (I think he means peculiar motion). I think we're still in the same galaxy. The problem is to find out where. That won't be hard if we're in the right galaxy, because there are still space-marks that will bring us near enough home so we can see old Sol and steer for him by direct astrogation. Thanks to that interspace speed escape, we can travel faster than light, so that isn't impossible to us."
     "What are your space-marks?" asked Carlisle.
     "Something far enough away so that moving about in the galaxy doesn't change them unrecognizably. Something far enough away so that lines drawn from them won't change so greatly as to make us mistake one for another, and yet near enough so that they do vary with the galaxy."
     "The exterior galaxies," said Carlisle, comprehending.

     "Exactly. But we can't do it ourselves."
     "Huh? We can't? Then what good does it do us?"
     "We'll have to ask somebody in the neighborhood," grinned Spencer. "We'll drop in and ask them: 'Do you know the way to the great nebula in Orion? Or Andromeda?' And the local boys will of course be polite and tell us."
     "Something like that," replied Aarn more seriously. "We will have to find a race near here, or somewhere in this galaxy for that matter, and tell them what we need. If they have telescopes, and photography, they'll have pictures that we can compare with our plates here in the star catalogues and locate certain very outstanding nebulae. The Greater and Lesser Magellanic clouds may help—though they are really part of this super-galaxy of ours, and very close. But they are distinctive."

From THE INCREDIBLE PLANET by John W. Campbell, Jr. (1949)

(ed note: the protagonists are attacked by hyper-intelligent discarnate aliens composed of pure mentality. The protagonists escape in their auxiliary spacecraft Skylark Two by making a short trip through the fourth dimension. This results in the ship reappearing hundreds of megaparsecs away.

(ed note: the protagonists are attacked by hyper-intelligent discarnate aliens composed of pure mentality. The protagonists escape in their BTW: an "object-compass" is a technobabble gadget containing a needle of activated copper, set to always point at the object it is set on. It is some kind of tractor-beam gizmo, but that doesn't matter. The more massive the object it is set to, the farther away the needle can be from the object and still point to it. )

      Seaton promised. "But to get back to our knitting, what's the good word, Mart—located us yet? Are we, or are we not, heading for that justly famed 'distant galaxy' of the Fenachrone?"
     "We are not," Crane replied flatly, "nor are we heading for any other point in space covered by the charts of Ravindau's astronomers."
     "Huh? Great Cat!" Seaton joined the physicist at his visiplate, and made complete observations upon the brightest nebulae visible.
     He turned then to the charts, and his findings confirmed those of Crane. They were so far away from our own galaxy that the space in which they were was unknown, even to those masters of astronomy and of intergalactic navigation, the Fenachrone.
     "Well, we're not lost, anyway, thanks to your cautious old bean." Seaton grinned as he stepped over to an object compass mounted upon the plane table.
     This particular instrument was equipped with every refinement known to the science of four great solar systems. Its exceedingly delicate needle, swinging in an almost-perfect vacuum upon practically frictionless jeweled bearings, was focused upon the unimaginable mass of the entire First Galaxy, a mass so inconceivably great that mathematics had shown—and even Crane would have stated as a fact—that it would affect that needle from any point whatever, however distant in macrocosmic space.
     Seaton actuated the minute force which set the needle in motion, but it did not oscillate.
     For minute after minute it revolved slowly but freely, coming ultimately to rest without any indication of having been affected in the least by any external influence. He stared at the compass in stark, unbelieving amazement, then tested its current and its every other factor. The instrument was in perfect order and in perfect adjustment. Grimly, quietly, he repeated the oscillatory test—with the same utterly negative result.
     "Well, that is eminently, conclusively, definitely, and unqualifiedly that." He stared at Crane, unseeing, his mind racing. "The most sensitive needle we've got, and she won't even register!"
     "In other words, we are lost." Crane's voice was level and calm. "We are so far away from the First Galaxy that even that compass, supposedly reactive from any possible location in space, is useless."
     "But I don't get it, at all, Mart!" Seaton exclaimed, paying no attention to the grim meaning underlying his friend's utterance. "With the whole mass of the galaxy as its object of attachment that needle absolutely will register from a distance greater than any possible diameter of the superuniverse…" His voice died away.
     "Go on; you are beginning to see the light," Crane prompted.
     "Yeah—no wonder I couldn't plot a curve to trace those Fenachrone torpedoes—our fundamental assumptions were unsound, The fact simply is that if space is curved at all, the radius of curvature is vastly greater than any figure as yet proposed, even by the Fenachrone astronomers. We certainly weren't out of our own space a thousandth of a second — more likely only a couple of millionths—do you suppose that there really are folds in the fourth dimension?"
     "That idea has been advanced, but folds are not strictly necessary, nor are they easy to defend. It has always seemed to me that the hypothesis of linear departure is much more tenable. The planes need not be parallel, you know—in fact, it is almost a mathematical certainty that they are not parallel."
     "That's so, too; and that hypothesis would account for everything, of course. But how are …"
     "What are you two talking about?" demanded Dorothy. "We simply couldn't have come that far—why, the Skylark was stuck in the ground the whole time!"
     "As a physicist, Red-Top, you're a fine little beauty-contest winner." Seaton grinned. "You forget that with the velocity she had, the Lark wouldn't have been stopped within three months, either—yet she seemed to stop. How about that, Mart?"
     "I have been thinking about that. It is all a question of relative velocities, of course; but even at that, the angle of departure of the two spaces must have been extreme indeed to account for our present location in three-dimensional space."
     "Extreme is right; but there's no use yapping about it now, any more than about any other spilled milk. We'll just have to go places and do things; that's all."
     "Go where and do what?" asked Dorothy pointedly.
     "Lost—lost in space!" Margaret breathed.
     As the dread import of their predicament struck into her consciousness she had seized the arm rests of her chair in a spasmodic clutch; but she forced herself to relax and her deep brown eyes held no sign of panic.
     "But we have been lost in space before, Dottie, apparently as badly as we are now. Worse, really, because we did not have Martin and Dick with us then."
     "At-a-girl, Peg!" Seaton cheered. "We may be lost—guess we are, temporarily, at least—but we're not licked, not by seven thousand rows of apple trees!"
     "I fail to perceive any very solid basis for your optimism," Crane remarked quietly, "but you have an idea, of course. What is it?"
     "Pick out the galaxy nearest our line of flight and brake down for it." Seaton's nimble mind was leaping ahead. "The Lark's so full of uranium that her skin's bulging, so we've got power to burn. In that galaxy there are—there must he—suns with habitable, possibly inhabited, planets. We'll find one such planet and land on it. Then we'll do with our might what our hands find to do."
     "Such as?"
     "Along what lines?" queried Dorothy and Crane simultaneously.
     "Space ship, probably—Two's entirely too small to be of any account in intergalactic work," Seaton replied promptly. "Or maybe fourth-, fifth-, and sixth-order projectors: or maybe some kind of an ultra-ultra radio or projector. How do I know, from here? But there's thousands of things that maybe we can do—we'll wait until we get there to worry about which one to try first."
     Seaton strode over to the control board and applied maximum acceleration. "Might as well start traveling, Mart," he remarked to Crane, who for almost as hour had been devoting the highest telescopic power of number six visiplate to spectroscopic, interferometric, and spectrophotometric studies of half a dozen selected nebulae. "No matter which one you pick out we'll have to have quite a lot of positive acceleration yet before we reverse to negative."
     "As a preliminary measure, might it not be a good idea to gain some idea as to our present line of flight?" Crane asked dryly, bending a quizzical glance upon his friend. "You know a great deal more than I do about the hypothesis of linear departure of incompatible and incommensurable spaces, however, and so perhaps you already know our true course."
     "Ouch! Pals, they got me!" Seaton clapped a hand over his heart; then, seizing his own ear, he led himself up to the switchboard and shut off the space drive, except for the practically negligible superimposed thirty-two feet per second per second which gave to the Skylark's occupants a normal gravitational force.
     "Why, Dick, how perfectly silly!" Dorothy chuckled. "What's the matter? All you've got to do is…"
     "Silly, says you?" Seaton, still blushing, interrupted her. "Woman, you don't know the half of it! I'm just plain dumb, and Mart was tactfully calling my attention to the fact. Them's soft words that the slatlike string bean just spoke, but believe me, Red-Top, he packs a wicked wallop in that silken glove!"
     "Keep still a minute, Dick, and look at the bar!" Dorothy protested. "Everything's on zero, so we must be still going straight up, and all you have to do to get back somewhere near our own galaxy is to turn it around. Why didn't one of you brilliant thinkers—or have I overlooked a bet?"
     "Not exactly. You don't know about those famous linear departures, but I do. I haven't that excuse—I simply went off half cocked again. You see, it's like this: Even if those gyroscopes retained their orientation unchanged through the fourth-dimensional translation, which may or may not be the case, that line wouldn't mean a thing as far as getting back is concerned. We took one gosh-awful jump in going through hyperspace, you know, and we have no means at all of determining whether we jumped up, down, or side wise. Nope, he's right, as usual—we can't do anything intelligently until he finds out, from the shifting of spectral lines and so on, in what direction we actually are traveling. How're you coming with it, Mart?"
     "For really precise work we shall require photographs, but I have made six preliminary observations, as nearly on rectangular coordinates as possible, from which you can calculate a first-approximation course which will serve until we can obtain more precise data. Here are my rough notes upon the spectra."
     "All right, while you're taking your pictures I'll run them off on the calculator. From the looks of those shifts I'd say I could hit our course within five degrees, which is close enough for a few days, at least." Seaton soon finished his calculations. He then read off from the great graduated hour- and declination-circles of the gyroscope cage the course upon which the power bar was then set, and turned with a grin to Crane, who had just opened the shutter for his first time exposure.
     "We were off plenty, Mart," he admitted. "About ninety degrees minus declination and something like plus seven hours' right ascension, so we'll have to forget all our old data and start out from scratch. That won't hurt us much, though, since we haven't any idea where we are, anyway. We're heading about ten degrees or so to the right of that nebula over there, which is certainly a mighty long ways off from where I thought we were going. I'll put on full positive and point ten degrees to the left of it. Probably you'd better read it now, and by taking a set of observations, say a hundred hours apart, we can figure when we'll have to reverse acceleration. While you're doing that I thought I'd start seeing what I could do about a fourth-order projector. It'll take a long time to build, and we'll need one bad when we get inside that galaxy. What do you think?"
     "I think that both of those ideas are sound," Crane assented, and each man bent to his task.
     Crane took his photographs and studied each of the six key nebulae with every resource of his ultra-refined instruments. Having determined the Skylark's course and speed, and knowing her acceleration, he was able at last to set upon the power bar an automatically varying control of such a nature that her resultant velocity was directly toward the lenticular nebula nearest her line of flight. That done, he continued his observations at regular intervals—constantly making smaller his limit of observational error, constantly so altering the power and course of the vessel that the selected galaxy would be reached in the shortest possible space of time consistent with a permissible final velocity.

(ed note: After many adventures, our hero Richard Seaton constructs a fourth-order projector, which is used to make a fifth-order projector, which is used to make a huge sixth-order projector. With the latter, he will located the Milky Way galaxy and Terra by the simple expedient of mapping the entire freaking universe.)

     At Seaton's signal the structure which was to be the nucleus of the new space traveler lifted effortlessly into the air its millions of tons of dead weight and soared, as lightly as little Two had done, out into the airless void. Taking up a position a few hundred miles away from the Terrestrial cruiser, it shot out a spherical screen of force to clear the ether of chance bits of debris. Then inside that screen there came into being a structure of gleaming inoson, so vast in size that to the startled onlookers it appeared almost of planetary dimensions.
     "Good heavens—it's stupendous!" Dorothy exclaimed. "What did you boys make it so big for just to show us you could, or what?"
     "Hardly! She's just as small as she can be and still do the work. You see, to find our own galaxy we will have to project a beam to a distance greater than any heretofore assigned diameter of the universe, and to control it really accurately its working base and the diameter of its hour and declination-circles would each have to be something like four light-years long. Since a ship of that size is of course impracticable, Mart and I did some figuring and decided that with circles one thousand kilometers in diameter we could chart galaxies accurately enough to find the one we're looking for—if you think of it, you'll realize that there are a lot of hundredth-millimeter marks around the circumference of circles of that size—and that they would probably be big enough to hold a broadcasting projection somewhere near a volume of space as large as that occupied by the Green System. Therefore, we built the Skylark of Valeron just large enough to contain those thousand-kilometer circles."
     As Skylark Two approached the looming planetoid the doors of vast airlocks opened. Fifty of those massive gates swung aside before her and closed behind her before she swam free in the cool, sweet air and bright artificial sunlight of the interior. She then floated along above an immense, grassy park toward two well-remembered and beloved buildings.
     "Well, let's call the Cranes and go into the control room," Seaton suggested. "The quicker we get started the quicker we'll get done." Accustomed as she was to the banks and tiers of keyboards, switches, dials, meters, and other operating paraphernalia of the control rooms of the previous Skylarks, Dorothy was taken aback when she passed through the thick, heavily insulated door into that of the Skylark of Valeron. For there were four gray walls, a gray ceiling, and a thick gray rug. There were low, broad double chairs and headsets. There was nothing else.
     "This is your seat, Dottie, here beside me, and this is your headset—it's just a visiset, so you can see what is going on, not a controller," he hastened to reassure her. "You have a better illusion of seeing if your eyes are open, that's why everything is neutral in color. But better still for you girls, we'll turn off the lights."
     The illumination, which had seemed to pervade the entire room instead of emanating from any definite sources, faded out; but in spite of the fact that the room was in absolute darkness Dorothy saw with a clarity and a depth of vision impossible to any Earthly eyes. She saw at one and the same time, with infinite precision of detail, the houses and their contents; the whole immense sphere of the planetoid, inside and out; Valeron and her sister planets circling their sun; and the stupendous full sphere of the vaulted heavens.
     She knew that her husband was motionless at her side, yet she saw him materialize in the control room of Skylark Two (what materialized is not Seaton, rather it is a remote pattern of force fields that looks like Seaton, and which can manipulate objects.). There he seized the cabinet which contained the space chart of the Fenachrone—that library of films portraying all the galaxies visible to the wonderfully powerful telescopes and projectors of that horrible but highly scientific race. That cabinet became instantly a manifold scanner, all its reels flashing through as one.
     Simultaneously there appeared in the air above the machine a three-dimensional model of all the galaxies there listed. A model upon such a scale that the First Galaxy was but a tiny lenticular pellet, although it was still disproportionately large; upon such a scale that the whole vast sphere of space covered by the hundreds of Fenachrone scrolls was compressed into a volume but little larger than a basketball. And yet each tiny galactic pellet bore its own peculiarly individual identifying marks.
     Then Dorothy felt as though she herself had been hurled out into the unthinkable reaches of space. In a fleeting instant of time she passed through thousands of star clusters, and not only knew the declination, right ascension, and distance of each galaxy, but saw it duplicated in miniature in its exact place in an immense, three-dimensional model in the hollow interior of the space-flyer in which she actually was.
     The mapping went on. To human brains and hands the task would have been one of countless years. Now, however, it was to prove only a matter of hours, for this was no human brain (the sixth-order projector is also a computer). Not only was it reactive and effective at distances to be expressed intelligibly in light-years or parsecs; because of the immeasurable sixth-order velocity of its carrier wave it was equally effective across reaches of space so incomprehensibly vast that the rays of visible light emitted at the birth of a sun so far away would reach the point of observation only after that sun had lived through its entire cycle of life and had disappeared.
     "Well, that's about enough of that for you, for a while," Seaton remarked in a matter-of-fact voice. "A little of that stuff goes a long ways at first-you have to get used to it."
     "I'll say you do! Why… I… it…" Dorothy paused, even her ready tongue at a loss for words.
     "You can't describe it in words…don't try," Seaton advised. "Let's go outdoors and watch the model grow."
     To the awe, if not to the amazement of the observers, the model had already begun to assume a lenticular pattern. Galaxies, then, really were arranged in general as were the stars composing them; there really were universes, and they really were lenticular…the vague speculations of the hardiest and most exploratory cosmic thinkers were being confirmed.
     For hour after hour the model continued to grow and Seaton's face began to take on a look of grave concern. At last, however, when the chart was three fourths done or more, a deep-toned bell clanged out the signal for which he had been waiting…the news that there was now being plotted a configuration of galaxies identical with that portrayed by the space chart of the Fenachrone.
     "Gosh!" Seaton sighed hugely. "I was beginning to be afraid that we had escaped clear out of our own universe, and that would have been bad…very, very bad, believe me! The rest of the mapping can wait…let's go!"

From SKYLARK OF VALERON by E. E. "Doc" Smith (1934)

Speed of Light Squared

There were a few early science fiction stories written where the authors went with something scientifically sounding instead of something well thought out. Perhaps taking a cue from Einstein's famous E = mc2 equation, the authors wrote in their stories that the starships could move at a velocity of "the speed of light — squared".

They said that if light moves at 186,282 miles per second, then a starship with a cee-squared-drive could move at 34,700,983,524 miles per second. Which is 186,282 times faster than light, obviously due to the definition of "squared."

This is utterly meaningless. The universe does not use imperial measurements. If you used the metric system's meters-per-second, then the starship would move 299,792,458 times faster than light. If you used relativistic measurements where the speed of c equals 1, then the starship would move 1 times faster than light (i.e., at exactly the same velocity). The starships speed alters according to which measurement system you use, which is ridiculous.

In the spirit of one-upmanship, in Thomas N. Scortia's short story Sea Change featured a c-cubed drive.

So, scifi authors, do not use this in your novels unless you are writing a satire. Otherwise your readers will snicker and point fingers at you.


(ed note: our heroes at the Venus Equilateral communication relay station are experimenting with something called "sub-etheric radiation". The concept was invented by E. E. "Doc" Smith in his Skylark series, but I digress. The Venus Equilateral engineers manage to use beams of sub-etherics to grab power from the surface of the Sun and transmit it back. Then they try to figure out the speed that it travels at...)

      Walt Franks, entered Channing's office with a wild-eyed look on his face. "Don! C2!"
     "Huh! What are you driving about?"
     "C2. The speed of light, squared!"
     "Fast—but what is it?"
     "The solar beam! It propagates at C2!"
     "Oh, now look. Nothing can travel that fast!"
     "Maybe this isn't something!"
     "It has energy, energy has mass, mass cannot travel faster than the limiting speed of light."
     "O.K. It can't do it. But unless my measurements are all haywire, the beam gets to Sol and back at C2. I can prove it."
     "Yeah? How? You couldn't possibly measure an interval so small as two times sixty-seven million miles—the radius of Venus' orbit—traversed at the speed of light, squared."
     "No. I admit that. But, Don, I got power out of Sirius!"
     "You WHAT?" yelled Channing.
     "Got power out of Sirius. And unless I've forgotten how to use a microclock, it figured out from here to Sirius and back with the bacon in just about ninety-three percent of the speed of light, squared. Seven percent is well within the experimental error, I think, since we think of Sirius as being eight and one-half light-years away. That's probably not too accurate as a matter of fact, but it's the figure I used. But here we are. Power from Sirius at C2. Thirty-five billion miles per second! (actually 34,700,983,524 miles/sec, but who's counting? So it takes about 0.008 seconds to travel to Sirius) This stuff doesn't care how many laws it breaks!"

From BEAM PIRATE by George O. Smith (1944)

     "Well, I've been a good boy for them once. After all, I did point out the error in their patent on the solar beam."
     "That isn't all. Don't forget that Terran Electric's patent was at error, too."
     "Frankly, it was a minor error. It's one of those things that is easy to get caught on. You know how it came about?"
     "Nope. I accepted it just like everybody else. It took some outsider to laugh at me and tell me why."
     Kingman smiled. "It's easy to get into easy thinking. They took power from Sirius—believe it or not—and then made some there-and-back time measurements and came up with a figure that was about the square of one hundred eighty-six thousand miles per second. But you know that you can't square a velocity and come up with anything that looks sensible. The square of a velocity must be some concept like an expanding area."
     "Or would it be two spots diverging along the sides of a right angle?" queried Herman idly. "What was their final answer?"
     "The velocity of light is a concept. It is based on the flexibility of space—its physical constants, so to speak. Channing claims that the sub-etheric radiation bands of what we have learned to call the driver radiation propagate along some other medium than space itself. I think they were trying to establish some mathematical relation—which might be all right, but you can't establish that kind of relation and hope to hold it. The square of C in meters comes out differently than the square of C in miles, inches, or a little-used standard, the light-second—in which the velocity of light is unity, or One. Follow? Anyway, they made modulation equipment of some sort and measured the velocity and came up with a finite figure which is slightly less than the square of one hundred eighty-six thousand miles per second. Their original idea was wrong. It was just coincidence that the two figures came out that way. Anyway," Kingman smiled, "I pointed it out to them and they quickly changed their patent letters. So, you see, I've been of some help."

From SPECIAL DELIVERY by George O. Smith (1945)


      Faster-than-light drive moves a ship at the square of the speed of light. It's usually referred to as C2, pronounced "cee-squared." C2 gets you from the solar system to Proxima Centuri in about 105 seconds (ed note: I figure about 1,274,657 c. If I've done my calculation properly , that's using a measuring unit of 266 kilometers to measure the speed of light. Go figure.). That is, it would if anyone had any reason to go to Proxima Centuri. Of course, one has to use the C2 drive well outside the gravity well of a solar system, or end up far, far, far away from the intended destination.

     There are other catches, as well. The jump between "normal" space and C2 takes a big jolt of power. If, God forbid, anything went wrong with your power supply and you got stuck in C2, well, the edge of the universe is over that way, and no one knows exactly what happens once you get there. Certainly, ships have been lost that way. Less catastrophic, but still very dangerous, is inaccurate astrogation. An error of 0.09 seconds in coming out of C2 would put you roughly as far from your target as Saturn is from the Sun. Navigation computers are good enough these days that pilots can feel safe with about a half-billion-kilometer miss-factor. The J.M. would shoot for about three times that, as we were headed into territory not as well charted as that on the regular space lines. Also, if we came out over the pole of the target star, as we hoped to do, we would have the best vantage point for us to look for planets.

     Most star systems (including Earth's) have the plane of rotation of their planets in the same plane as the equator of the star in question. So, if you looked at, say, the Solar System from the plane of the Sun's equator, the planets, asteroids, and what have you would be moving in orbits that would be seen edge-on from where you stood. If you watched the Earth for a year-that is, one orbit-it would simply appear to move in a straight line from one side of the sun to the other, and then back again, moving once in front of the Sun's disk, and once behind it. From a point far enough away to observe the entire orbit, the change in size of the Earth's disk as it moves toward and away from you, inscribing a circle seen edge-on, would be difficult to measure accurately. Seen from the north or south polar regions, however, the orbits of the planets would be laid out before the observer face-on and so would be easy to observe. This in turn makes it easy to measure motions of planets and other bodies and put together reasonably accurate charts and ephemera of their orbits.

     What all this boils down to is that it is best to come in over a star system and look down on it, rather than come in at the side and see it edge-on. Fine. It has been found that planets usually rotate in the plane of a star's equator. So how do we determine where the equator is? One star seen from another is a featureless dot of light.

     The standard technique is to use the Doppler effect. Light of a given frequency has a higher apparent frequency when it is moving toward you, and a lower apparent frequency when it is moving away from you. The light doesn't change, the way you perceive it does. Obviously, one side of a rotating object will be moving toward you and the other side will be moving away. The difference is measurable over stellar distances. Very careful measurements can usually yield the plane of rotation, and thus the equator and poles, within about ten degrees or so.

     Ten degrees is a lot. Stack on top of that the fact that the actual distance to a target star is rarely known to any degree of accuracy, and you'll see that there is a certain degree of luck in Survey work. Get bad data, use it to put your ship in the wrong plane, and you'll have to waste fuel getting the ship to where it was supposed to be. Waste too much fuel and you come back early, or not at all. It is possible to "mine" hydrogen fuel from an ice moon, but finding suitable ice is rare, and the process is a long and tedious one. You come out of C2 with precisely the heading and velocity you start out with. The stars orbit the center of the galaxy, just as planets move about a star. Thus, they move relative to each other. A typical velocity difference would be on the order of about 70 kilometers a second. A ship travelling from one star to the other would have to match that velocity shift.

     Joslyn and I lived to wander the sky and do as we pleased. It was the happiest time of our life together.
     And then they found us.
     We were in the vicinity of our sixth target when they did. We had been there for about ten days. We were just about finished with the location-and-orbit survey search for major planets, and were ready to start down from our perch far above the star's north pole to take a close-up look at some of the better real estate we had spotted.
     We were in bed, asleep, when the alarm sounded. It was the general-alert buzzer, which meant the emergency was rare enough that it didn't rate its own alarm code.

     Joslyn and I scrambled out of bed, bounced off a few bulkheads, and made our way to the command deck. I fumbled a hand to a switch and killed the alert buzzer.
     Joslyn, who usually wakes up faster than I do, got the computer to decode the alert before I was even in my flight chair. "It's a courier drone!" she said.
     "You heard me."
     "Yeah, but it doesn't make any sense." Courier drones were expensive, and the odds of one finding us all the way out here were remote, at best.
     "Tell the drone that. Get on your board and pull a printout of the drone ops manual, will you?" Joslyn was studying her screen, trying to squeeze more information out of the words on it.

     I typed in a few commands and a book-length manual buzzed its way into the line printer's hopper. I instructed the computer to convert the courier's beacon signal into something we could use.
     "So when is it going to transmit its message to us?" Joslyn asked. I looked at my screen and whistled. "Never. Don't ask me why, but there's a security block on all the information aboard except the beacon."
     "Can we get it to home in on us?" Joslyn was thinking like a pilot—if the drone did the maneuvering, that would save on our fuel.
     "The decode of the beacon signal shows tanks nearly dry."
     "Oh, wacko. It can't get to us?"
     "Not unless you want our grandkids to pick it up. That 'nearly' dry is close to being 'completely'."
     "They shouldn't be, with a direct boost from base."
     "I'll bet you who fixes dinner it isn't a direct boost. I think it tried our last survey system first, then headed here."
     "Mac! Do you have any idea how difficult it would be to program a drone to do that? The search gear it would need? The instruments? The power? It would have to be huge."
     "I know, I know, I know. That's why this is a manned ship we're flying. But we left the last system a week ahead of schedule. We're still supposed to be there. And the heading that thing's on is almost exactly the heading we used to come from there—and about 120 degrees away from where it would be on a direct boost from Columbia."

     "Bloody. You're right. The velocity is all wrong for Columbia, too." I stared at the screen full of numbers. "Get some rendezvous data. Give us a set of three trajectories—reasonable economy, mid-range, and minimum time. I'll make coffee."
     "We'll need it," Joslyn said, and started plotting courses. Fifteen minutes later she had some rough figures to show me. "One percent of our fuel gets us there in a month. Five percent gets us there in five and a half days." She paused.
     "And what's the minimum trajectory?"
     She bit her lip. "Thirty-six hours. Fifteen percent of our remaining fuel."
     "Is that assuming we fly the Joslyn Marie?"
     "Oh, goodness no! All of these are assuming we fly Stars (an auxiliary spacecraft they carry). She seems to fly a trifle more efficiently than Stripes."
     "Fifteen percent … damn. Okay, feed the minimum time course to Stars' computer. I'll start a systems check on her." I started for the airlock level.
     "Mac!" Joslyn called. "We—we can't lose that much fuel! We do that and we might as well pack up the rest of the mission!"
     I sighed. "Joz—I know you're the pilot. You're in charge of flying the ship without wasting fuel and keeping our options open. Driscoll put me in command, so I have to be in charge of choosing which options we take. Now, whyever base sent that drone after us, they judged it more important than our mission, or else they wouldn't have sent it."
     "But what could they have to say that would be important enough to send a drone after the ship?"
     "I don't know. But if it's so important that it was worth tracking us across two star systems, it's certainly urgent. The party's over, Joz. The real world just caught up." I went below to start on powering up the lander. What could be important enough? I simply couldn't think of a single possibility. I did a rough guess in my head on what the drone would cost, juggling the figures as I worked. The answer was impressive. For a robot ship smart enough to scan one system, search it, and then reject it, plus the computers to hack a course to another system, plus the engines, the fusion plant, the C2 plant, the communications gear-probably more than the Joslyn Marie, since it would be a custom job, not mass-produced like the J.M. Getting the J.M. for this job was a miracle. What was big enough to spend that kind of money?

     Three hours later we cast off from the Joslyn Marie, leaving her powered down to wait for our return. Stars was a trim little ship, and Joslyn even let me do the flying, for once. I lined us up with the gyros to save fuel on the attitude jets, just to keep on Joslyn's good side.
     The course was a hair-raising one. We had to blip into C2 for a few milliseconds, pop out and change our heading, then into C2 again. All this to avoid falling into the local sun, which was dangerously close to what would be a direct course to the drone. Then a long cruise while we gunned out fusion engine in earnest and lined up for the final jump to the drone's position and velocity.
     It was a dull 36 hours, besides the few minutes required now and again to monitor the ship and guide the computer through the course. It was not made any more pleasant by the fact that Joslyn was mad at me. While she understood the need to get to the drone fast, she didn't have to like it, and she couldn't yell at the base personnel who had sent it out after us. Well, she didn't exactly yell at me, either, but the effect was the same: what she did was barely speak to me at all. I was left without much to do besides trying to figure out what the drone was. And I still didn't get anywhere with that.

     By the time we were within visual range of the drone, I was more than glad of the change of pace—to say nothing of going out of my mind with curiosity. Stars didn't have all the fancy optical gadgets we had on board the J.M., but she carried a pretty fair long-range camera. As soon as there was the slightest hope of picking up the drone with it, I brought it to bear. And got one of the great shocks of my life. Drones are usually about the size of a torpedo—maybe five meters long, and most of that fuel tanks. This thing was the size of the Joslyn Marie. Most of it fuel tanks. The only cargo seemed to be in a blister on the apex of the drone. Huge arrows, painted on the hull, pointed to it.
     "It must have five times the fuel capacity of the J.M.," Joslyn said, her voice betraying as much shock as I felt. Surprise had evaporated all her annoyance with me.
     "If they burned all that fuel getting here, they must have tracked us through three star systems...."
     "If not more. And at high acceleration, too. See all the structural bracing?"
     "Yes. The aft end is pointed along the direction of flight, too. It must have burned its last fuel slowing to a velocity we could match. One thing on the bright side—if the drone has scavenger pumps, we could take the last of its fuel for Stars' tanks."
     "Even if that monster's tanks are down to one percent, that'd be enough to top us off. Here's hoping, Mac, what could it be?"
     "We'll know soon."

     We approached the giant ship slowly. As we closed to within a hundred meters or so, Joslyn pointed to one side of the screen. "There! A fuel hose waiting for us. They did think to set up a scavenger."
     "Good. Maybe we'll have some fuel when this is over. Whatever it is." I switched on our fueling system and forgot about it. It was an automatic that was supposed to call to a fuel system at a commercial port and request fueling. The port's robots were supposed to come and tend to the ship without bothering the crew. The home office had been kind enough to arrange that kind of service out here.

     We came in over the docking port and swung our topside around to meet it, so that the two ships came together nose to nose. I made the docking run on the first pass and activated the capture latches to hold us solidly to the other ship.
     We got out of our crash couches and climbed over each other getting to the nose airlock door, both of us burning with curiosity. I cracked open a bleeder valve to match our ship's air pressure with the drone's cabin pressure. There was a brief wooshing of air, and I swallowed to make my eardrums pop. At a nod from me, Joslyn undogged Stars' hatch, and then opened the drone's hatchway, a meter or so beyond it.
     The drone's hatch swung open, revealing the interior. Since the ships were docked nose to nose, we were looking straight down from the top of the drone's cabin. The only thing in it was a great black cylinder, exactly the size to fit through the airlock passage. It was pointed right for the hatchway joining the ships; all it needed was a good push from below to send it through the lock into Stars.
     We kicked off from the hatchway and drifted into the drone's cabin, staring at the cylinder. It was big, and its base was heavily braced against acceleration.

     Joslyn hung in midair, fascinated. "My God, it's like a totem pole ready for—" But a giant, booming voice suddenly shouted out from a speaker by the overhead hatch. "THIS IS A WAR EMERGENCY SITUATION," it roared. "TRANSFER THE CYLINDER TO YOUR SHIP WITH ALL POSSIBLE SPEED. DO NOT DELAY FOR ANY REASON. THE MOMENT AUTOMATIC REFUELING IS COMPLETED, CAST OFF AND RETURN TO THE JOSLYN MARIE AT MAXIMUM SPEED. DELAY FOR NOTHING. YOU MAY EXAMINE THE CYLINDER EN ROUTE. HURRY. HURRY. THIS IS A WAR EMERGENCY SITUATION. THAT IS ALL." I clapped my hands over my ears and heard the great voice that way. The moment it was over, Joslyn and I looked at each other in something close to shock, and instantly got to work on the cylinder. That wasn't the sort of voice you argued with.

     There was a very simple, straightforward quick-release device holding the cylinder to its bracing, and a diagram painted on it in bright red paint, showing how to use it. I pulled at one lever, Joslyn at the other, and the cylinder popped off its moorings with a deep sprung. A spring-loaded pusher had been cocked underneath it, and gave it a gentle shove toward the overhead hatch, moving it at about half a meter a second. I kicked over to one side of the cabin, scrambled up a set of handholds, and beat the cylinder through the hatch by only a few seconds. I cleared the hatchway and got to one side. As the cylinder came through Stars' hatch, the forward end of the great black shape sprouted a set of legs, a tripod, that swung into place and locked, forming a solid support for the thing. The legs touched Stars' inner hull and I heard a thunk, thunk, thunk—electromagnets coming on to further brace our new cargo.
     Joslyn came into Stars' forward cabin right behind the cylinder, squeezing past it as she sealed the hatches. The cylinder was a good eight meters long: it took up the entire height of the cabin, with just room to get around it to go out the nose hatch. Someone had done very careful planning—apparently down to figuring out which ship type we'd use.
     Just as Joslyn dogged the inside hatch, a speaker hooked into the cylinder came on, cued by radio from the drone. It wasn't quite as loud, but that voice still had authority. "REFUELING IS COMPLETED. CAST OFF. GET UNDER WAY. GET UNDER WAY. THAT IS ALL."
     But Joslyn was already at the command seat, working the joystick. She snapped Stars through a tight head-over-tail loop and gunned the engine, bathing the drone's cabin in fusion flame, vaporizing part of it. The robot ship was a derelict now, and she wasn't going to waste time being careful of it. I held on as best I could through the loop, and made it to my own couch as she started the main engine and we set out home. I looked at the base of the cylinder that sat in the centerline of our lander.

     What had we gotten ourselves into? War emergency situation?

From THE TORCH OF HONOR by Roger MacBride Allen (1985)

Receiver Required Matter Transmitter

Matter transmitters (transmats) or stargates come under the Landis classification of [1.0] Discontinuous Drives ("teleport-like"). Basically the starship vanishes at point A and suddenly appears at point B, without traveling through the points in between.

The transmat type with the fewest nasty unintended consequences is the kind that requires both a transmitter and a receiver. And there are quite a few science fiction stories that impose the same restriction on their starships in order to make interesting implications.

The fundamental idea is that FTL starships can travel between transmat pairs instantaneously (or at least vastly faster than light would take). BUT before starships can travel to a new star, some poor SLOWER-than-light starship has to take several decades slogging through the light years in order to transport a transmat to the new destination. Once it arrives, it activates the transmat and suddenly the new star is part of the stargate network.

There are a few interesting implications:

  • The rate of expansion of an interstellar empire is limited to less than the speed of light, quite a bit less if the slower-than-light ships are underpowered.

  • If a star system only has one transmat and that is rendered inoperable, the system is cut off from the stargate network. At least until a new one can be manufactured (in some science fiction they cannot) or until an STL ship takes several decades to ship a new one.

  • If both transmitting and receiving transmats have to cooperate, then it is very difficult to invade another star system. In Stargate SG-1, the Earth stargate is equipped with a metal iris to prevent the emergence of alien invaders.

  • Some transmats have a aperture size. Meaning a starship with a cross-section larger than the aperture cannot travel through the stargate, at least without slicing off parts of the hull. This is used in John Lumpkin's Human Reach novels.

  • A star system that wanted to break away from their interstellar empire would gain independence by destroying all the transmats connected to the empire. They now have time to build defences, up to the point when an imperial STL ship arrives with a replacement transmat.

  • It is very difficult to invade another star system by STL ship lugging a transmat. The defender wil have decades to detect the incoming STL ship and attack it. The invader's task is even more difficult since STL ships are always severely mass limited; i.e., it cannot afford fancy extra like weapons or armor. It takes unreasonable amounts of energy to delta V the STL ship's mass up to relativistic velocities. This is used in the game Web and Starship.

  • There has been a science fiction story or two where the expanding Terran civilization sends a starship through a transmat and the ship accidentally arrives at an alien built transmat of which the Terrans were unaware. This is used in Poul Anderson's The Enemy Stars.

  • If rival starfleets are doing battle in a star system, they generally are scrupulously careful not to damage the transmat. Since doing so can cut off the star system from the transmat network for times ranging from several decades to forever, deliberate destruction is considered to be the nuclear option. War to the knife, in other words. This is used in Babylon-5.


(ed note:In John Lumpkin's Human Reach novels, the "Krasnikov-Hiraski Event Keyholes" (wormhole stargates) have openings that are only 40 meters in diameter (spherical because they are four dimensional). The implication is that starships can be a long as desired, but they have to be able to retract all their components such that the ship has a diameter of only 40 meters. This is much the same situation as old naval battleships with respect to the Panama canal. They can be arbitrarily long but cannot be wider than the canal.

      Neil said, “It’s my first trip out, too.” Sanchez was the only other who had not been through a keyhole before.
     “Why do we call it a keyhole, anyway?” put in Garcia. The construction of the first traversable wormholes in the last century had opened up the stars for colonization. To expand to a new star, countries launched tiny carrier craft, bearing one mouth of a wormhole pair, through interstellar space at relativistic speeds. The other mouth stayed at the origin. When its mobile partner arrived at its destination, they were widened to create a perpetual shortcut through space.
     Tom said, “This one I know. It’s shorthand. We’re too bureaucratic to call it a wormhole, so we use the formal, scientific name, ‘Krasnikov-Hirasaki Event.’ But that’s a mouthful, so we shortened it to ‘KH.’ But that’s too hard to understand over comms, so we expanded it again, to ‘keyhole,’ because Kilo-Hotel sounds stupid.”

     It had been three weeks since San Jacinto had departed Vandenberg, and the destroyer now waited, motionless, near the Wolf 359FL Virginis keyhole, for an inbound space train to clear. She had made her first wormhole transit this cruise 19 days prior, from the international station at the Earth-Moon L-4 point into Wolf 359. After this transit, she would have two additional red dwarf systems to cross before reaching the Entente system.
     Wormhole stations always included two curved plates at opposite sides of the wormhole loop, which maintained the opening with energy from the attached solar array. On one side was a series of guidance rings that directed ships into the mouth. Many wormhole stations had refueling facilities for ships; some, like the Sol — Wolf 359 junction, served as a port for the big colony ships headed out to the International Ring. Millions of colonists had passed through there, trading whatever life they had on Earth for land on virgin planets.
     The warship had about an hour before the wormhole’s traffic control computer would give it clearance to pass through, and Neil reported to the CIC to assist Stahl in preparing a report on the vessels known to be in the system beyond.

     He quickly hit a snag. The robotic U.N. wormhole stations were supposed to keep freely accessible data on the locations of ships in international space, but Neil could only call up month-old reports. He had the comms officer, Daphne Vikram, contact the manned U.N. station elsewhere in the system, which confirmed that, yes, some kind of computer virus had wiped the database, and they hadn’t been able to restore any recent data.
     When the noise subsided, Neil said, “I’m afraid so, sir. Best guess is either the Hans or the Sakis have released a virus into U.N. traffic control to cover their tracks.”
     “What about our intel packet on the comm buoy?” he asked. The fleet stored encrypted intelligence on commercial communications buoys, which was, in theory, available for download only to other U.S. warships.
     Stahl shook his head. “Sir, I queried it, but it’s even more out of date. Once we get through we can ping some freighters for their data in addition to our own sensor sweep.”
     “Ugh. I hate to ask the merchies for help, but we’ll do it if we have to. Could you guys ask the station for their logs of who has passed through here recently?”

     Passage through a wormhole is unremarkable; it is as complicated as walking through an open door. A ship accelerates toward it and goes through. Those on board experience no particular sensation; visually, there’s no long tunnel or bright flash, just a shift in the field of stars.
     San Jacinto emerged from the wormhole in largely empty space, save for the wormhole’s support structures: guidance rings, solar panels, a cluster of containers and the robot ballast tug. The destroyer’s gyms were retracted, so the ship’s extremities didn’t brush the extreme spacetime curvature marking the outer edge of the wormhole. Given the tidal forces there, that would be catastrophic.

     Wormholes were initially discovered not by some deep-space telescope but as an odd solution to Einstein’s theory of general relativity. It wasn’t until the 2050s that Japanese scientist Hirasaki Masuyo isolated one as it bubbled up from the quantum foam on Phobos. It was infinitesimally small, and it didn’t lead anywhere exotic: Its two mouths were a mere Planck length apart.
     But Hirasaki developed techniques to grab each mouth and keep them from winking out of existence. He learned how to incorporate mass and energy into the wormhole, widening it. Separating the mouths allowed him to connect two points as if they were right next to each other.
     Japan’s then-monopoly on solar power stations, asteroid mining and antimatter manufacturing allowed it to finance the grandest project of all: sending a wormhole mouth to Proxima Centauri, the nearest star to Earth. The first men and women transited the wormhole a little more than a decade after Hirasaki’s discovery.

     To open up new stars, nations employed big breeder ships to detect and capture wormholes before they evaporated. When one was secured, one mouth was placed on a tiny robotic wormhole transport, called a "Valkyrie," which relied on direct antimatter annihilation to achieve relativistic speeds. The antimatter fuel – far more than conventional ships used to spark their fusion drives – made them terribly expensive, but they could reach a star five light-years away in just under six years for the people waiting back home.
     Once the distant Valkyrie entered orbit around the destination star, engineers at the origin would widen both mouths to the standard Jumpmax diameter of 40 meters and change; any larger required prohibitive amounts of energy (this limit was invented by the author to create interesting ship limitations). They would construct a solar array at both ends to provide the energy to maintain the opening, and a new star system was free for exploration.
     It wasn't easy or cheap: Typically, about a quarter of Valkyries didn't survive the trip, lost to high-speed collisions with interstellar dust. And no nation had managed to build a Valkyrie that didn't break down after nine or ten light-years' travel, so reaching distant stars required accessing a series of lily pads, usually dim red dwarf systems without hope of habitable worlds (this limit was invented by the author to create a militarily interesting star map. Choke points and transport nexuses).

     Hirasaki and his successors also learned that wormholes were funny, fragile things, and they came with rules. It was as if the universe only grudgingly allowed them, and took every opportunity to attempt to make them go away. To prevent wormholes from collapsing, nations were forced to keep their wormholes in space and distant from one another.
     For example, they could collapse if you only used them in one direction. Mass must be conserved on both sides, so a 10,000-ton freighter going from Sol to Sirius would eventually need to be balanced by an equal mass going in the other direction. Outside each mouth of a wormhole was a robot tug that pushed ballast – usually rocks mined from a nearby asteroid – into the guidance rings, which formed a weak electromagnetic catapult to propel it through. Typically, a single ship won’t destabilize a balanced wormhole; however, a fleet in a hurry might if it doesn’t stop for the tugs to take load-balancing measures. Occasionally, newer wormholes would temporarily prohibit transit while waiting for a delivery of new ballast mass on the far side. This was one reason to keep wormholes out in space: On a planetary surface, differences in air pressure, gravity and other factors at each mouth will draw stray matter from one side to the other, and, over time, crash it.
     Many of the remaining restrictions on wormhole travel extend from what most believe is a universal law: “Thou shalt not travel back in time!” But that isn’t quite accurate. The real law is more particular: “Thou shalt not be able to travel back in time to interfere with your own past.

     Thanks to the time dilation effects of traveling at high velocities, a robot Valkyrie could conceivably reach a five-light-year-distant destination star in just three years in its own time frame, potentially opening up a new colony two years early! The wormhole-crossing colonists would leave their origin in 2105, but arrive in 2103. Wormhole theory said this should be fine, as long as they were unable to pass stock tips from the future to everyone else in 2103. Going back through the original wormhole would put them in 2105 again, so they would need a loop of other early-arriving wormholes to attempt to pass people or information to influence their own past.
     However, the moment anyone tried to build such a loop, some or all of the wormholes collapsed, just as wormhole theory predicted. But what didn’t mesh with the theory was the fact that every Valkyrie that had tried to take advantage of time dilation had lost its wormhole anyway, even when no offending loop was created! After the loss of several early Valkyries, everyone took care to set up a wormhole link using a synchrotron that kept the stay-at-home wormhole mouth at the same speed as its counterpart on the Valkyrie. They stayed in synch, neither ahead nor behind each other in time. But physicists struggled to explain why any and all out-of-synch wormholes still collapsed. Their chief theory involved infinitesimally small, primordial wormholes arrayed around the galaxy, which interfered with the manufactured wormholes. But no one had found any.
     The mystery deepened in the 2120s when a malfunctioning Japanese Valkyrie deposited its wormhole at the red dwarf AT Microscopii B three months before its counterpart at the origin had fully decelerated. The wormhole pair should have crashed, and it ultimately did, but only a month later, after the Japanese breeder ship entered the system and tried launching another wormhole toward a nearby star with an existing European wormhole. It was several years until AT Microscopii B was reopened, this time with in-synch wormholes. The breeder ship was quickly located, as were the bodies of the crew. They had starved to death.

     Enlarged mouths from different wormhole pairs were also territorial: They could destabilize if they passed within several million kilometers of each other, as even small differences in the velocities of close wormholes could create an out-of-synch loop and thus a time machine. This effect prevented you from sending a wormhole through a wormhole or mounting a wormhole on a regular ship. Earth’s stellar nations kept their wormholes distant from one another, often at Lagrange and Trojan points where they could anchor mass for ballast.

From THROUGH STRUGGLE, THE STARS by John Lumpkin (2011)

      THE ASSUMPTIONS: Teleportation requires both a transmitter and a receiver. Conservation holds. Teleportation is instantaneous, and does not involve beaming.

     THE RESULT: See Figure 3. The ship consists mainly of a couple of rocket motors, fuel tanks, and an open-ended teleportation receiver open to the rear. You can leave it open because, in vacuum, you don’t need to worry about air getting in the receiver.

     The ship, unmanned, is fired from Earth orbit or from further out. Probably it should be fired in the direction of the galactic core, where we anticipate more traffic. By firing the ship from, say, Jupiter orbit, we can pack quite a lot of fuel-water, for reaction mass-outside the ship. (See Isaac Asimov, THE MARTIAN WAY.)
     We use all the fuel except a reserve for steering. The ship coasts.
     It passes through a star system. Let it be about the size of the solar system; then we have ten hours (assuming our ship is near lightspeed) to shove an entire prefab colony into the Earth-based transmitter. If all ten hours are used, then the colony building materials are strewn across the entire system. Each piece of equipment arrives at rest with respect to Earth, and thus leaves the receiver at a speed approaching lightspeed. (Now you know why we put a hole in the receiver.)
     Last through the receiver are the ships designed to collect all this crap. Since they are manned, we had better not send them from Earth. Conservation of energy would freeze the pilots to ice in an instant. Consider the irony: to keep them from freezing, we must ship them from Pluto orbit!

     It might be more efficient to send through the teleport system only a few ships and another prefab teleport receiver. The rest of the colony comes through the second receiver.

     In any case, notice four advantages. You don’t have to carry the entire cargo, or waste fuel accelerating it. You don’t decelerate the ship, so none of your limited fuel supply need be reserved for that purpose.
     The colonists need not twiddle their thumbs for decades. And the ship can be re-used.
     Can and will. You just let it coast. Every time it comes near a star system, you have another colony. In eighty thousand years we leave a line of colonies clear across the galaxy, before we finally run out of stars.
     Less peaceful societies would shove war fleets through the teleport system. It is hard to imagine a safer way to make war. The fleet is strewn all across the system, with all the warships at rest with respect to the universe at large. And how could the target system counterattack? To reach the invading system, they would have to catch a ship which has had years to accelerate to its tremendous velocity, and which is long gone into interstellar space before the attack can even begin.

     During the Boston speech, a member of the audience suggested that teleportation be used to fuel the above craft. Specifically: the motor is a receiver, Open, with a flared nozzle attached. We drop a transmitter on Jupiter. Presto! Hellishly dense high-pressure gas expands explosively into the vacuum of space, driving the ship forward. Fuel supply: inefficient compared to ion drives or the like, but almost literally unlimited.
     It won’t work. Rather, it won’t work for long. Remember, we have assumed that conservation holds.
     The motor’s exhaust velocity is the ship’s own limiting velocity if we use teleportation to fuel the ship. Jupiter’s atmosphere wouldn’t expand fast enough to be useful. Even with a fusion drive, we lose momentum every time a droplet of hydrogen reaches the fuel tank. We have to get it back by firing the droplet through the rocket motor. When the two velocities balance…we can’t go any faster.
     Total conversion of matter to light does give us unlimited velocity. Then we have only the problem of what to do with the incoming fuel. We always have that problem. A droplet of hydrogen moving at a tenth of lightspeed would vaporize any fuel tank we can build today. Maybe in the future … with new materials… plenty of padding…springs…


(ed note: This technically is not a faster than light drive, the ships travel at lightspeed. But when a ship enters a matter transmitter and becomes encoded as a transition particle, time stops for the ship. When it travels from Terra to Alpha Centauri the ship materializes at the receiver 4.3 years later. However, for the crew, zero time has elapsed.)

      Take a point in space.
     Take a specific point near the star system Alpha Centaurus, on the line linking the center of mass of that system with Sol. Follow it as it moves toward Sol system at lightspeed. We presume a particle in this point.
     Men who deal in the physics of teleportation would speak of it as a “transition particle.” But think of it as a kind of superneutrino. Clearly it must have a rest mass of zero, like a neutrino. Like a neutrino, it must be fearfully difficult to find or stop. Despite several decades in which teleportation has been in common use, nobody has ever directly demonstrated the existence of a “transition particle.” It must be taken on faith.
     Its internal structure would be fearfully complex in terms of energy states. Its relativistic mass would be twelve thousand two hundred tons.
     One more property can be postulated. Its location in space is uncertain: a probability density, thousands of miles across as it passes Proxima Centauri, and spreading. The mass of the tiny red dwarf does not bend its path significantly. As it approaches the solar system the particle may be found anywhere within a vaguely bounded wave front several hundred thousand miles across. This vagueness of position is part of what makes teleportation work. One’s aim need not be so accurate.
     Near Pluto the particle changes state.
     Its relativistic mass converts to rest mass within the receiver cage of a drop ship (a spaceship with a teleportation receiver with the back end open). Its structure is still fearfully complex for an elementary particle: a twelve-thousand-two-hundred-ton spacecraft (the good ship Phoenix), loaded with instruments, its hull windowless and very smoothly contoured. Its presence here is the only evidence that a transition particle ever existed. Within the control cabin, the pilot’s finger is still on the TRANSMIT button.

     But she (captain Karin Sagan) remembered the shock of relief when the heat struck. She had pushed the TRANSMIT button a light-month out from Alpha Centaurus B. An instant later sweat was running from every pore of her body.
     There had been no guarantee. The probability density that physicists called a transition particle could have gone past the drop ship and out into the universe at large, beyond rescue forever. Or … a lot could happen in nine years. The station might have been wrecked or abandoned.
     But the heat meant that they had made it. Phoenix had lost potential energy entering Sol’s gravitational field and had gained it back in heat. The cabin felt like a furnace, but it was their body temperature that had jumped from 98.6° to 102°, all in an instant.

(ed note: the Phoenix is self-teleporting, but there has to be a drop ship with a receiver cage in the path of the transition particle. Or the Phoenix transition particle will just sail off to the far side of the universe, and never change back into the ship and crew.)

(ed note: captain Karin Sagan has an interview on live TV)

     Q: What about the Centaurus planets? Are they habitable?
     “No.” It hurt to say that. She saw the disappointment around her.
     Q: Neither of them checked out?
     “That’s right. There are six known planets circling Alpha Centaurus B. We may have missed a couple that were too small or too far out. We had to do all our looking from a light-month away. We had good hopes for B-2 and B-3 — remember, we knew they were there before we set out — but B-2 turns out to be a Venus-type with too much atmosphere, and B-3’s got a reducing atmosphere, something like Earth’s atmosphere three billion years ago.”
     Q: The colonists aren’t going to like that, are they?
     “I don’t expect they will. We messaged the (uncrewed) drop ship Lazarus II to turn off its JumpShift unit for a year. That means that the colony ships won’t convert to rest mass when they reach the receiver. They’ll be reflected back to the solar system. They should appear in the Pluto, drop ship about a month from now.”
     Q: Having lost nine years.
     “That’s right. Just like me and the rest of the crew of Phoenix. The colonists left the Pluto transmitter two months after we did.”
     "At the moment it’ll pay us better to go on looking for worlds around other stars. It’s so bloody easy, with these interstellar drop ships.”
     Them was nodding among the newstapers. They knew about drop ships, and they had been briefed. In principle there was no difference between Lazarus II and the drop ships circling every planet and most of the interesting moons and asteroids in the solar system. A drop ship need not be moving at the same velocity as its cargo. The Phoenix, at rest with respect to Sol and the Centaurus suns, had emerged from Lazarus II’s receiver cage at a third of lightspeed (i.e., the velocity that Lazarus II is traveling at).
“The point is that you can use a drop ship more than once,” Karin went on. “By now Lazarus II is one and a third light-years past Centaurus. We burned most of its fuel to get the ship up to speed, but there’s still a maneuver reserve. Its next target is an orange-yellow dwarf, Epsilon Indi. Lazarus II will be there in about twenty eight years. Then maybe we’ll send another colony group.”     Karen giggled. ‘We were as far from any star as anyone’s ever gotten. It was a long night. Maybe it was getting to us. We had a bad moment when we thought there was an alien ship coming up behind us.” She sobered, for that moment of relief had cost six people dearly. “It turned out to be Lazarus. I’m afraid that’s more bad news. Lazarus should have been decelerating. It wasn’t. We’re afraid something’s happened to their drive.”
     That caused some commotion. It developed that many of the newstapers had never heard of the first Lazarus. Karin started to explain…and that turned out to be a mistake.

     The first interstellar spacecraft had been launched in 2004, thirty-one years ago.
     Lazarus had been ten years in the building, but far more than ten years of labor had gone into her. Her life-support systems ran in a clear line of development back to the first capsules to orbit Earth. The first fusion-electric power plants had much in common with her main drive, and her hydrogen fuel tanks were the result of several decades of trial and error. Liquid hydrogen is tricky stuff. Centuries of medicine had produced suspended-animation treatments that allowed Lazarus to carry six crew members with life-support supplies sufficient for two.
     The ship was lovely-at least, her re-entry system was lovely, a swing-wing streamlined exploration vehicle as big as any hypersonic passenger plane. Fully assembled, she looked like a haphazard collection of junk. But she was loved.
     There had been displacement booths in 2004: the network of passenger teleportation had already replaced other forms of transportation over most of the world. The cargo ships that lifted Lazarus’ components into orbit had been fueled in flight by JumpShift units in the tanks. It was a pity that Lazarus could not, take advantage of such a method. But conservation of momentum held. Fuel droplets entering Lazarus’s tanks at a seventh of lightspeed would tear them apart.
     So Lazarus had left Earth at the end of the Corliss accelerator, an improbably tall tower standing up from a flat asteroid a mile across (a mass driver). The fuel tanks-most of Lazarus’s mass-had been launched first. Then the ship itself, with enough maneuvering reserve to run them down. Lazarus had left Earth like a string of toy balloons, and telescopes had watched as she assembled herself in deep space.
     She had not been launched into the unknown. The telescopes of Ceres Base had found planets orbiting Alpha Centaurus B. Two of these might be habitable. Failing that, there might at least be seas from which hydrogen could be extracted for a return voyage.
     “The first drop ship was launched six years later,” Karin told them. “We should have waited. I was five when they launched Lazarus, but I’ve been told that everyone thought that teleportation couldn’t possibly be used for space exploration because of velocity differences. If we’d waited we could have put a drop ship receiver cage on Lazarus and taken out the life-support system. As it was, we didn’t launch Lazarus II until—” She stopped to add up dates. “Seventeen years ago. 2018.”
     Q: Weren’t you expecting Lazarus to pass you?
     “Not so soon. In fact, we had this timed pretty well. If everything had gone right, the crew of Lazarus I would have found a string of colony ships pouring out of Lazarus II as it fell across the system. They could have joined up to explore the system, and later joined the colony if that was feasible, or come home on the colony return ship if it wasn’t.”

(ed note: Karin Sagan off-handedly mentions a couple of ways the ill-fated Lazarus and her crew can be rescued)

(ed note: Robin Whyte, former CEO of JumpShift Inc. and holder of lots of shares, sees the interview and realizes JumpShift is facing a public relations nightmare. He gets a meeting with Karin Sagan and Jerryberry Jansen)

     (Robin Whyte said) “I do want to know why you went into so much detail on Lazarus.”
     “They asked me. If someone had asked me to keep my mouth shut on the subject I might have. Might not.”
     “We can’t rescue Lazarus,” said Whyte.
     There was an uncomfortable silence. Perhaps it was in both their minds, but it was Jerryberry who said it. “Can’t or won’t?”
     “How long have you known me?”
     Jerryberry stopped to count. “Fourteen years, on and off. Look, I’m not saying you’d leave a six-man crew in the lurch if it were feasible to rescue them. But is it economically infeasible? Is that it?”
     “No. It’s impossible.” Whyte glared at Karin, who glared back. “You should have figured it out, even if he didn’t.” He transferred the glare to Jansen. “About that rescue mission you proposed on nationwide teevee. Did you have any details worked out?”
     Jerryberry sipped at his screwdriver. “I’d think it would be obvious. Send a rescue ship. Our ships are infinitely better than anything they had in 2004.”
     “They’re moving at a seventh of lightspeed. What kind of ship could get up the velocity to catch Lazarus and still get back?”
     “A drop ship, of course! A drop ship burns all its fuel getting up to speed. Lazarus II is doing a third of lightspeed, and it cost about a quarter of what Lazarus cost—it’s so much simpler. You send a drop ship. When it passes Lazarus you drop a rescue ship through.”
     “Uh huh. And how fast is the rescue ship moving?”
     “…Oh.” Lazarus would flash past the rescue ship at a seventh of lightspeed.
     “We’ve got better ships than the best they could do in 2004. Sure we do. But, censored dammit, they don’t travel the same way!”
     “Well, yes, but there’s got to be—"
     “You’re cheating a little,” Karin said. “A rescue ship of the Lazarus type could get up to speed and still have the fuel to get home. Meanwhile you send a drop ship to intercept Lazarus. The rescue ship drops through the receiver cage, picks them up—hmm.”
     “It would have to be self-teleporting, wouldn’t it? Like Phoenix.”
     “Yah. Hmmm.”
     “If you put a transmitter hull around something the size of Lazarus, fuel tanks included, you’d pretty near double the weight. It couldn’t get up to speed and then decelerate afterward. You’d need more fuel, more weight, a bigger hull. Maybe it couldn’t be done at all, but sure as hell we’re talking about something a lot bigger than Lazarus.”
     There had never been another ship as big as Lazarus.
     Karin said, “Yah. You’d ditch a lot of fuel tanks getting up to speed, but still—hmmm. Fuel to get home. Dammit, Whyte, I left Earth nine years ago. You’ve had nine years to improve your space industry! What have you done?”
     “We’ve got lots better drop ships,” Whyte said quietly. Then, “Don’t you understand? We’re improving our ships, but not in the direction of a bigger and better Lazarus.”
     “Then there’s the drop ship itself. We’ve never built a receiver cage big enough to take another Lazarus. Phoenix isn’t big; it doesn’t have to go anywhere. I won’t swear it’s impossible to build a drop ship that size, but I wouldn’t doubt it either. It doesn’t matter. We can’t build the rescue ship. We don’t even have the technology to build Lazarus again! It’s gone, junked when we started building drop ships!”
     “Like those damn big bridges in San Francisco Bay,” whispered Karin. “Sorry, gentlemen. I hadn’t thought it out.”
     Jerryberry said, “You’ve still got the Corliss accelerator. And we still use reaction drives.”
     “Sure. For interplanetary speeds. And drop ships.”

(ed note: the double whammy of no habitable planets at Alpha Centauri plus the doomed Lazarus II will destroy public support for space exploration)

     Gemini Jones was JumpShift’s senior research physicist, an improbably tall and slender black woman made even taller by a head of hair like a great white dandelion. “We get this free,” she said, rapping the schematic diagrams spread across the table. “The Corliss accelerator. Robin wants to build another of these. We don’t have the money yet. Anyway, we can use it for the initial boost.”
     On a flattish disk of asteroidal rock a mile across, engineers of the past generation had raised a tower of metal rings. The electromagnetic cannon had been firing ships from Earth orbit since A.D. 2004. Today it was used more than ever, to accelerate the self-transmitting ships partway toward the orbital velocities of Mars, Jupiter, Mercury.

(ed note: JumpShift plans out a rescue mission. It will cost a gazillion dollars. The public relations nightmare will intensify. But one hour before they reveal the expensive plan on TV, Robin Whyte looks at a diagram of the Corliss accelerator and suddenly has an idea. They frantically work it up and display it on the TV show)

     Gen Jones’s big white-on-blue schematic had been thumbtacked to the white wall over the table and chairs. Below it, Jerryberry Jansen leaned back, seemingly relaxed, watching Whyte move about with a piece of chalk.
     A thumbtacked blueprint and a piece of chalk. It was slipshod by professional standards. Robin Whyte had not appeared on teevee in a couple of decades. He made professional mistakes: he turned his back on the audience, he covered what he was drawing with the chalk. But he didn’t look nervous. He grinned into the cameras as if he could see old friends out there.
     “The heart of it is the Corliss accelerator,” he said, and with the chalk he drew an arc underneath the tower’s launch cradle, through the rock itself. “We excavate here, carve out a space to get the room. Then—” He drew it in.
     A JumpShift drop ship receiver cage.
     “The rescue ship is self-transmitting, of course. As it leaves the accelerator it transmits back to the launch end. What we have then is an electromagnetic cannon of infinite length. We spin it on its axis so it doesn’t get out of alignment. We give the ship an acceleration of one gee for a bit less than two months to boost it to the velocity of Lazarus, then we flick it out to the drop ship.

(ed note: since the external Corliss accelerator is boosting the ship up to one-seventh of lightspeed the ship does not have to carry a millon billon tonnes of propellant. They can use an off-the-rack ship.)

     “This turns out to be a relatively cheap operation,” Whyte said. “We could put some extra couches in Phoenix and use that. We could even use the accelerator to boost the drop ship up to speed, but that would take four months, and we’d have to do it now. It would mean building another Corliss accelerator, but—“, Whyte grinned into the cameras, “we should have done that anyway, years ago. There’s enough traffic to justify it.
     “Return voyage is just as simple. After they pick up the crew of Lazarus, they flick to the Pluto drop ship, which is big enough to catch them, then to the Mercury drop ship to lose their potential energy, then back to the Corliss accelerator drop cage. We use the accelerator for another two months to slow it down. The cost of an interstellar drop ship is half a billion new dollars. A new Corliss accelerator would cost us about the same, and we can use it commercially. Total price is half of what Lazarus cost.” Whyte put down the chalk and sat.
     Jerryberry said, “When can you go ahead with this, Doctor?”
     “JumpShift will submit a time-and-costs schedule to the UN Space Authority. I expect it’ll go to the world vote.”

From ALL THE BRIDGES RUSTING by Larry Niven (1973)

      His footfalls soundless on the deep pile of the carpet in reception, he walked past the robots already handling routine staff duties at the counters and headed for the elevator banks. He had an hours office work before his first trip. All about him rose the monstrous hundred and fifty storey edifice of Solterran Space Agency. Here many-thousands of men and women attended to the needs and problems of Earth’s position in space. Here policies were initiated and investigated and matured so that Man’s outward thrust for the stars should be ordered and economical and of most effect.
     These days you couldn’t just slam the airlock on your spaceship and blast off for the planets. Anyway, spaceships were absolutely useless for interstellar work, even interplanetary, and as such performed their tasks well within reach of their planetary bases.
     Except for the Carriers.
     The box bags.
     Those were what was carrying mankind out to the stars and they were what made life real and earnest for Ward and for men like him. He checked his clip for the day’s assignments and grimaced as he saw they’d set him up for three carriers. Three. Well, if nothing went wrong and each box bag behaved itself there still should be a little overtime in it for him.

     “The Gershmi.” (hostile alien empire)
     “Seems like it, Dave. It would explain the facts.”
     Ward suddenly didn’t feel too well.
     “Is this official, Bill? Are you telling me I’m laid off these assignments today?”
     Slowly Roscoe shook his head. “No, Dave. You’re not. You’ll be transitting as planned—”
     “But, Bill, for gosh sakes! I don’t want to step out of the box and be blasted or something by a damned Gershmi!”
     “Wait a minute. I’m going along too. We’ll go ready for trouble. But those three carriers need servicing. They haven’t been looked at for a year. They’ll run out of steam and that will foul up the whole landing pattern.”
     “I know that. But why me? I’m a civilian. They ought to send the Navy in. It’s their pigeon.”
     “I’m going along too, remember? And I’m Navy.”
     “But I’m not—!
     “Maybe. But you’re a Solterran Government employee; a civilian, yes, but a civilian with special rights and privileges and duties. We’ll have a back-up team of marines—”
     “I don’t like the sound of that back up. Why can’t they go first?”
Roscoe laughed. “Maybe they will, at that. Come on. We ought to get down to the Drain.”
     “The Drain,” said Ward, rising and looking unhappy. “That doesn’t sound so funny now.”
     Going down in the elevator through the armored shell covering the elevator and trolley lines, and boarding a trolley that soughed off into the lighted tube slanting into the ground away from the SSA building, Ward tried to tell himself that Salter, the big boss, wouldn’t send men out to their deaths. That wouldn’t be economical Men’s lives were the most precious single asset that Solterra possessed. You don’t throw away your best cards … unless you’re backed up against a wall and have nothing left to lose.

     The trolley contained half a dozen other operators, a few techs and a sprinkling of Naval personnel. The lighted tube leveled off and the airpumps smoothly evened out the momentary imbalance of air pressure so that no ears popped. Down here they were a mile or more beneath the ground. The Drain was even lower.
     Above them, half a mile beneath the surface, stretched the armored membrane protecting the Drain. That membrane completely surrounded the Drain, like a gigantic ball, allowing of ingress only through miserly orifices deep below the topmost levels. The biggest concentration of nuclear weapons known to man could explode all around the concentric ring of defences, could rip and tear the very Earth apart, and still the ball containing the Drain would remain impervious.
     The trolley halted silently at the last station before the armor and everyone everyone alighted for security check. Normally security checks were strict but formal; it was hardly likely that anyone of Earth would wish to destroy the Drain, but the eventuality must be taken into account. And as all aliens so far encountered by Earthmen were humanoid, then checks against them, also, must be stringent. Today Ward caught a tenseness, a more than usual alertness, a sense of urgency that, he supposed with a little shiver, must originate in snap orders sent down by Salter after the incident of Jimmy Kinross’s disappearance.
     Checks over, they waited quietly in line before their assigned box door. Ward stepped through, emerging from the matching door on the inside of the armored membrane. Quickly, he and Roscoe walked through to the trolley waiting to take them to their work area.
     The Marines formed a single file and unlimbered their weapons, holding them ready for instant action. In back of the group a second team of Marines waited by the single exit door from this flat. They were there in case the operation backfired and the Drain was faced with an incursion of Gershmi out for blood.

     A bull-necked, craggy, immense Marine with enough stripes on his arm to fence in a state prison stood at the head of the line. Plastic sheathed concrete walls surrounded them, fluorescents blazed down, air filters maintained the atmosphere at its best level for human toleration. Ward and the team going through couldn’t feel that; they were already on suit air, their helmets battened down and clamped. Major Perry slammed his own visor down, gave a single curt gesture with his hand, and stepped forward as the fire-engine red door silently opened.
     Ward licked his lips. Despite the filters and wipers in his suit, he was sweating, and he felt the dizzying fingers of fear clawing at him. He wasn’t enjoying this one little bit.
     The big top sergeant stepped in, the door shut, the scarlet transitter light glowed for the second time, the door opened as more air gushed into the waiting vacuum. The line moved up one.
     Now why should he get all het up now about this transit when everything had gone well? If there hadn’t been this stupid hitch,’ the disappearance of Jimmy Kinross, the intervention of Major Perry and the Marines, he would have been halfway through servicing the carrier by now. And he wouldn’t have been in a blue funk about stepping past that red door into the box, either.
     The green ready light glowed as air pumped hissingly into the vacuum of the box. The fire-engine red door opened and he stepped through. The door closed and the internal red light cycled.

     The door in front of him opened and he stepped through. He hadn’t switched on his exo-skeleton power and he drifted easily across in free fall to grasp a stanchion anchoring the box to the floor of the carrier deck. Roscoe hung at right angles to him half way up one wall. Perry and his Marines were fanned out all around the box and the big top sergeant was just going through the lock out onto the hull.
     A fraction of a second before he had been standing on concrete deep within the Earth, surrounded by armor and machines and men and women; now he stood in the hollow steel hull of a spaceship spearing through space fifty light years or more from Earth.
     That meant little; it was his condition of work.

     He set about servicing the carrier with methodical thoroughness, forcing himself to slow down, to make a good job of it.
     No damn Gershmi would make him skimp a job.
     The fuel bins were nearly empty. He’d do those first, as per schedule. He unhooked the phone and called Earth on the direct line. Mainwaring answered.
     “Put Chuck on, will you, Captain? Let’s get this heap serviced fast.”
     “Chuck, here,” came Marlow’s familiar voice from Earth, riding along the carrier waves that had a moment before brought Ward and Roscoe and Perry and his men through some queer non-space to the carrier fifty light years from the planet of their birth. “Everything okay?”
     “Sure. Sorry I didn’t get to speak to you; too many uniforms around.”
     Chuck Marlow was a civilian, too, the switch operator on this shift for Earth.
     “You’re fueling from Zanzibar Twenty today. I’m on the line to them. Switching you—now.”
     The phone crackled softly, like soggy cereal. Then a new voice: “Zanzibar Twenty here. Smithson. All ready when you are, Dave.”
     “Hi, Smitty.” Ward set up the deflector circuits, checked that the red box door was shut—he didn’t want a spray of dirt sprouting through the crew flat of the carrier—and thumbed the toggle. “Start her going.”
     The control board lit up with the telltales, indicating that the deflectors were in operation and functioning on the top line. From Zanzibar Twenty—a small outer planet five thousand million miles from a minor sun—in the Zanzibar system, thirty light years from Earth and thus about twenty from the carrier, a stream of rock and minerals and dirt dug from the soil, loosened by robot mining equipment and funneled through the box, spouted across space and into the box aboard the carrier and was deflected into the fuel bins. For a moment Ward watched the fuel meters, noted their steady rise.
     “Okay, Smitty. Your stuff is coming in fine.” He had no need for the servicing manuals or schedules in their plastic sheaths tagged to the control fascia. He’d been servicing earners for six years now and knew the drill. After an hour of general checks, minor adjustments, a thorough going-over, he felt satisfied that this Ganges carrier was functioning on all systems go.

     “I’m going outside now,” he called to Roscoe.
     The Navy man had been perched up in the angle of deck and wall, wedged comfortably in, watching Ward at work.
     “Right, Dave. If you want to make course corrections you’ll have to check with the Major first.”
     “What the-! Why? Roscoe’s words came thinly.
     “Use your head, Dave. If there are Gershmi hanging around a flare of energy will bring them like hungry sharks.”
     The decision whether or not to fire the steering tubes lay with the Major. Ward would see the reasonableness of the Marine’s position; the stern engines to which Ward was now sailing through the empty hull gave off a steady beat of energy as they converted the rocky fuel and thrust the carrier forward steadily at a low g acceleration, safe and economical and quite insufficient to give the semblance of gravity aboard, so that free tall conditions prevailed. But to introduce a sudden modulation to the energy pattern radiating from the carrier would indicate the presence of life; the carrier’s energy patterns would no longer be swallowed up by the eternal beat of power from the stars and the waiting Gershmi would home in to rend and destroy.
     If Perry decided not to fire the jets, Ward, for one, wouldn’t object.

     Trouble there, though, was that the carrier would continue on a diverging course from the Ganges run. Just how much later on the corrections could be made, Ward, of course, could not know; but he did know that the longer they were left the more violent they would have to be.
     The engines were running sweetly and Ward saw at a glance that his ministrations were not needed. Rock and dirt from the bins fed through hoppers into the converters, driving the ship gently forward. That gentle drive steadily pulsing away over the years had already built up a sizeable c number. The carrier, in theory, if propelled at one g for a year or so should attain c unity—the velocity of light. They hadn’t done that yet, although they’d struck very near it, and some of the effects had been very peculiar indeed.
     He checked that the dials gave the same values as the repeaters on the control panel. Current speed—point three two one seven c. Nearly a third of the speed of light. Not bad. The Ganges cluster of stars lay sixty-nine fight years from Earth. The carrier had reached to within nineteen light years. There was still some way and time to go before she would be turned end for end—exactly at the halfway mark—and her speed be meticulously dropped off in the same ratio as she had built it up.

     The really exciting times for a carrier supervisor were the days when a carrier reached her objective. Ward had shared in three of those in his six years’ service and he really yearned for more. That was when all the toil and planning and sweat paid off.
     When you were filling a carrier’s fuel bins with matter—any matter would do if it had a good mass to bulk ratio—you could transmit anything fifty light years from Earth. Earth had no problem of refuse disposal now. But you couldn’t keep on sending out chunks of your own home planet, or of those green and pleasant planets of other suns settled by Homo sapiens, or even, really, of planets belonging to quondam enemies like the Venies. You’d soon end up with no place to live. So you picked out some otherwise useless hunks of rock orbiting suns no one had yet got around to settling, the vermin of space, and you mined what you wanted and transmitted that.
     Zanzibar was the current fuel supply, a minor sun with a swarming brood of planetoids of rock and metal and dirt. The rock and dirt went carrierwards, the minerals to the ever-hungry furnaces back on Earth or to any other of Solterra’s federated planets. As a system it was divine. No waste anywhere.
     All a carrier consisted of were the essentials. The fuel bins containing rock and compressed rubbish, anything that could be spared, that slid down the hoppers under pressure into the converter to be ripped asunder into primitive particles and ejected from the Venturis as a wash of ionized dust. That gave sufficient thrust for the carrier; over the years that slow but steady thrust built up into quite high orders of c.
     In front of the engines a simple tubular framework supported the control cabin globe, housing the matter transmitter and the controls. There was an air lock, and various aerial arrays. And that was all, apart from the tubing to the forward steering tubes extended widely on outriggers. All that the carriers were was explained by their name. They carried matter transmitters out to alien planets of alien stars.

     “This is Major Perry. Go ahead, Ward. Our detectors show no signs of Gershmi. If they were around they’d have been here by this time.”
     That made sense. The only way the Gershmi, like men, could arrive at this spot in space was via matter transmitter. One of their carriers would have had to have passed close to those from Earth—although the Solterran carriers had not been sent off from Earth herself. Obviously, the nearer you got to the planet you were aiming at the better; these carriers aimed at the Ganges cluster had been sent off from the furthest outposts of the Solterran interstellar sphere of influence…
     As soon as the Ganges cluster had been reached the first job would be to assemble fresh carriers and send them off the deeper into the Galaxy. The system was akin to interstellar leapfrog.
     These three carriers, now. Two were for insurance, in case something went wrong. The third would still go on past Ganges, if everything else went right, spearing out past what would by then have become a nearer cluster of stars, aiming for the deeper reaches, the inner spaces, the glowing populations of stars along this spiral arm.
     He didn’t like the idea of going off to a singleton. If the matter transmitter aboard the carrier failed whilst he was aboard—that would be his finish. Nobody older than his hypothetical grandchildren would ever be in time to reach him.
     Travel by matter transmitter across the gulfs between the stars contained seeds of its own danger; you became blasé. The thought that he’d be eighty or so light years from Earth, at least fifteen from the nearest inhabited planet, meant little when those distances could be covered almost instantaneously. The great gulfs shrank. But when you had no transmitter; when you were thrown back on mere physical transport—fifteen light years marooned … The thought was suddenly ghastly and he stepped quickly to the fire-engine red door and watched the green ready light.
     He stepped through.

     Zukowsky switched his train of thought: “Pal of mine working for SSA tells me they’re still a million parsecs from ever pushing a ship along at FTL.”
     “I don’t think they ever will. Einstein won’t be mocked.”
     “We do, don’t we, every day, after a fashion? We break down a person or a load of freight, shoot them along our beams from one box to the receiver box and recreate them. Just about instantaneously, too.”
     Mikardo for all his faults spoke now like any ordinary man of Earth. “We of Solterra,” he said slowly, “must expand our civilization to other planets orbiting other stars. But they’re all so far off. We would take generations in traveling to them aboard an ordinary spaceship—”
     “And who’s going to spend his whole life cooped up aboard a so-called generation ship? When he knows the scientific brains of the world are working on FTL travel? He wouldn’t want to waste his whole life, would he?”
     “Point taken—was taken. So they began to send out the carriers, spaceships carrying a matter transmitter. When they reached the planet at which they were aimed then you just went through the box and set about colonizing the new world with materials and men almost instantaneously transmitted from Earth. I bet you do wish you’d been alive then!”

(ed note: The main card that I see Mr. Bulmer palming off the deck is Larry Niven's assumption that the law of conservation holds true in teleportation. Which means that the teleporter has to gives Dave's mass enough energy to delta-V him up to 0.3217 c, or when he emerges the carrier's floor will smite him at a relative velocity of 0.3217 c and destroy everything. The same goes for the dirt used for fuel, which makes transmitting the dirt to the carrier a hideously energy-expensive operation.)

From BEHOLD THE STARS by Kenneth Bulmer (1965)
Web and Starship

We must not forget the masterful selection of FTL limitations which created the fascinating tactical situation in the wargame Web and Starship (keep in mind this is a paper-and cardboard tabletop game, not a computer game). The game designer (the legendary Greg Costikyan) wanted to create the world's first balanced three-player game. Up until now, all three player games in practice tend to devolve into two players ganging up on the third player (i.e., they are unbalanced). Mr. Costikyan wanted to design a game that avoided this. The mechanism depended upon the constraints of the FTL system.

The situation starts with two alien races: the Gwynhyfarr (hereafter referred to as "Birds") and the Pereen (hereafter referred to as "Moles"). Each has a totally different type of FTL transport system. And, as will become an important point later, neither can use or even comprehend the others FTL system.

The Birds have FTL starships that can travel anywhere in the universe at will. No special launch or landing sites are required. The trouble is that the starships are expensive to build (i.e., there are not many of them), and each has a limited cargo capacity.

The Moles have FTL teleportation devices. A teleporter unit must be present both at the start and at the destination. Teleportation is instantaneous. Unfortunately in order to teleport to a new planet, a teleporter unit must by shipped to the planet by a Slower-than-light robot ship. This of course takes years. The advantage of teleporter units is that they have huge cargo capacities. The Moles can move entire armies through a teleporter in a matter of hours.

When the Bird Empire and the Mole Empire expanded to the point where their borders contacted each other, war was inevitable, but futile. Both empires wanted to destroy the other and take over the enemy's habitable planets. Unfortunately, due to the limitations of their respective FTL, war was impossible.

Say the Birds want to invade a Mole planet. The Bird starships can go anywhere, so the Birds load up their limited number of starships with the few numbers of solders each ship can carry, and invade the Mole planet. Whereupon the Moles use their teleporters to instantly transport in the planetary armies of all the other Mole planets, and the combined Mole armies turn the pathetically small Bird invasion force into a smoking crater.

Say the Moles want to invade a Bird planet. The Moles load a teleport unit into a STL robot ship, aim it at the Bird planet to invade, and wait a few years for it to arrive. Years later, as it approaches the Bird planet, it is noticed by Bird space patrols, who promptly shoot it to pieces.


Until one fine day both the Birds and the Moles notice radio waves being emitted by a small planet set right in between the two empires. A planet called Earth.

Naturally both empires want to conquer Earth. It is in a very strategic position and it has an industrial base that can produce war material once the population has been enslaved. And since Earth has no empire (or even FTL capability of any kind), it should be an easy conquest.

However, Earth has a few things in its favor. For one, it knows that one empire cannot attempt to conquer it without the other empire trying to prevent it. Earth has limited diplomatic contact with both empires, so it can make deals and otherwise try to keep the two empires off balance. And in the long term, Earth has a wild card. Unlike the two empires, Earth can comprehend and eventually produce both types of FTL system. In fact, they can eventually produce the game-changing "Web Starship". This is a Bird style starship which ferries a Mole style teleport unit to strategic locations.

So as you can see, careful selection of the limits on ones FTL drive can force the desired situation to come to pass.

Terrans invented the radio in the early part of the 20th century. At first, it was a toy, suitable for very limited uses; spark-gap radio provided very little band-width over which to transmit messages. But it rapidly became one of Terra's most important tools. By the 1930's, hundreds of radio stations were broadcasting news, stories, music and innumerable other programs. It became the primary medium for military messages, for local communication with mobile cabs and cars, for long distance broadcasts, for global communication. In the 1950's, television became important, and soon whole new sections of the broadcast spectrum were used to transmit messages.

At the speed of light, Terra's earliest messages flew starward. At first they were ignored, for the universe is vast and radio noise common, and receivers are not always listening for odd phenomena. Too, advanced civilizations use radio very little—planetary communications are carried via cable, or narrow-beamed to transmission satellites, while long-distance communications can be beamed via hyperwave or through the Web.

But modulated radio noise is the first sign of an emerging technological civilization, and sooner or later a radio astronomer was bound to turn his telescope to that obscure G-class star in the Carina arm....

Two great civilizations faced each other across the arm. The Gwynhyfarr, proud descendants of an aerial race, roamed the stars in mighty quantum-leap vessels. The Pereen, the children of burrowing animals, linked their worlds together with the Web. The two found each other incomprehensible. Their mathematics were incompatible, their languages based on different principles, their psychologies entirely at variance. They could not live with each other, and yet they must. Neither was sufficiently mighty to conquer its foe.

But more than this: technologies have military implications. The Gwynhyfarr ships could travel light-years in weeks, could dart from star to star and drive deep into enemy territory. They could also carry only small numbers of troops. Transporting even an infantry division required huge ships in large numbers. In a space battle, the Gwynhyfarr had no match. But the Pereen did not travel space.

The Pereen knew how to conquer intervening distance. Two points could be "gated" together, linked so that one object could pass from one point to another without travelling through the intervening space. Once a gate was constructed on a new world, it was linked via other gates to every world in the Pereen hegemony. The Web permitted instantaneous transmission of huge quantities of materiel from one world to another. The Gwynhyfarr might land a division on a Pereen world—but the Web would immediately transmit an army to that world to defeat its enemies.

But to open a gate, the Pereen must transport the necessary machinery to a new world to make the link to the Web. And the Pereen do not understand Gwynhyfarr faster-than-light travel, and have no such system of their own. Instead, sublight Pereen probes must drone their weary way across space-time toward their targets. When a target is reached, a new world can be added to the Web.

But sublight probes are small and defenseless; they cannot be otherwise, because moving anything at sublight speeds from one star to another requires a tremendous investment in energy and time. Only small objects can affordably make the trip. If a Pereen probe enters a Gwynhyfarr world, its fusion flare will almost certainly be enemy starships, and the probe destroyed.

And so, for decades, the two races bided their time in armed hostility, watching each other across the Carina arm. Limited by their technologies and systems of war, neither could defeat the other.

Then came the radio signals from Terra...

To the Pereen, Terra meant only one thing: a possible forward base from which to launch probes at the enemy; a base, moreover, with a well-advanced technology.

To the Gwynhyfarr, too, Terra meant only one thing: an industrial world where starships could be based and constructed and from which an attack on the enemy could be more easily launched.

Terra would be a valuable ally—or, failing that, a valuable slave planet.

The war began in earnest.

     Another goal was to depict two incompatible systems of warfare. An analogy to Renaissance naval warfare may be useful here; warfare in the Mediterranean was dominated by the galley. that in the Atlantic by the sailing ship. Gunnery was considerably more primitive than in later eras. primarily because gunports had not been invented, but also because bronze cannon were hideously expensive and iron cannon had a nasty tendency to explode. Consequently, sailing ships. with their relatively small manpower component, were unable to do much damage to galleys. Galleys were crammed with men — who could do little faced with a sheer wall of wood. A sailing vessel could not reasonably hope to attack a galley, nor vice versa.

     The situation in Web And Starship is similar; the Gwynhyfarr are masters of space, able to strike where they will, but without the ability to transport large numbers of troops quickly. FTL navies are all very fine, but in the final analysis, it’s the poor bloody infantry who gets the job done, as always. The Pereen can mass troops at a moment’s notice — but have very limited ability to send them anyplace. The result is a series of strategic and tactical problems that require some ingenuity to solve.

From WEB AND STARSHIP GAME MANUAL, Greg Costikyan (1984)

Northshield's Triumverate

In the story Northshield's Triumvirate by Joseph F. Patrouch, Jr. the author deliberately mandates some limitations on the FTL drive in order to force some limitations on spacecraft design, for purposes of the plot.

The waiting game, the stalemate, had developed because of the restrictions hyperspace drives put on the size of ships; too small a ship couldn't carry the hyperdrive unit plus the weapons and computers necessary for modern warfare, while too large a ship required too large a hyperdrive unit to leave room for anything else. So all the interstellar warships were approximately the same size with the same armament and capabilities.

Only one thing really differentiated the ships; the quality of the men inside them. The men who fought in this interstellar warfare did so out of pride and confidence in themselves and in their ships. If the battles were short, violently swerving periods when whirring computers directed laser beams and nuclear-armed missiles to the enemy’s weakest points, then the days and weeks in hyperdrive before and after engagements were lonely periods of work, preparing for battle, repairing after battle. Men could do nothing during those raging minutes, but men did maintain the ship and its military capabilities. All things being equal, as they usually were, the best maintenanced ship had the best chance for survival.

The captain of an interstellar warship did not fight. The computers did that. He did not decide the course or the targets or the weapons. The computers did all those things. The captain was a chief maintenance engineer in charge of the human components on board his ship. During a battle he remained in the Communications Center, desperately trying to keep track of the damage situation so that he could send crews wherever they might be needed. The First. Exec was stationed with the hyperdrive unit and did what he could to handle any immediate damage there, while the Second Exec was with the computers, trying to maintain the purity of the programming inserted by United Stellar in the face of heat, radiation and excessive gravity strains caused by battle maneuvers. This arrangement also distributed the members of the Triumvirate throughout the ship and made the survival of at least one of them more likely.

Interstellar warships could be any shape their designers wished, but the needs of interstellar war made them almost always cigarshaped. In this way they presented only the smallest of targets when two of them were approaching each other. Such a shape also made possible the fragmenting or compartmentalizing of the defensive shields along the sides of the ships. Most warships were about three hundred feet long, divided into some fifteen sections, each section with its own shield.

The Thopas and the Oliphant slowed rapidly as they neared one another. Gradually, the Oliphant began to pivot. Its circular front elongated as its weaponed sides swung around to bear on the Thopas. The Thopas matched the pivot, so that the ships stayed parallel as the distance between them shrank. The two ships floated to within ten miles of one another, then paused.

Northshield knew that sensing devices along both ships w'ere receiving data from each other’s shields and transmitting that information directly to their computers. The computers instantly sifted through that data seeking a clue to any deficiencies in shield strengths. The computer display panel in front of Northshield showed him that the Oliphant was the first to send its lasers lancing through the blackness to the Thopas, concentrating on section eleven. Eleven was a decoy section, purposely sending out faulty shield data, and the Thopas’ computer corrected the shield an instant before the lasers struck. A precious few moments had been gained while the Thopas evaluated more data before going offensive. Then it sent a warhead towards the number one section of the Oliphant. Simultaneously it swept its lasers randomly—so far as any human being could tell—along the Oliphant’s shields.

No ship was large enough and well enough equipped to pour full power into both offense and defense at the same time, especially when both ships had to keep enough power in reserve to enable it to get back home. All things being equal, two ships engaged in broadside conflict would fight to a stalemate; half power for offense, half for defense, until one ship was down to minimum power reserves for the return trip, at which time it would break off the engagement simply by warping into hyperspace and heading home. No decision. This sort of stalemate was avoided by segmenting the ships and using different amounts of power to attack and defend from each segment. Only computers could direct and respond quickly enough through such complex offensive and defensive maneuvers. And only well-maintenanced computers, weapons and shields had any hope of continuing to operate through such crazy manipulations and fluctuations.

The Thopas’ warhead shifted course and came in at the Oliphant on an angle cutting across shield areas. Suddenly it speeded up and darted in at section three. The three shield doubled its power to detonate the warhead before the nuclear. blast could shed radiation close enough to be dangerous to the computers’ delicate synapses. The Thopas then sent its concentrated laser beams to sections four, seven and five in rapid succession. Section five flared, every useable item in it, men and machines, destroyed.

“Score one for us,” Northshield said aloud. Then the Thopas lost section eleven. “Lucky for us eleven was a decoy,” he thought. Then, frustrated, he recalled that five may have been a decoy section for them.

The fluctuating shield strengths, the laser strikes, the warhead deployments and detonations all caused the Thopas to vibrate and even to rock slightly. Suddenly the Oliphant went to full defensive shields and rotated ninety degrees to bring a fresh set of warheads and lasers to bear. The Thopas started to follow suit, but after strengthening its shields and beginning its rotation, it abruptly halted at seventy-six degrees.

“Maintenance crew to gyros!” Northshield ordered urgently. Every second on full defense meant that much power expended non-offensively and that much less chance of destroying the Oliphant. With the Thopas presenting no offensive threat, the Oliphant cut its shields completely so that it could pour forth its power offensively. Northshield noticed then that the Thopas was drifting around ever so slightly, to eighty, then to eighty-one degrees.

“Cancel that last order.” He had finally realized what the computer was up to. The Oliphant’s computer probably had the Thopas' old laser angles of eighty-five to ninety-five degrees, and so it wouldn’t step up its shields again until the Thopas came around to eighty-four plus degrees. But new laser mounts had increased their angle one degree at each limit. At eighty-four degrees—

At eighty-four degrees the Thopas drained enough of its energy away from its defensive shields to blast the Oliphant out of the sky. The lasers detonated first the defensive shields’ power supplies and then the hyperdrive unit.

Suddenly, unexpectedly, incredibly, the atomic warheads went, all of them, simultaneously. In one gigantic globular flash the Thopas was washed with radiation all along the surface facing the Oliphant. The defensive shield protecting section four must have deteriorated because the radiation got through to the men and computers working there. The men, including Second Exec Johnson, received fatal dosages, and the computers were rendered useless.

Automatically, but too late, the Thopas lurched into hyperspace. Computerless and with a fifth of its crew dying of radiation poisoning, the Thopas had to be brought back to a central world. It had not been an easy flight. Even now, in his harness on board the Ulysses, Northshield felt the disappointment and guilt of what had happened. The Oliphant had been an unmanned decoy ship, sent up to engage in battle, then detonate. The Thopas, his command, had failed in its mission of destroying the Confederation outpost. In fact it had barely succeeded in escaping a trap. The other two planets which the United Stellar computers had predicted would be destroyed were in fact destroyed. The Confederation plan had succeeded, and Northshield had failed. No matter that even the computers on the Thopas had been fooled. As Triumvirate Captain, Northshield had been held directly responsible for the failure of the mission and the loss of two planets.

“I don’t see how,” he admitted. He slumped and waited for the death-dealing beams from the Monitor.

Incredibly, none came. Instead, the cylinder’s rocket came to life, pushing the weapon toward the Ulysses.

Northshield jumped. “The Monitor!" he exclaimed. “It’s not armed!”

The others stared at him. “Of course it’s not armed. Cromwell was lying to us about its armaments, trying to keep us in line. And we were so stupid it worked. Look; no ship that size could have both hyperdrive units and laser banks, and it couldn’t be here without hyperdrive. The only weapon they’ve got is the alien power drain and the cylinder they’ve mounted it in.”

Orlando joined in. “He’ll stay in reg-space, too. He wants to destroy us before we can repair the hyperdrive, and he can’t afford to leave and take the chance that somehow we’ll disable the alien weapon and get it for our own use. Circumstances tie him to reg-space as firmly as our inoperative hyperdrive ties us. We may yet pull it off. Captain.”

From NORTHSHIELD'S TRIUMVIRATE by Joseph F. Patrouch, Jr. (1975)

Designing Your Drive

If you want to do the job right, work backwards. Decide what type of universe you want for your book, figure out what implications it must have, then figure what constraints on the FTL will create the desired implications. Finally add a bit of colorful technobabble to describe the cause.

If you want to explore uncharted terrain, work forwards. Create a few unusual constraints, spend some time deducing some implications from the constraints, and see what sort of SF universe flows from the implications. You might stumble over an interesting universe for your next novel and/or game.


The Eschaton-verse has multiple solutions to FTL. There are starships; big lumps of moving matter that shuffle from planetary orbit out into deep space, push a magic button, and re-appear in deep space a very long way away from where they started (and hopefully a little bit closer to their destination planet). It's your classic 1950s space operatic jump drive, chosen simply because it makes for good fiction. But there are also "causal channels" — limited bandwidth instantaneous communicators. The snag with causal channels is that they are created as a quantum-entangled one time pad: you create a limited number of bits that, once used up, can't be replenished. You then have to send them to their destination without violating causality (which scrambles them), i.e. on a slower-than-light freighter that takes decades or centuries to arrive.

Finally, starships don't land on planetary surfaces. For getting goods and passengers on board and off again, they dock with space elevators (the one component of this transport set-up that is theoretically plausible).

Have you noticed something? This set-up allows for narrative structures that map onto intercontinental travel circa 1880-1914; we have railroads space elevators that link national planetary populations to ports space stations where steam starships dock, to transport passengers and cargo slowly between stops; and we have trans-oceanic telegraph cables causal channels to allow instantaneous (but expensive and limited-bandwidth) information transfer.

Designing For Combat

If you want to write science fiction stories about starship combat, you jolly well better have a set of limitations on your FTL drive that allows starship combat. Or your readers are going to point at you and laugh, and not buy any more of your books.

Ambush Drives

For instance, you do not want your FTL to permit nuclear sucker-punches.

If your FTL warships can fly through hyperspace (a "continuous" drive) and cannot be detected until they re-enter normal space, they can sucker-punch. Or if your FTL warships can instantly "jump" or teleport from one spot to any other spot they chose (a "discontinuous" drive), they too can sucker-punch.

Call it an Ambush Drive. If it is a "continuous" drive it is a Stealth Ambush Drive. If it is a "discontinuous" drive it is a Teleport Ambush Drive.

By "nuclear sucker-punch" I mean that interstellar wars only last long enough for your hyperspace bombers to fly to the enemy's unsuspecting planets, then surprise them with an emergence into normal space lasting just long enough to spit out a hellburner, a planet-wrecker nuclear bomb, a planet-sterilizing torch warhead, a planet-cracker antimatter warhead, or a planet-buster neutronium-antimatter warhead. Or take a bit more time to simply carpet-bomb the planet with old-school nuclear bombs. The enemy planets will be caught flat-footed, and be seared clear of life before they realized what hit them. The hyperspace bombers then fly home, only to discover that the enemy's bombers were on a similar mission and your homeworlds have also been burnt off.

Sort of like the US and Russia armed with invisible ICBMs. The first who launches will win. The winning strategy is First-Strike.

The war, the lifespan of everything on Terra, and your novel will be over far too quickly (like five minutes, tops). As will the number of readers you have, because reading about such wars is intensely boring.

(There actually is an Ambush Drive in David Drake's THE FORLORN HOPE. For some odd reason nobody uses nuclear bombs, just chemical explosives.)

A defender can attempt to surround all their planets with defending fleets and orbital fortresses to counter sucker-punches, but this is a losing game. The attacking enemy always has the initative, and they can show up with a much larger fleet (the enemy has the power of Concentration of Force). Unless you happen to have enough surplus manufacturing capacity so you can park a defending fleet as large as the enemy's entire star fleet around every single one of your worlds. Which is still a waste of good manufacturing ability.

Even if for some reason Ambush Drives are not used to incinerate enemy planets at the earliest opportunity, the other problem is that it makes all interstellar battles occur only by mutual consent. No intercepting incoming starfleets, no heading them off at the pass, no dry gulching, no nothing. No dramatic tales of piracy either. Your fleet and the enemy will have to come to an agreement on when and where the battle will happen. As will the pirate corsair and the hapless merchant ship, which presents a bit of a problem for the pirate. Again, makes for a quite boring scifi plot. And also damaging to sales of your novels.

These start-anywhere go-anywhere drives (Teleport Ambush Drives) play merry Hell with concepts like 'distance', 'remoteness', 'proximity', 'adjacency', 'line of communication', 'border', and 'defence', while reinforcing such concepts as 'trade', 'concentration of force', and 'first strike'.

(Please avoid such stupid FTL drives and) Give me a setting in which the map still matters.

Mr. Evill points out that a Teleport Ambush Drive has no conception of distance, remoteness, proximity, and adjacency since all voyages are one jump regardless of distance. There is no concept of lines of communication, border, and defense because starships on defense cannot stop the progress of attacking Ambush ships. The defenders don't even see the attackers, because the attackers jump right over them. Teleport Ambush Drives make the tactics of concentration of force, and first strike even more effective: the defender cannot see you coming so why not attack first with your entire fleet? And Teleport Ambush Drives encourage trade because all possible trading sites are the same distance (one jump) regardless of where they are physically located in space.

Christopher Weuve (who works for the US Department of Defense) found a disappointing "border" failure in Stephen R. Donaldson's The Gap series. In the first book of the series the reader learns two facts:

  1. The FTL drives can travel to any single particular cubic meter location in the entirely of known space
  2. The Human empire has all of its combat starships spread out at the rim of Human empire space in order to stop an enemy invasion at the border.

At this point, Mr. Weuve looked up from the novel, raised one eyebrow, and noted those two facts contradict each other. Fact #1 mean the FTL drives are those accurséd "start-anywhere go-anywhere" Ambush Drives that play merry Hell with concepts like "border", the kind that Mr. Evill was unhappy about. Fact #2 was that the Human empire was apparently unaware of this since they stationed their defending ships on the border.

Then in a later Gap book, an alien invasion fleet starts outside the Human empire, makes one jump directly to Terra while totally bypassing all the Human combat starships at the border, and sucker-punches a defenseless Terra.

It takes all of Mr. Weuve's self-control to avoid throwing the novel across the room.

Cut and Run Drives

Another author FTL design goal is keeping your opponent from running away. If you are fighting in normal space (not hyperspace or something) and have shot enough holes in your opponent to convince them that they are losing, they'll dodge into hyperspace and flee at many multiples of the speed of light. They will travel to a repair dock and return to fight another day. The same thing will happen when a pirate corsair attacks a merchant ship. The merchant will skedaddle into hyperspace like a scared jack rabbit. Chances are the readers fill find this frustrating.

Limitations to prevent this include:

  • The FTL drive requires a long time to charge up the capacitors to the point where the drive can be activated. And/or require energy to be diverted from weapons and defenses into the FTL drive.
  • The FTL drive can only be activated if the ship is at a certain location (see jump points). If the FTL method is some kind of stargate or other installation, you can position your ships to interdict the gate, forcing your opponent to run the gauntlet.
  • If your ship grabs your opponent with a "tractor beam" or other handwaving device it will prevent your opponent from escaping.
  • Mandate that combat occurs within hyperspace (not normal space), so enemy ships cannot escape unless they can out-run you. And out-run your missiles.

Otherwise you the author can just assume enemy ships fleeing is just one of those unpleasant aspects of starship combat. And forego writing romantic tales of pirates.

Anti-Combat Drives

Greg Costikyan created a rather interesting military situation in his tabletop wargame Web and Starship. One race uses a Continuous drive (hyperspace starships), the other uses a Discontinuous drive (stargates). The consequence is side neither can invade each other due to how each FTL method's advantages and disadvantages interact with the other.

Combat Rating Hyperdrives

If your spacecraft use a continuous drive (hyperdrive, warp drive, or other drive where they "fly" through space instead of teleporting), there are three limits that together will allow starship combat:

  • Invading starship must travel slow enough that a defender has enough time to try and stop them. if the time between being spotted at the limits of detector range and arriving at bombing positions over Terra is two nanoseconds, mutual combat is impractical. The same goes for a pirate corsair trying to jump a merchant ship.

  • There must exist some kind of faster-than-light radar that can detect the invading ships. It will warn the defender planet about the invading fleet, and it will allow the defending starships to intercept said fleet. This can be a large hyper-radar installation on the planet, a network of patrolling scoutships armed with FTL radar and FTL radios to shout the alert, interstellar spy satellites, whatever. The defender ships need such radar or they won't be able to find the invaders. Nor can the pirates find the merchants.

  • There must exist some kind of anti-ship weapons that will function under FTL drive. The defender has to be able to shoot at the invaders or the invaders will just go whizzing by while flipping you the bird. If your ship is travelling at twenty times the speed of light, firing a laser beam at only light speed will just have the beam pile up in front of the cannon like unrolling a roll of glowing toilet paper.

The idea is to set up some sort of situation similar to wet navy combat in the Pacific ocean in the period after the time the navy was equipped with radar, but before the advent of orbital spy satellites that can see every ship on the ocean. This is more or less the situation in the Star Trek TV show(s).

Note that Star Wars does not have FTL radar, so they can do nuclear sucker-punches. The only reason the Empire is still around is because they have thousands of times more ships than the rebels. Apparently the ships in Star Wars have no weapons that operate under FTL drive, they always exit hyperspace for normal space before they start shooting.

Often the weapons take the form of missiles equipped with their own little FTL drives. Sometimes they are laser-like directed energy weapons using some sort of energy that is faster than light. Other novels postulate that conventional weapons will work as normal, provided that you and the enemy are in the same continuum. That is weapons will work if you are both in hyperspace or both in normal space, but not if you are in one and they are in the other.

In his Polesotechnic series, Poul Anderson postulated that starship moved FTL by microjumping at a certain frequency. If the enemy ship was at a different frequency, or at the same freqency but out of phase, your ship would be transparent to the enemy's weapon fire. At least until the enemy adjusted their frequency and phase to match yours, so watch out! In Star Trek phaser beams are "warp-accelerated" to faster than light speeds, whatever that technobabble means. In David Gerrold's Yesterdays' Children the warp drive ships fire warp-drive missiles. The missiles have no explosive warhead, instead they try to ram the target. The intersection of the two warp fields will overload the target's stasis generators, instantly destroying the enemy ship.


(ed note: In Star Trek, starships use warp drive to envelope themselves in a bubble of warped space, that can somehow allow the ship to move faster than light. The bubble does not exist in normal space, it protrudes into something called "subspace.")

      Most battles in space are either over almost the instant they begin—as had evidently been the case with the two surprised Klingon vessels—or became very protracted affairs, because of the immense distances involved. (The first sentence of Starfleet Academy’s Fundamentals of Naval Engagement reads: “The chief obstacle facing a Starship Captain who wishes to join battle is that battle is almost impossible to join.”)

      And they won't be alone, Kirk thought. Nevertheless, he could forget about it for the time being. That still left the problem of the Klingon ships on the tail of the Enterprise.
     Sowing a mine field in the ship's wake would be useless; the enemy craft doubtless had deflectors, and in any event the mines, being too small to carry their own warp generators, would simply fall out into normal space and become a hazard to peacetime navigation. But wait a minute…

     "Mr. Spock, check me on something. When we put out a deflector beam when we're on warp drive, the warp field flows along the beam to the limit of the surface area of the field. Then, theoretically, the field fails and we're back in normal space. All right so far?"
     "Yes, Captain, a simple inverse-square-law effect."
     "And contrariwise," Kirk said, "using a tractor beam on warp drive pulls the field in around the beam, which gives us a little extra velocity but dangerously biases our heading." Spock Two nodded. "All right, I think we've got the basis for a little experiment. I want to plant a mine right under the bow of that cruiser, using a deflector and a tractor beam in tandem, with a little more power on the deflector. At the same time, I want our velocity run up so that our warp field will fail just as the mine explodes. Fill in the parameters, including the cruiser's pseudo distance and relative velocity, and see if it's feasible."

     Spock Two turned to the computer and worked silently for a few moments. Then he said, "Yes, Captain, mathematically it is not a complex operation. But the library has no record of any Starship ever surviving the puncturing of its warp field by a deflector while under drive."
     "And when nearly balanced by a tractor?"
     "No pertinent data. At best, I would estimate, the strain on the Enterprise would be severe."
     Yes, Kirk thought, and just maybe you don't much want that Klingon cruiser knocked out, either.

     "We'll try it anyhow. Mr. Sulu, arm a mine and program the operation. Also—the instant we are back in normal space, give us maximum acceleration along our present heading on reaction drive."
     "That," Spock Two said in the original Spock's most neutral voice, "involves a high probability of shearing the command section free of the engineering section."
     "Why? We've done it before."
     "Because of the compounding of the shock incident upon the puncturing of the warp field, Captain."
     "We'll take that chance too. In case it has escaped your attention, we happen to be in the middle of a battle. Lieutenant, warn ship's personnel to beware shock. Stand to, all, and execute."

     Spock Two offered no further obstructions. Silently, Uhura set up on the main viewing screen a panorama of the sector in which the trap—if it worked—was to be sprung. The Klingon cruiser would have looked like a distorted mass of tubes and bulbs even close on, under the strange conditions of subspace; at its present distance, it was little more than a wobbly shadow.
     Then the dense, irregular mass, made fuzzy with interference fringes, which was the best view they could hope to get of the mine, pushed its way onto the screen, held at the tip of two feathers of pale light, their pinnae pointing in opposite directions, which were the paired deflector and tractor beams (which in normal space would have been invisible). As the mine reached the inside surface of the warp field, that too became faintly visible, and in a moment was bulging toward the Klingon vessel. The impression it gave, of a monstrous balloon about to have a blowout, was alarming.
     "Mr. Sulu, can the Klingon see what's going on there from the outside, or otherwise sense it?"
     "I don't know, Captain. I wish I couldn't."
     "Lieutenant Uhura?"
     "It's quite possible, Captain, considering how excited the warp field is becoming. But perhaps they won't know how to interpret it. Like the library, I've never heard of this having been tried before, and maybe the Klingons haven't either. But I'm only guessing."
     The bulge in the warp field grew, gradually becoming a blunt pseudopod groping into subspace. From the Enterprise it was like staring down a dim tunnel, with the twin beams as its axis. From the depths of his memory there came to Kirk a biology-class vision of the long glass spike of a radiolarian, a microscopic marine animal, with protoplasm streaming along it, mindless and voracious.

     "Captain," the intercom squawked. "I've got trouble down here already. My engines are croonin' like kine with the indigestion."
     "Ride with it, Mr. Scott, there's worse to come." The blunt projection became a finger, at the tip of which the mine, looking as harmless as a laburnum seed, dwindled into the false night of subspace. Very faintly, the hull of the Enterprise began to groan. It was the first time in years that Kirk had heard his ship betray any signs of structural strain serious enough to be audible.
     "Thirty seconds to breakout," Spock Two said. "The Klingon's peeling off!" Uhura cried. "He's detected something he doesn't like, that's for sure. And he's under full drive. If…"
     Was the mine close enough? Never mind, it would never be any closer.
     "Fire, Mr. Sulu," Kirk said.

     An immense ball of flame blossomed on the view screen—and then vanished as the Enterprise dropped into normal space. One second later, deprived of the ship's warp field, the fireball, too, was back again. "Got him!" Sulu crowed.
     The fireball swelled intolerably as the matter and anti-matter in the doomed Klingon's warp-drive pods fused and added their violence to the raging hydrogen explosion of the mine. The viewing screen dimmed the light hurriedly, but finally could accommodate it no longer, and blacked out entirely.
     At the same time, the Enterprise rang with the blowtorch howling of the reaction engines coming up to full thrust, and a colossal lurch threw them all to the deck. The light flickered.

     "Posts!" Kirk shouted, scrambling back to his command chair. "All department heads, report!"
     The ship was screaming so fearfully in all its members that he could not have heard the answers even had his staff been able to hear the order. But a sweeping glance over the boards told him the bare-knuckle essentials; the rest could wait though not for long.
     The Enterprise had held together—just barely. The three surviving Klingon corvettes had taken several seconds to react to the destruction of their command cruiser and the disappearance of their quarry. They had dropped out of warp drive now, but in those few seconds had overshot their target by nearly a million miles, and the long, separating arcs they were executing now to retrace their steps were eloquent of caution and bafflement—and, if Kirk knew his Klingons, of mind-clouding fury.

     The Enterprise, so fleet on warp drive, was something of a pig under reaction thrust, but she was wallowing forward bravely, and gaining legs with every stride. Within only a few minutes she would be plowing through the very midst of her erstwhile harriers.
     "Klingons launching missiles, Captain," Uhura reported.
     Pure, random desperation. "Disregard. Mr. Sulu, engage the enemy and fire at will. When you're through with them, I don't want one single atom left sticking to another."
     "Yes, sir," Sulu said, a wolfish grin on his normally cheerful face. This was the opportunity of a lifetime for a Starship gunnery officer, and he was obviously enjoying it thoroughly.

     As the Enterprise picked up speed, she responded better to her helm; in that respect she did not differ much from a nineteenth-century clipper ship on the high seas, though the comparison failed utterly on warp drive. And she had a tremendous amount of energy to expand—indeed, even to waste—through her reaction engines. The Klingons apparently were stunned to see her bearing down on them, but their stupor didn't matter now. The corvettes could not have reformed in time to meet her, even had their commanders understood the situation instantly.
     Sulu's hands danced over the studs before him. A stabbing barrage of phaser fire shot out from the Enterprise. The deflector screens of the corvettes fought back with coruscating brilliance; the viewing screen, which had crept cautiously back into operation after the death of the cruiser, dimmed hastily again.
     Then there were no Klingon corvettes—only clouds of incandescent gas, through which the Enterprise sailed as majestically as an ancient Spanish galleon over a placid Caribbean bay.

From SPOCK MUST DIE! by James Blish (1970)

(ed note: Warning, Spoilers for the story "Margin of Profit". Nicholas van Rijn is the master of an interstellar trading corporation. One of their trade routes goes through a choke point, right past the dreaded Borthudians. The Borthudians are using their navy to capture the merchant ships, seizing the ships and cargo, and electronically brain-washing the valuable crew so they will use their technical training on behalf of the navy. Bypassing the planet would render the trade route unprofitable, but neither van Rijn nor the guild of ship crews are happy about the piracy.)

(Nicholas van Rijn has an idea. He makes a Q-ship that looks just like a merchant ship [the Mercury], sends it past the Borthudians, and captures the next Borthudian raider [the Gantok]. Then he explains the facts of life to the Borthudian captain, and sends the captain home with the bad news.)

      Torres licked sandy lips. Turning up the magnification in a viewscreen, he picked out the Borthudian frigate. She was a darkling shark-form, only half the tonnage of the dumpy merchantman but with gun turrets etched against remote star-clouds. She came riding in along a smooth curve, matched hypervelocities with practiced grace, and flew parallel to her prey, a few kilometers off.
     A small, pulsing jar went through hull and bones. Gantok had reached forth a tractor beam and laid hold of Mercury.
     "Torres," said van Rijn. "You stand by, boy, and take over if somewhat happens to me. I maybe want your help anyway, if the game gets too gamy. Petrovich, Seiichi, you got to maintain our own beams and hold them tight, no matter what. Hokay? We go!"
     Gantok was pulling herself closer. Petrovich kicked in full power. For a moment, safety arcs blazed blue, ozone spat forth a smell of thunder, a roar filled the air. Then equilibrium was reached, with only a low droning to bespeak unthinkable energies at work.
     A pressor beam lashed out, an invisible hammerblow of repulsion, five times the strength of the enemy tractor. Van Rijn heard Mercury's ribs groan with the stress. Gantok shot away, turning end over end, until she was lost to vision among the stars.
     "Ha, ha!" bellowed van Rijn. "We spill their apples, eh? By damn! Next we show them real fun!"

     The Borthudian hove back in sight. She clamped on again, full-strength attraction. Despite the pressor, Mercury was yanked toward her. Seiichi cursed and gave back his full thrust.
     For a moment van Rijn thought his ship would burst open. He saw a deckplate buckle under his feet and heard metal elsewhere shear. But Gantok was batted away as if by a troll's fist.
     "Not so hard! Not so hard, you dumbhead! Let me control the beams." Van Rijn's hands danced over the console. "We want to keep him for a souvenir, remember?"
     He used a spurt of drive to overhaul the foe. His right hand steered Mercury while his left wielded the tractor and the pressor, seeking a balance. The engine noise rose to a sound like heavy surf. The interior gee-field could not compensate for all the violence of accelerations now going on; harness creaked as his weight was hurled against it. Torres, Petrovich, and Seiichi made themselves part of the machinery, additions to the computer systems which implemented the commands his fingers gave.

     The Borthudian's image vanished out of viewscreens as he slipped Mercury into a different phase. Ordinarily this would have sundered every contact between the vessels. However, the gravitic forces which he had locked onto his opponent paid no heed to how she was oscillating between relativistic and nonrelativistic quantum states; her mass remained the same. He had simply made her weapons useless against him, unless her pilot matched his travel pattern again. To prevent that, he ordered a program of random variations, within feasible limits. Given time to collect data, perform stochastic analysis, and exercise the intuition of a skilled living brain, the enemy pilot could still have matched; such a program could not be random in an absolute sense. Van Rijn did not propose to give him time.
     Now thoroughly scared, the Borthudian opened full drive and tried to break away. Van Rijn equalized positive and negative forces in a heterodyning interplay which, in effect, welded him fast. Laughing, he threw his own superpowered engine into reverse. Gantok shuddered to a halt and went backwards with him. The fury of that made Mercury cry out in every member. He could not keep the linkage rigid without danger of being broken apart; he must vary it, flexibly, yet always shortening the gap between hulls.
     "Ha, like a fish we play him! Good St. Peter the Fisherman, help us not let him get away!"

     Through the racket around him, van Rijn heard something snap, and felt a rushing of air. Petrovich cried it for him: "Burst plate—section four. If it isn't welded back soon, we'll take worse damage."
     The merchant leaned toward Torres. "Can you take this rod and reel?" he asked. "I need a break from it, I feel my judgment getting less quick, and as for the repair, we must often make such in my primitive old days."
     Torres nodded, grim-faced. "You ought to enjoy this, you know," van Rijn reproved him, and undid his harness.
     Rising, he crossed a deck which pitched beneath his feet almost as if he were in a watercraft. Gantok was still making full-powered spurts of drive, trying to stress Mercury into ruin. She might succeed yet. The hole in the side had sealed itself, but remained a point of weakness from which further destruction could spread.

     At the lockers, van Rijn clambered into his outsize spacesuit. Hadn't worn armor in a long time … forgotten how quickly sweat made it stink. … The equipment he would need was racked nearby. He loaded it onto his back and cycled through the airlock. Emerging on the hull, he was surrounded by a darkness-whitening starblaze.
     Any of those shocks that rolled and yawed the ship underfoot could prove too much for the grip of his bootsoles upon her. Pitched out beyond the hyperdrive fields and reverting to normal state, he would be forever lost in a microsecond as the craft flashed by at translight hyperspeed. Infinity was a long ways to fall.
     Electric discharges wavered blue around him. Occasionally he saw a flash in the direction of Gantok, when phasings happened momentarily to coincide. She must be shooting wildly, on the one-in-a-billion chance that some missile would be in exactly the right state when it passed through Mercury … or through van Rijn's stomach … no, through the volume of space where these things coexisted with different frequencies … must be precise. …

     There was the fit-for-perdition hull plate. Clamp on the jack, bend the thing back toward some rough semblance of its proper shape … ah, heave ho … electric-powered hydraulics or not, it still took strength to do this; maybe some muscle remained under the blubber … lay out the reinforcing bars, secure them temporarily, unlimber your torch, slap down your glare filter … handle a flame and recall past years when he went hell-roaring in his own person … whoops, that lunge nearly tossed him off into God's great icebox!
     He finished his job, reflected that the next ship of this model would need still heavier bracing, and crept back to the airlock, trying to ignore the aches that throbbed in his entire body. As he came inside, the rolling and plunging and racketing stopped. For an instant he wondered if he had been stricken deaf.
     Torres' face, wet and haggard, popped into an intercom screen. Hoarsely, he said: "They've quit. They must realize their own boat will most likely go to pieces before ours—"
     Van Rijn, who had heard him through a sonic pickup in his space helmet, straightened his bruised back and whooped. "Excellent! Now pull us up quick according to plan, you butterbrain!"

     He felt the twisting sensation of reversion to normal state, and the hyperdrive thrum died away. Almost he lost his footing as Mercury flew off sidewise.
     It had been Rentharik's last, desperate move, killing his oscillations, dropping solidly back into the ordinary condition of things where no speed can be greater than that of light. Had his opponent not done likewise, had the ships drawn apart at such an unnatural rate, stresses along the force-beams linking them would promptly have destroyed both, and he would have had that much vengeance. The Terran craft was, however, equipped with a detector coupled to an automatic cutoff, for just this possibility.

     Torres barely averted a collision. At once he shifted Mercury around until her beams, unbreakably strong, held her within a few meters of Gantok, at a point where the weapons of the latter could not be brought to bear. If the Borthudian crew should be wild enough to suit up and try to cross the intervening small distance, to cut a way in and board, it would be no trick to flick them off into the deeps with a small auxiliary pressor.
     Van Rijn bellowed mirth, hastened to discard his gear, and sought the bridge for a heart-to-heart talk with Rentharik. "—You is now enveloped in our hyperfield any time we switch it on, and it is strong enough to drag you along no matter what you do with your engines, understand? We is got several times your power. You better relax and let us take you with us peaceful, because if we get any suspicions about you, we will use our beams to pluck your vessel in small bits. Like they say on Earth, what is sauce for the stews is sauce for the pander… Do not use bad language, please; my receiver is blushing." To his men: "Hokay, full speed ahead with this little minnow what thought it was a shark!"

From MARGIN OF PROFIT by Poul Anderson (1956)
Combat Rating Jump Drives

The standard way to allow combat with discontinuous drives (jump drives or teleporting drives) is to drastically limit the locations a jump drive ship can travel to. A faster-than-light jump drive that can jump anywhere is too powerful. It can do nuke sucker-punches at will.

  • A matter transmitter needing both transmitter and receiver, large enough to teleport an entire starship. Ship requires no FTL drive, the external transmitter is the drive. The locations are the sites of the transmitters and receivers. Sometimes a transmitter can send a ship to any receiver in range, sometimes they can only send ships to its paired receiver.
  • A portal-to-portal "stargate". When energized this opens a hole in space between two fixed points that lots of starships can pass through. Once the power is off the gate closes. Again the ships require not FTL drive, the external stargate is the drive. Like matter transmitter these might be paired, or to selectable destinations as in Stargate SG-1.
  • A permanent gate or "wormhole". This is like a stargate except it requires no power and is always open. The two ends of the wormhole are fixed, starting at one end the only possible destination is the other end.
  • A multiple-connection jump drive. Fixed locations in space are "jump points", paired to another jump point light-years away. A starship equipped with a jump drive can enter a jump point location, energize its jump drive, and the ship will instantly teleport to the paired jump point. Discovering new jump points is usually difficult and tedious.

The locations ("jump points") become military choke points, thus allowing starship combat (the invader cannot avoid the defenders choking off the choke point). The combat occurs in normal space after the invading starships materialize in the destination jump point, so conventional weapons can be used. Generally the starship is in wacky-hyper-FTL-UpYoursEinstein-space for no longer than a fraction of a second, so there is no combat in wacky-hyper-FTL space requiring bizarre hyperspace weapons. The invader enters the start jump point, activates their jump drive, vanishes from the start jump point and instantly appears at the destination jump point.

Arguably this was invented by Larry Niven and Jerry Pournelle (contracting Dan Alderson), under the name "Alderson Drive". It has been used in many tabletop SF starship combat games since game designers knew a good thing when they saw it. I think the first was the game Starfire.

Jump points can range in size from barely big enough for a starship to squeeze through to regions a couple of hundred or couple of thousand kilometers in diameter (generally with incoming ships arriving at a random location within the region). If the jump point covers a larger area than can be comfortably interdicted by defending orbital fortresses and task forces, then it really ain't a military choke point now is it?. Meaning it is disqualified as being a jump drive which allows combat.

In science fiction, jump points are generally very limited in number within a star system.

If jump points occur naturally, there are usually fewer than 10 in any given star system.

If jump points are artificial, they are either very difficult to construct, or they are left-over technology from some long-gone Forerunner culture (i.e., they are impossible to construct, by us). In either case battle fleets will generally never ever destroy such a point, for reasons supplied by the author.

Now, in most science fiction, jump points are always detectable. If it is a permanent wormhole gate, the jump point is pretty obviously the swirly hole thingy throwing off rainbow sparks. If it is an ordinarily invisible "jump point", special detection equipment can locate them ("clumping of isogravity lines" or similar technobabble). Usually exploration scout ships when entering a new star system will use such equipment to locate all the system's jump points. After the system has been scouted, each new jump point will be explored by a scout ship to see what new system is on the other side.

The main exception I ran across was with the Starfire game and related novels. The reason was to craft a militarily interesting setup. There were a small number of jump points that were undetectable by sensor (the game called them "closed warp points"). The only way they could be found is if a ship entered the paired jump point (which had to be a detectable kind of course). The ship who transited the jump point would discover the location of the undetectable jump point, as would anybody nearby who noticed the transiting ship appearing out of nowhere (presumably there exist jump point pairs where both points are undetectable, but for practical purposes they do not exist since they are unfindable).

What was the game designer's motiviation to make such points? To allow (one-time) strategic surprise.

Say there was no such thing as an undetectable jump point. When a new star system was colonized, the owner would naturally build bastion space forts around all the jump points. An invasion would automatically be a slog through an endless series of defended jump points. Very boring.

Things become much more exciting if undetectable jump points exist. The star system may think it is utterly safe behind a wall of heavily defended jump points. Up until the moment when the enemy invasion fleet comes pouring through a previously unknown and totally undefended jump point, turning the system of space forts into a worthless Maginot Line.

The star system can now fortify this undetectable previously-unknown jump point. Assuming it survives the invasion fleet. The surprise only works once, but sometimes once is enough.

Undetectable jump points can provide strategic surprise more than once if the nobody else observes you using it.

For example, say one of system Alfa's jump points links to system Bravo, and Bravo only has a link to system Alfa and system Charlie. You have an inhabited planet at Alfa and Charlie, Bravo is uninhabited.

If Alfa is part of the heavily defended inner empire, system Charlie might not bother setting up space forts around the jump point to Bravo. Those forts are expensive so it is better to fortify the other jump points and assume that system Alfa will be guarding the Bravo point.

Up until the point when the enemy discovers the undetectable jump point into Bravo.

As long as the enemy is lucky, they can use the hidden jump point multiple times. As long as there are none of your ships present in system Bravo to see the enemy ships. Or if one is present, and the enemy manages to destroy it before it can escape system Bravo and sound the alarm. The enemy can vacate system Bravo through the hidden jump point, leaving you the mystery of the vanishing ship when you send your own ships into Bravo looking for the lost stray.

Later, the enemy can use system Bravo as a staging point for their invasion of system Charlie.


(ed note: In the map, the empire of the Khanate of Orion and the dreaded Arachnid Omnivoracity are unaware that their empires are connected at the Shanak star system. That system has two warp points, both of them closed warp points. Remember that closed warp points are undetectable, they are discovered by somebody exiting the closed point and by anybody observing somebody exiting the closed point.

Boxes are star systems. Systems Alowan, Kilean, and Hairnow are inhabited systems of the Khanate of Orion. Octagons labled "KON" lead to the rest of the Khanate empire. Home Hive II is an inhabited system of the dreaded Arachnids.

Lines show jump connections between systems, with paired warp points, one point in each system. So the Telmasa system has three warp points, one leading to system Alowan, one to Kilean, and one to Hairnow.

Solid lines have detectable warp points in both systems. Dotted arrow lines have an undetectable closed warp point at the arrowhead, and a detectable warp point at the butt end. So system Shanak has two closed warp points, while both Kilean and Bug 06 have detectable warp points leading to Shanak.

The bottom line is that both the Khanate of Orion and the Arachnid Omnivoracity think the Shanak system is a dead-end system. Neither know that there are two closed war points, not one.)

(ed note: The Khanate of Orion survey ship Acutar and five sister ships are re-surveying the dead-end Shanak system, then exit via the closed warp point to return to Kilean)

      Least Claw of the Khan Shaiaasu'aaithnau sighed in relief as his six Lahstyn-class light cruisers headed for the warp point. Under other circumstances, he would have enjoyed exercising his first squadron command, but the Shanak System was and always had been as useful as a screen door on an airlock. It was lifeless, a cul-de-sac accessible only via a single closed warp point, whose sole claim to importance was that it lay adjacent to the extremely useful Kliean System. Unlike Shanak, Kliean boasted two habitable planets and an immensely rich asteroid belt. It was one of the Khanate's oldest and wealthiest inhabited systems … and the only reason Shaiaasu and his ships had just spent a thoroughly boring month resurveying Shanak.

     He let himself relax as his lead ship entered the warp point, and lazy thoughts chased about his brain. He understood the panic behind his orders. If the rumors from the Human's Justin System were true, even the potential for a similar threat to a system like Kliean must be terrifying to the Khan's administrators. And, he admitted, the survey data on Shanak had been over four Orion centuries old. Improved instrumentation might have discovered a second warp point—it had not, but it might have—yet that had made the mission no less boring, and he felt abandoned so far from the front. Not that Lahstyn-class cruisers would have been much use in combat.

     He purred a chuckle at the thought of his little survey ships leading a life-or-death attack. He had seen one of Humans' Hun-class cruisers. Now there was a survey ship! But the Federation was wealthy enough to build such vessels for survey work, and the Zheeerlikou'valkhannaieee were not. Indeed, he took a sort of perverse pride in his command's austerity. Humans might need big, comfortable ships; Orions did not. Not, he admitted, that he would refuse one!

     He chuckled again, then braced himself as his own ship entered the warp point. Acutar seemed to twitch around him in the familiar stress of transit, and he carefully did not grunt in relief as the brief nausea eased. He gazed longingly into his plot at the blue dot of the planet Masiahn. He had relatives down there—and he wished he had time to visit them. Masiahn was one of the jewels in the Khan's crown, a beautiful world of mountains, forests, and swift, white-foaming rivers. The planet had an enormous tourist trade, and Shaiaasu would have loved to spend a few weeks there. The jahar hunting was excellent, and not many could mount one of the needle-tipped antler racks on his wall or claim he'd taken the beast with no weapon but his own claws.

(ed note: in a strategic disaster for the Khanate, lurking in the Shanak System is a picket ship of the dreaded Arachnid Omnivoracity, hidden by a cloaking device)

     The cloaked cruiser watched the last enemy vessel disappear. It had been astounded when the enemy first appeared, for this system had always been useless. Reachable only via a closed warp point and with no outbound warp points, it had never attracted any attention. Yet doctrine was inflexible: any star system, however useless, must be picketed, and so this one had.

     Now the cruiser waited, making absolutely certain of the coordinates of the second closed warp point through which the enemy vessels had vanished before it fired its courier drone home.

(ed note: Later a cloaked invasion force of Arachnid warships uses the closed warp point to enter the Kliean system.)

     The freighter Sellykha was no swift thirahk. In fact, she was big, ugly, ungainly, and about as maneuverable as an over-age asteroid, but her captain loved her. The resource extraction ship had never been out of Kliean. She made her routine trips between the asteroid belt and the orbital smelters, earning her owners a steady if unspectacular profit, and if it was a boring berth, well, Shipmaster Faarsaahl'ynaara had earned a bit of boredom in the autumn of his life.

     He stepped onto the bridge, crossed to his command chair, and paused to check the engineering readouts. Number Two engine room had reported the recurrence of that irritating harmonic, and he wanted a detailed record for the yard techs. "Engineer's imagination" indeed! This time he would make those thaarkoni admit there was a problem and do something about it.

     "Shipmaster?" He looked up at his fourth officers call. The youngsters ears were half-flattened, and he waved at his display. "Could you look at this, Sir?"
     Faarsaahl crossed the bridge, wondering what fresh totally prosaic discovery Huaath had made. You were young once yourself, he chided himself, but the cub was so shiny and new Faarsaahl kept looking for milk on his lips.
     "What is it?"
     "I am not certain, Sir." Huaath peered intently into his display as his claws ticked gently over his panel. "I seem to be picking up some sort of drive field."
     "A drive field? Out here?" Faarsaahl tried to keep the incredulity out of his voice.
     "Yes, Sir. Its frequency matches nothing in our database, however." Huaath waved at his display. "Look for yourself."

     Faarsaahl peered over the youngster's shoulder, and his spine stiffened, for there was a drive field out there. Sellykha's sensors fell far short of Navy standards, but the signature burned clear and sharp, and Faarsaahl felt his claws slip from their sheaths in sudden, terrible suspicion.
     "Its vector?" he asked quietly.
     "It appears to be inbound from Shanak," Huaath said, and Faarsaahl's belly knotted. He stared at the display for one more moment, then turned sharply to his communications officer.

     "Get your transmitter on line!" The com officer blinked in surprise, and Faarsaahl bared his fangs. "Quickly! Alert Masiahn and Zhardak that unknown starships have entered the system!"
     The com officer stiffened, whiskers aquiver in sudden understanding, and bent over his panel with frantic haste. Faarsaahl watched him, then turned back to his fourth officer and laid a clawed hand on the confused youngster's shoulder.
     "Inform them that Fourth Officer Huaath'raamahl spotted them," he told the com officer quietly. "See to it that they know it was only his alertness which let us get the warning off."
     "Aye, Shipmaster," the com officer said equally quietly, and Faarsaahl squeezed Huaath's shoulder. The cub still hadn't realized, he thought sadly. Sellykha had only a freighter's speed, but at least he could insure that Clan Raamahl knew it had a new father-in-honor. (meaning there is no way they can outrun the invaders, they are all going to die)

(ed note: In the uninhabited Telmasa system, commander Zhaarnak and his battle group gets the bad news about the Arachnid invasion of Kilean via the interstellar communication network)

     Zhaarnak'diaano stared at his flag captain.
     "What strength?" he demanded.
     "The Governor had little data when he transmitted the alert," Daarsaahl replied flatly. "Sellykha was destroyed within minutes of sending her warning. Shipmaster Faarsaahl continued sending updates to the last, but he had seen only twenty or thirty light cruisers at that time."

     "Valkha," Zhaarnak whispered. At least the message had reached him quickly via the interstellar communication network comsats that relayed light-speed transmissions between warp points, but his thoughts seemed frozen. Shanak. They had come from Shanak, but how—?
     "They tracked Shaiaasu," he said softly. "They must have. But how did they get there?"
     "There must be a second closed warp point." Daarsaahl's ears went flat as she spoke. "Minisharhuaak! Our own survey showed them the way!"

     Zhaarnak shook off his paralysis and spun to his com section.
     "Emergency priority, Juaahr! All units are to form on Dashyr for transit to Kliean. Then set up a conference link with the carrier commanders. Request an immediate update on squadron readiness states from farshathkhanaak Derikaal. Then send our own alert up the ICN. Request any available support—utmost priority." The com officer nodded, and Zhaarnak wheeled to his operations officer. "If this is only a probe, we may be able to stop it, Theerah. Configure Derikaal's squadrons for an antishipping strike. If we can destroy them or drive them back on Shanak, we have a chance to delay them long enough for someone else to get here."

     "Who, Sir?" Son of the Khan Theerah'jihaal asked quietly.
     "Anyone!" Zhaarnak snapped, then flicked his ears in apology. His fear and anger were not the ops officer's fault. Oh, no. It was the four billion civilians in Kliean who woke the terror at his heart, and he turned back to his console as the first carrier commander appeared on his com.

From IN DEATH GROUND by David Weber and Steve White (1997)

Babylon 5
The huge jump gate installations in Babylon 5 are constructed by titanic starships capable of FTL travel without using jump gates. But the vast majority of ships need jump gates to do FTL. There are jump gates still around that were constructed by alien civilizations long gone. There is a strong prohibition from destroying jump gates. Traveling from entry gate to exit gate is not instant. The entry gate puts you into hyperspace, which is a chaotic place full of flaming static. You locate the gate beacon of the desired exit gate and carefully fly to it. If you lose contact with all the gate beacons, you will become lost in hyperspace and never be seen again.
The Human Reach
"Breeder" ships detect and capture wormholes as they bubble up out of the quantum foam. One end of the wormhold is left at the starting point. The unmanned breeder ship then use antimatter drives to travel to another star, carrying the other end of the wormhole. This takes years, and is not feasible to travel more than about ten light-years (the breeder ships tend to suffer high-speed collisions with interstellar dust). At the destination, the breeder constructs a stargate frame for the spherical wormhole mouth. The frame uses solar energy panels, feeding power into the mouth in order to inflate it to 40 meters in diameter. This means that starships can be as long as possible, but must be able to retract all of its components so it will fit through a 40 meter diameter circle. This is much like the navy ship maximum width limit imposed by the Panama Canal. The stargate frame has guide rails to help the starship enter the mouth squarely. If it does not, the spherical edge of the mouth will slice the ship in twain.
Stargate SG-1
The Stargates are wormhole based devices constructed out of a heavy mineral called naqahdah. They were created by a Foreruner civilization called the Ancients, and are more or less impossible for current civilzations to construct. A gate can link to many other gates, selected by different combinations of chevrons locked into rotating rings. Covering a gate opening with an iris of armor will prevent other aliens from traveling through your gate in order to invade your planet.
Antares Series
Foldpoints are areas about a thousand kilometers in diameter which are weak points in the space-time continuum. They occur in pairs, one at each end of a "foldline". A starship with a foldspace generator can enter the fold point, radiate a precise pattern of energy, and be instantly transported along a "foldline" to the foldpoint at the other end of the line (in another solar system). Foldlines do not usually connect one solar system to the next nearest, they randomly connect to a solar system tens or hundreds of light-years away. The connectivity of the foldlines has major strategic implications for interstellar empires.
Web and Starship
The Pereen web gates are teleportation devices. They can transport massive quantities of people and material objects instantly to any other web gate in existence. The trouble is that a web gate for a new star has to be transported by a slower than light starship. The Gwynhyfarr hyperspace starships do not have that limit, but they are cursed with the limitation of a miniscule cargo capacity.
Independence War computer game
Starships have a FTL method called the capsule drive. It can instantly teleport a ship from one jump point to another within range. Jump points are where all gravitational fields balance out, i.e., a solar system's Lagrange points (describing a Lagrange point as where gravity fields balance out is almost but not quite totally wrong). Since there are five L-points for every planet paired with the center sun, and paired with every large moon the planet has, there are lots and lots of L-points in each solar system. It is also possible to jump to L-points in nearby solar systems.
Jump Drive Bridgehead

With jump points, you have choke points that can be defended. Battles occur because the enemy has no choice but to invade though the jump point, where the defenders will be waiting. In science fiction, jump points within a solar system belonging to a star empire typically will be surrounded by orbital fortresses, space mine fields, and defensive task forces; all shouting "YOU SHALL NOT PASS!!". Well, the important jump points at least, why waste resources guarding points that lead to uninhabited dead-end systems?

By the same token the capital system of a galactic empire will build a ridiculously over-powered fortification around all the capital's jump points, composed of significant fractions of their entire galactic navy's military assets. Hey, it's the throne world! If the enemy can capture or destroy it, they've decapitated your entire empire.

The technical term for such defensive works is "Bridgehead."

Yes, I know the term now is commonly used for "an advanced position seized in hostile territory". But it originally meant "a fortification around the end of a bridge." Since a jump point is topographically equivalent to one end of a bridge over a river, it makes sense to call the military defensive works around a jump point a bridgehead.

Occasionally you'll find the bridgehead taking the form of something closing off the jump point. Invaders trying to jump to a closed-off destination jump point will be destroyed like bugs on a windshield. Examples include the "iris" in the Stargate franchise and the L-point blocker from the classic video game Independence War.


A bridgehead (or bridge-head) is the strategically important area of ground around the end of a bridge or other place of possible crossing over a body of water which at time of conflict is sought to be defended or taken over by the belligerent forces.

Bridgeheads typically exist for only a few days, the invading forces either being thrown back or expanding the bridgehead to create a secure defensive lodgement area, before breaking out into enemy territory, such as when the U.S. 9th Armored Division seized the Ludendorff Bridge at Remagen in 1945 during World War II. In some cases a bridgehead may exist for months.


Bridgehead (French tête de pont) is a High Middle Ages military term, which before the invention of cannons meant the military fortification that protects the end of a bridge. Like many older terms, the meaning of the word drifted with the passage of time, becoming used for something not exactly true to its initial usage.

With the introduction of cannons, the term was morphed to a generalized term for field fortifications lying some distance beyond the ends of the bridge that were emplaced to protect both the bridge and any troops crossing it to the far bank, so became in that era a term used when referring to both the fortifications and the small lodgement on the bank that was closest to the enemy. As the process of moving an army over bridges is slow and complicated, it is usually necessary to secure it from hostile interruption, and the works constituting the bridge-head must therefore be sufficiently far advanced to keep the enemy's artillery out of range of the bridges—hence as artillery grew in power, so did the size of the lodgements necessary. In addition, room is required for the troops to form up on the farther bank. Formerly, with short-range weapons, a bridgehead was often little more than a screen for the bridge itself, but modern conditions have rendered necessary far greater extensions of bridge defenses.

Then armies and military formations grew, so needed more lodgement area to organize a force large enough to stage a break out against a determined enemy, and again the technical meaning of the term expanded, again referring to a large fortified area about at bridge end. With the advent of modern warfare capabilities, including long-range tube artillery and high-powered rifles with effective ranges measured in the thousands of yards (metres), the term of art again had to expand in area, but now morphed to be just an area defended and controlled by ample firepower, with or without constructed fortifications.

The term in colloquial usage refers to any kind of defended area that is extended into hostile territory – also called a foothold and sometimes the technically incorrect 'beachhead', which is frequently mistaken colloquially as synonymous terminology. The technical term refers in particular to the specific area on the far side of a defended river bank or a segment of a lake or riverine coastline held by the enemy forces, such as the Bridge at Remagen. The term is especially applied when such a territory is initially seized by an amphibious assault with the tactical intent of establishing a supply line across the geographic barrier feature to allow further operational manoeuvring. In that sense, it has much in common with the popular misconception of a beachhead.

See also

From the Wikipedia entry for BRIDGEHEAD

(ed note: The novel uses the Foldspace system of FTL. The planet Alta in the Valeria system is in a jump-route cul-de-sac, having only one jump point. The human colony flourished for a bit more than two hundred years. They were quite upset when the system's sole jump point unexpectedly vanished. They were cut off from the rest of human space.

120 years later they found out why. The star Antares had gone supernova and messed up all the nearby jump routes. This was obvious since Antares was 120 light-years away from Alta. Oh, and Alta's jump point reappeared.

An expedition was launched to find out what's been going on in the rest of human space. As it turns out: quite a bit. First stop is New Providence, the system that colonized Alta. The planet was dead, first because it was only 15 light-years from Antares and had been fried by the radiation. Second because the supernova had opened new jump points, through which poured battlefleets belonging to previously unknown xenophobic aliens called Ryall, who carpet-bombed Napier with nuclear bombs.

Napier only had three jump points: [1] to Antares, [2] to Alta, and [3] to Sandarson’s World. Presumably any survivors of the New Providence armageddon would escape to [3], since [2] had been shut until now and [1] leads to a deadly post-supernova radioactive nebula. The Altan expedition jumps to Sandarson’s World to try and contact the rest of human space.

      “Attention, all hands! This is the Captain speaking. We have arrived in the Hellsgate System in good order. Keep alert. Departments assigned to survey duty are to commence their activities immediately. Report findings as you get them. Captain, out.”
     If Drake had had any concern that they would find Sandarson’s World as dead as New Providence, that fear was quickly dispelled. Even without the aid of astrogation tables more than a century and a quarter out of date, it would have been difficult to overlook the planet. Sandarson’s World was a radio star of the first magnitude and the source of unusually high neutrino emissions. Similar emissions from a number of other planetary bodies within the system betrayed the presence of several thriving subsidiary colonies.
     “We’re intercepting strong broadcast signals, Captain,” Slater reported shortly after the planet was pinpointed by questing radio telescopes.
     “Human or Ryall?”
     “Definitely human, sir. They are speaking Standard. The accent is a bit thick, but I have no trouble understanding them.”
     “What are they saying?”
     “It’s all commercial broadcasting so far, sir. Entertainment programs mostly.”
     “Let me know if you intercept anything that sounds like military traffic.”
“Yes, sir.”      Other observers reported detecting the drive flares of spacecraft in transit between several of the system’s inner planets. As far as could be told from long-range spectroscopic analysis, the ships’ flares were virtually identical to those of the Altan fleet — indicating a roughly comparable technology base. In Richard Drake’s mind, that one fact alone justified the decision to push on to Hellsgate. It proved that Alta had not fallen hopelessly behind the rest of human space during its long isolation.

     Four hours after breakout, Alexandria’s astronomers noticed a cluster of some sixty separate space installations high above the ecliptic on the opposite side of the system primary. The location was so far removed from Hellsgate’s planets, and the cluster so large, that they began immediately to investigate with long-range instruments.
     “That is approximately where the foldpoint from the Aezer System was prior to the nova,” Nathaniel Gordon told Drake when he reported the discovery.
     “Space stations around a foldpoint?” Drake asked. “Why? I would think it more economical to offload cargo at Sandarson’s World.”
     “Perhaps the economics of cargo handling aren’t quite the same here as they are at home,” Gordon theorized.
     Bethany Lindquist (historian), who had been listening to Drake’s conversation, strode across the bridge to his command chair. “Cargo facilities, my eye! I’ll bet you anything that those are military.”
     “What sort of military?”
     “I would imagine they’re a series of orbital fortresses designed to discourage intruders from using the foldpoint.”
     “How do you come to that conclusion, Miss Lindquist?”
     “You’ve studied military history, Captain. Where do you build fortifications? At navigation choke points, of course, which is precisely what any foldpoint is. Circle a foldpoint with enough firepower and you can keep anyone out of your system you choose.”

(ed note: in other words: make a bridgehead)

     “If that’s the case, we should see similar installations quite close by, Bethany,” Dr. Gordon said from Alexandria (because they just arrived through another jump point). “Where are they?”
     “They aren’t there, Nathaniel. Why should they be? As far as the inhabitants of Sandarson’s World know, the only place this foldpoint leads is to the dead world of their ancestors. Why guard a cul-de-sac?”
     “Who do you think they’re defending against?” Drake asked. “The Ryall?”
     “Could be.”

     “I wish you both all happiness,” she said. Then her manner changed abruptly. It was as though someone had thrown a switch. She shouldered her way past Bethany to where Drake was still hastily fastening the closures on his uniform tunic. “Captain Drake, I must speak with you. Something very curious happened tonight at the banquet. Halfway through dinner, all the highest ranking Sandarians were called away!”
     “I don’t understand.”
     “Neither do I. The first we knew of it was when a messenger stopped to confer with Minister Haliver. I was watching Haliver’s face. Whatever the news was, it caused him to go white as one of the local glaciers. The first minister then leaned over and whispered in the king’s ear. John-Philip said something to the queen, and all three of them rose in unison and left. By then, other messengers had entered the hall. They worked like skilled gransi pickers back home. They swept among the tables, stopping to harvest someone here and there. Invariably, wherever they whispered in someone’s ear, that worthy made his excuses and left the hall. The whole process took no longer than five minutes, and you could feel the tension building the whole time.”
     “How long ago did this happen?”
     “No more than twenty minutes. Carl and I slipped out a side door while everyone was preoccupied. We made our way here to tell you about it.”

     Drake strode to the viewphone, activated the instrument, and asked for the palace operator. A pretty, young woman came on the line immediately.
     “Yes, Fleet-Captain Drake. How may I help you?”
     “You may put me through to my ship.”
     “Sorry, sir, but all orbital transmission circuits are currently in use. I’ll be happy to put you on the waiting list and call when a circuit frees up, if you like.”
     “I wouldn’t like. I need that circuit now!”
     “I’m sorry, sir, but all circuits are currently in use.”

     “What are you going to do now?” Bethany asked as Drake switched the telephone off.
     “I’m going to call the ship,” he said. He reached into his uniform tunic and pulled forth a hand held communicator marked with the insignia of the Altan Space Navy. Every member of the ground party carried a similar device, although the Sandarians had requested that they not use them. The reason given had been the possibility that the communicator signals might interfere with the operation of various pieces of automated equipment.
     Drake thumbed the emergency call button on the communicator and was rewarded by the appearance of Bela Marston’s features on the instrument’s screen. His executive officer looked grim.
      “Ah, Captain! I thought I was going to have to send the Marines down to find you.”
     “Report, Commander!” Drake ordered. “What’s the situation up there?”
     “Approximately half an hour ago, sir, space-side sensors detected a large number of weapons discharges in the Hellsgate/Aezer foldpoint. I thought they were testing their ordnance until one of the fortresses exploded.”
     “A fortress was destroyed?”
     “More than one, Captain. Whomever they were shooting at was well shielded and well armed. After awhile, things quieted down. Over the last fifteen minutes or so, we have been tracking the drive flares of at least a dozen ships accelerating away from the foldpoint at high gravities. Whoever they are, they’re scattering all over the place!”
     “Any identification on the ship types from their flares?”
     “They aren’t like either Altan or Sandarian drives, if that’s what you mean.”
     “I’d put money on it, sir.”
     “What’s Discovery’s current status, Mr. Marston?”
     “We can be ready to leave orbit as soon as your ground party is aboard, sir. Captain Fallan says that Alexandria can do the same as quickly as he gets his own people back. I am having all personnel run continuous maintenance tests on all equipment, with emphasis on engines and weapons. I’ve told the chief engineer that if he’s got anything dismantled, I want it put back together on the double.”
     “Good man!”
     “When can we expect you back onboard, Captain?”
     “Give me some time to find out what’s going on down here, Bela. I’ll call you again in an hour.”
     “Very good, sir.”
     “In the meantime, keep buttoning up the ship. Drake out.”
     “Marston out.”

     Drake turned to Bethany and Alicia and was about to speak when the suite door opened and four burly Sandarian Marines rushed in. They were followed by the palace major-domo.
     Opteris’s gaze fastened on the communicator in Drake’s hand. “Please turn that damned thing off, Captain Drake. Your transmissions are giving the palace security system a nervous breakdown.”
     “What’s going on, Opteris?”
     The major-domo shrugged. “Nothing to become unduly concerned about, I assure you. The Ryall tried to force our foldpoint defenses a short while ago.
     “My people tell me that they not only tried, they succeeded!”
     Opteris sighed. “Early reports indicate that most of their ships were destroyed in the fortresses’ crossfire. However, we did take some damage. Several of their ships managed to exploit a gap in our defenses to break out into open space. We are now mobilizing our fleet to deal with them. At this time, there is no cause for alarm.

     Opteris led him to another nondescript door and inserted his identification card once more. Again, the muted clicking noise was followed by the door sliding quietly out of their way. Inside, they found a small room in which a dozen Sandarians were clustered around a table. Their backs were to the door and their attention was focused on a large situation display on the far wall.
     John-Philip Walkirk swiveled in his chair and glanced at Drake as he and the major-domo entered the conference room. He got to his feet and crossed the distance between them in four long strides.
     “Welcome, Fleet-Captain,” John-Philip said, holding out his hand.
     “Thank you, Your Majesty,” Drake replied, taking the proffered hand. It was not until he felt John-Philip’s strong grip that he became conscious of the departure from normal court etiquette that the gesture represented. He also noted how much John-Philip seemed to have aged in the week since their first meeting. In addition to the king, Drake recognized Chief-of-War-Operations Walkirk, First Minister Haliver, and Duke Bardak among the Sandarians present. 

     “What do you think of our little command center here?” the king asked.
     “I’m very impressed,” Drake replied. “I had no idea that this existed.”
     John-Philip smiled. “It isn’t something that we advertise. Now then, you asked to see me. I imagine you are concerned about the recent visit to this system of our centauroid antagonists.”
     “Yes, sir. Very concerned. I have two ships in orbit and people spread out all over Sandar. I’d hate to be attacked in parking orbit without room to maneuver.”

     “No possibility of that, Fleet-Captain,” John-Philip replied. He gestured toward the wall-size screen. “The display should convince you of our situation.”
     The display was of a type not too different from those used by the Altan Navy. The Hellsgate/Aezer foldpoint was depicted as a red ellipsoid around which sixty golden sparks were arrayed in a perfect globular formation. Only, the globe was no longer perfect. Seven of the sparks were gone, replaced by crimson crosses to mark their former positions. Soft, green lettering beside other markers told of battle damage sustained. Trailing away from the foldpoint, radiating outward in all directions, were twelve red arrowheads. Attached to each arrowhead was a pair of lines showing velocity and acceleration vectors. Several green arrowheads could be seen chasing their red counterparts. One glance at the vectors involved told Drake that it was going to be a long chase.
     “Approximately fifty Ryall ships materialized in the foldpoint last night,” John-Philip began. “They were automatically identified and immediately attacked by our guard fortresses. Overall, we did well. We destroyed eighteen outright and forced another twenty to jump back to Aezer. However, the remaining twelve concentrated their fire on one particular section of our defensive globe and punched through. What you see are the surviving Ryall ships trying to outrun our pursuit craft. Of course, they have no hope. Once we get the Third Fleet out there, they’ll face an overwhelming force.”
     “You are dispatching one of your fleets, Your Majesty?” Drake asked. “Is it that serious?”
     “It’s serious until the last of those marauders is destroyed! However, that is not the main reason for dispatching the fleet. We have been fighting the Ryall for a century, Captain. We are getting to know their habits quite well. They may attempt probing attacks on the foldpoint for the next several weeks to gauge how badly we have been hurt. Reinforcing our defense line with the Third Fleet will help convince them that their attack has failed.

     As John-Philip had predicted, the Third Space Fleet departed Sandar within twelve hours after Drake’s audience in the war room. Drake hurried from the boat bay to the bridge in order to watch the departure. It was an impressive sight in the cruiser’s telescopes and on its radar screens. One by one, four separate flotillas boosted away from the planet. Each consisted of a blastship, twenty armed escorts, and three times that many support vessels. Drake identified heavy and light cruisers, destroyers, and even relatively tiny long-range scout boats. The support craft included all manner of tankers, freighters, and ammunition ships. As he watched them go, he was reminded of something one of his professors at the Altan Space Academy had once said: “Never forget, young gentlemen, that space war is ten percent offense and ninety percent logistics!
     For a day and a half after departing orbit, the Sandarian ships’ drive flares were visible in Discovery’s telescopes. They showed as a star cluster composed entirely of violet-white stars of varying intensity. The main body of the fleet accelerated at two standard gravities for forty hours before turning end-for-end and decelerating for a like time until they reached the Hellsgate/Aezer foldpoint. After arriving at the foldpoint, they took up guard positions interspersed with the surviving orbital fortresses.
     Not all ships of the Third Fleet headed for the foldpoint, however. Several small groups split off to intercept the surviving Ryall raiders (two of which had already been destroyed by their pursuers). By the fifth day after the Third Fleet’s departure, it was clear that the Sandarians had the situation under control. Nearly fifty warships had joined an equal number of surviving fortresses at the foldpoint, and the fleeing Ryall raiders were scattered across the sky in disarray with thirty Sandarian ships in pursuit.

     Even so, Richard Drake found it difficult to shake his feeling of unease as he reviewed the Sandarian formations.

     “What’s the matter with you?” Bethany asked when she brought his lunch to the bridge. “You look like you just bit into something rancid!”
     He grinned, leaned back in his chair, and stretched to relieve the ache of sitting too long in one position. The ship was at one-quarter spin-gravity, but that did nothing to relieve the aches and pains induced by tension. “I guess I worry too much.”
     “What do you mean?” Bethany asked as she handed him one of the trays she carried.
     Drake pressed a control that slaved Bethany’s screen to one of his own. “Here, I want you to see something!”

     Two more commands to Discovery’s computer brought up the Sandarian record of the battle at the foldpoint. Drake had studied the record nearly continuously over the past five days, hoping to divine something from the tactics the Ryall had used. The more he learned, the more troubled he became.
     The record began with a close up of one of the foldpoint fortresses. This was obviously library footage tacked on by the Sandarians for Altan benefit. The screen showed a great sphere that bristled with weapons and sensors. The dark snouts of several hundred laser ports dotted the surface of the sphere, as did a like number of missile launchers. Other features included thick layers of ablative shielding, power plant exhaust ports, and vast radiators to rid the fortresses of internal heat. A destroyer cruised past the fortress in the foreground of the picture, giving a sense of scale to the scene. The battle station was as large as a small asteroid, and brimming with destructive power.
     “My God, what a behemoth!” Bethany said.
     Drake nodded. “It’s even more impressive when you realize how much ship volume is normally taken up by photon engines and foldspace generators. That monster was designed to deliver its punch to the target without worrying about maneuvering. I’d estimate its power at about five blast ships, maybe more!”
     “If one fortress is that powerful, how did the Ryall manage to break out of a foldpoint guarded by sixty of them?” Bethany asked.
     “Watch the next sequence and find out.”

     Drake touched a control and the scene changed to a view of a starfield. The background stars were jittery enough to show that the scene was from a long-range camera set at maximum magnification. As Bethany watched, a ship materialized in the center of the screen. The ship was cylindrical, and not unlike similar ships of both the Altan and Sandarian navies. As they watched, the dull gray surface of the newly arrived starship turned brilliant against the black backdrop of the sky. A filter snapped into operation and the stars dimmed until the ship’s outline was once more visible. Vivid points of violet light could be seen stabbing at the hapless ship in dozens of places. With so much laser energy being poured into its hull, the Ryall craft had no hope.
     Yet, somehow it survived.
     From each of the points of radiance came incandescent plumes of vaporized material. For long seconds, the Ryall craft had the appearance of a multi-tailed comet. Nor was the ship placid. It fought back hard. Beams of its own could be seen piercing the sudden fog that was softening its outlines. Violet-white specks marked the drive flares of missiles on their way to their target. The spacecraft seemed to hover unmoving for perhaps ten seconds before the ravening beams finally ate their way into something vital. Then, almost in slow motion, the ship exploded in a blinding flash and began to expand in a cooling cloud of plasma. The faraway telescopic camera reduced its magnification in order to keep the fireball in its field of view until it had dimmed to darkness.
     “That was one of the first raiders through the foldpoint,” Drake said.
     “How could it have survived so long?” Bethany asked.
     “Did you see the geysers spouting from its sides? That was anti-laser ablative shielding being vaporized. Ablative shielding has billions of tiny glass prisms in every cubic centimeter. Laser beams tend to get scattered in a hurry in the stuff. It takes a long time to drill a hole through to get at the ship underneath.”

     The screen changed to show another star field. This time fifty Ryall starships materialized within the foldpoint. They were far enough away to be invisible, but their positions were marked by electronic symbols. Again, the Ryall ships blazed bright as the Sandarian fortresses opened up on them. Repeatedly, the attackers’ shields failed within a matter of seconds, but not before they had released a swarm of missiles at one section of the defensive globe. The interior of the globe filled with the flashes of fusion weapons. Most were detonated harmlessly in space, but some got through in both directions. And anti-laser ablative did little to thwart the power of a nearby nuclear burst. Wherever the missiles got through, that target died. Drake and Bethany watched as one of Sandar’s fortresses exploded. It was followed quickly by several others.
     “Our people have analyzed the record until they can barely see,” Drake said. “It took about twelve seconds on average for the fortresses to overcome the Ryall shielding on each ship. That gave most of the Ryall ships time to unload their missiles against one section of the defensive globe and then jump back to the safety of the Aezer system. They managed to tear a hole in the globe and a dozen of the raiders slipped through the gap.”
     “It hasn’t done them any good,” Bethany said. “The Sandarian fleet has them outnumbered and outgunned. Mr. Cristobal says the last of them will be hunted down in another hundred hours.”

     “Still,” Drake said, “I wonder if the fact that they were able to break out at all doesn’t point out a weakness in the Sandarian defenses.”
     “What weakness?”
     “Look at the way they hug the foldpoint,” he said, gesturing toward the red ellipse with its covering of Sandarian ships. “They are getting in close in order to concentrate their firepower. However, that formation does not give them much defense in depth. Once the Ryall broke through, there was nothing between them and Sandar except four hundred million kilometers of vacuum. That is why they had to scramble the Third Fleet.
     “Now, if I were running this show, I’d station a blocking force right about here,” he said, pointing to a spot halfway between the foldpoint and Sandar. “That would give a lot more depth to the defense while cutting down on the response time should the Ryall achieve a breakout. That way, the Sandarians could enfilade an attacker all the way to the planet, and then let the planetary defense centers take care of any survivors.”
     “You are worrying too much, Richard,” Bethany said around a sandwich into which she had just bitten. “The Sandarians have been fighting the Ryall for more than a century now. They must know what they’re doing!”
     “I hope you’re right,” Drake responded.

     The sound of the alarm brought Drake to instant wakefulness. He sat up in bed and triggered the interphone screen on the nightstand beside him. The screen lit to show Karl Slater, who was serving as Officer of the Watch.
     “What is it, Mr. Slater?” Drake asked gruffly, noting the digits 03:28 in the screen’s chronometer display (actually a military ship would use a 24 hour clock).
     “You’d better come to the bridge, sir. All hell has broken loose in the foldpoint!”
     “I’ll be right up.”
     Drake slipped into a jumpsuit and a pair of ship shoes and headed for the bridge at a run. He arrived to find the complete bridge crew settling into their stations. From the looks of most of them, they too had been rousted out of a warm bed on short notice.

     “Report!” Drake ordered as he slipped into his command chair.
     “Yes, sir,” Karl Slater replied. “Pursuant to orders, we have been monitoring the Hellsgate/Aezer foldpoint for signs of activity all through the night watch. All was quiet save for normal Sandarian communications traffic until zero-three-twenty-five hours, or approximately three minutes ago. It was then that we observed an explosion of massive proportions within the foldpoint.”
     “How massive?”
     “Several orders of magnitude larger than what we observed during the battle of six days ago, sir. We are trying to compute the power level now. Since the explosion, we’ve also detected fusion weapon bursts and a large number of high power laser flashes.”
     “Let’s see a replay!”
     “Yes, sir.”

     As Slater had reported, the second battle for the Hellsgate/Aezer foldpoint had begun with a titanic blast from within the foldpoint itself. Drake watched as the eternal night of space was turned suddenly into day. At first, there was only a single point of light at the center of a small starfield. The point brightened and grew until it was a tiny disk the color of an arc welder’s spark. The disk continued to expand. It changed color as it did so. The actinic blue-white shaded slowly to green, and then to yellow. Orange splotches appeared, and the sphere turned orange before shading down to red, where it lingered for long seconds before disappearing completely. In the meantime, other lights had appeared. These were the familiar white flashes that accompanied the detonation of a nuclear tipped missile, and the pure violet sparks of high-powered military lasers in action.
     Drake tapped a control and watched the sequence again. When it was over, he turned to his chief communicator. “What do you want to bet that every Sandarian ship and orbital fortress around the foldpoint just had half their sensors burned out?”
     “No bet, sir.”
     “Yes, Captain,” the technician charged with spectral analysis answered.
     “What have you got?”
     “I’m having trouble extrapolating the power of that first big bang, sir. I keep getting an answer that I do not believe. The spectrum indicates that it was a matter/anti-matter annihilation reaction, though where anyone would find that much antimatter in this galaxy is beyond me.
     “They didn’t have to find it, Mr. Creighton. They manufactured it.”
     “A couple of hundred kilograms, sir? (3.6×1019 joules, 8.6 gigatons) That would take years!”

     Drake nodded. “And be highly dangerous to all concerned. Gentlemen, I think our Sandarian cousins have just fallen headlong into a Ryall trap.
     “I don’t understand, Captain.”
     “Imagine that you are the Ryall commander, Slater. You have been assigned to attack this system. What is your greatest difficulty?”
     “Breaking out of the foldpoint defenses.”
     “Not at all. You proved you could do that six days ago. No, the prime difficulty is knowing the disposition of the defenders in advance. Remember, you have no reconnaissance capability. Yet, you need to know where the Sandarian fleet is if you are to have a chance.
     “That was what the initial raid was about. The Ryall used their normal pattern during the attack. They led the Sandarians to expect additional raids against the defense globe. The Sandarians reacted as they normally would by massively reinforcing the foldpoint. In so doing, they concentrated a significant percentage of their forces in a single spot. Don’t forget that some of the Ryall raiders broke out of the defense globe. What did they do? They immediately scattered across half the sky, forcing the Sandarians to give chase, thus drawing off another sizable chunk of Sandar’s strength.
     “Six days later, you – as commander of the forces of the Ryall Hegemony – can now confidently predict where you will find a large percentage of the Sandarian fleet. At the proper time, you send your planet buster through the foldpoint and set it off. The explosion temporarily blinds the defenders, and being an antimatter reaction, produces only high-energy photons. In other words, it produces a hollow shell of radiation that expands at the speed of light leaving no nasty fireball of electrically charged plasma behind! One second after the explosion, your invasion fleet jumps into a foldpoint clear of residual energy and immediately breaks through the encircling globe of human warships and fortresses. It will not really matter how many human ships survive your attack. If you can get to Sandar half an hour before they do, your mission is a total success. In a way, it’s ironic.”
     “What is, Captain?”
     “We keep telling ourselves that a hundred years of war should have taught the Sandarians all there is to learn about the Ryall. It never occurred to us that the converse must also be true!”

     “Some hours ago, Captain Drake, you told a duty officer at headquarters your suspicion that we had fallen into a Ryall trap. I am chagrined to say that I agree with you. Apparently, the Ryall know us far better than we realized. For reasons that I will explain shortly, the timing of their attack and its method of execution were masterstrokes!
     “The attack began with the detonation of a very large antimatter bomb. Two of our ships on patrol within the foldpoint at the time were destroyed outright. The rest of our fleet, including the orbital fortresses, was blinded by the explosion. Approximately half of our sensors and seventy percent of our communications were temporarily knocked out by the explosion shockwave.
     “Six-tenths of a second following the antimatter blast, sixty five Ryall warships materialized within the foldpoint. Our forces immediately began to enfilade them with laser, antimatter projector, and missile fire. We took a heavy toll, but not nearly as heavy as we would have if our defense had been better coordinated. The Ryall used the same tactic they did six days ago. They concentrated their fire on one section of the defensive globe and were able to clear a hole through which they could pass. The last Ryall ship extricated itself from the foldpoint eight minutes and seventeen seconds after the initial explosion.”
     “Of the 65 hostiles originally engaged, a total of 36 survived to break out of the foldpoint. They formed up in good order and immediately began accelerating toward Sandar. The Third Fleet is giving chase, and in fact, has superior numbers and ship-to-ship firepower. Unfortunately, in the last couple of hours we have seen a tendency for the Ryall fleet to break into two distinct groups.”
     “Why ‘unfortunately?’” Barrett asked. “I would think you would prefer to take them in small groups.”
     “Because, Mr. Ambassador, we think we are beginning to understand their strategy. A group of eight ships has pulled ahead of the main body. They are continuing to accelerate at 5.2 standard gravities. The remaining twenty-eight ships have reduced their acceleration level to 4.5 standard gravities. The larger group is obviously acting as a blocking force to shield the smaller group from the Third Fleet. We will have to defeat each of the ships in the main force before we can attempt to close with the leaders. To do otherwise would place the Third Fleet in a crossfire that would be murderous.

     “How can they possibly maintain five gravs?” Bela Marston asked. “They’ll run their tanks dry before they reach Sandar.”
     “Or shortly thereafter,” Bardak agreed.
     “But they won’t be able to slow down. Once their fuel is gone, they are on a one-way trip to infinity.”
     “The Ryall are out to destroy a human occupied planet, Commander Marston. By their standards, trading sixty-plus ships for Sandar is a bargain.”

     “Any idea what sort of ships are in that leading group?” Drake asked.
     Bardak manipulated the remote control again, and the scene zoomed in on the lead group of Ryall ships. The markers for three ships in the center of the group began to blink rapidly.
     “These three are the ones that concern us the most. They are the main strike force. The other vessels are merely armed escorts.”
     “Any identification as to type?”
     “We believe them to be attack carriers!”
     There was sudden silence in the room, followed by a low whistle from Argos Cristobal and a quick, nervous cough from Bela Marston. Drake glanced at Bethany and saw from the horror in her eyes that she understood the significance. Only the two ambassadors looked perplexed.
     “What the hell is an attack carrier?” Alicia Delevan asked.
     Richard Drake turned to her and said, “An attack carrier is a large converted freighter that has been jammed to the hull plates with nuclear missiles. Considering the number and power of Sandar’s planetary defense centers, if the Ryall were to use a conventional attack on Sandar as they did at the foldpoint, they would be vaporized before they could get within striking distance.
     “That is where attack carriers come into play. Because a missile is small, its range is limited. On the other hand, it is possible to construct and transport a lot of missiles in an attack carrier. Each Ryall carrier probably has a hundred thousand short-range missiles onboard, maybe more. They will release their cargo of missiles just before they get within range of the PDCs. Each one of those missiles represents a dead Sandarian city, so the defense centers will not be able to ignore them. Instead of having eight targets to fire at, they will have three hundred thousand! The Ryall aim is to saturate the defense and cause their computers to break down from overload.” Alicia Delevan turned to Duke Bardak and said, “If I were you, Commodore, I would be getting the First and Second Fleets on their way to intercepting those attack carriers!”
     Bardak looked pained for an instant, and then sighed deeply. “That is excellent advice, Madame Ambassador. I wish that I could do so. Unfortunately, we possess no other fleets. Except for my own squadron of interceptors and a few dozen other craft of dubious age and condition, there are no warships left in orbit about Sandar at this time.”


(ed note: in the Starfire board game and the Starfire novels, the jump points are called "warp points." Invading through a defended warp point is so common that is has its own special term: Warp Point Assault.

Our heroes are trying to stop an invasion of the "Bugs", the Arachnid Omnivoracity. So called because of their resemblance to giant spiders and their hideous habit of eating captured humans while the humans are still alive.)

      Zhaarnak gestured at something outside the range of his com pickup—probably, Prescott guessed, an auxiliary plot like his own, displaying Task Force 63 as a cloud of color-coded lights swarming in stately procession around the violet circle of the warp point.
     Sixth Fleet's third task force hadn't joined the other two in the scorching of Home Hive three for the excellent reason that it didn't include a single vessel that could move under its own power. Instead, Vice Admiral Alex Mordechai commanded orbital fortresses—fifty-seven of them, the smallest as big as a superdreadnought and the largest even bigger than the Bug monitors. Untrained eyes might have looked at the arrangement of those icons in the sphere and seen chaos. But Prescott recognized the product of careful planning rooted in well-developed tactical doctrine.

     Interstellar travel was possible only via warp transit, and only one ship at a time could safely perform such transit, lest multiple ones irritate the gods of physics by trying to materialize in overlapping volumes of space. So it had always been a truism of interstellar war that the defender of a known warp point knew exactly where attacking ships had to appear . . . one at a time. In the face of such an advantage, many people—disproportionately represented, it often seemed, in the fields of politics and journalism—were at a loss to understand how any warp point assault could possibly succeed except through the defenders' incompetence. To be fair, a similar attitude hadn't been unknown among military officers in the early days—especially given the momentary disorientation that overtook both minds and instruments after the profoundly unnatural experience of warp transit. With beam-weapon-armed ships or fortresses stationed right on top of the warp point, the befuddled attackers would emerge one by one into a ravening hell of directed-energy fire. If missile-armed vessels were available for supporting bombardment from longer ranges, so much the better. The pre-space expression "make the rubble bounce" wasn't apropos to the environment, but it nevertheless came to mind.
     Things hadn't quite worked out that way, for the lovely picture had run aground on certain hard realities. One was that, while the defender knew where the attack would come, he had no way of knowing when it would come. Another was that no military organization could keep all its units permanently at the highest state of alert. Taken together, those facts meant that attackers might appear at any time, without warning and in unanticipated strength, to pour their own point-blank energy fire into surprised defenders. Nor had it proven possible to clog the mouth of a warp point with mines; the grav surge and tidal forces associated with the warp phenomenon made it impossible to keep the things on station directly atop it. The space around a point could be—and was—covered with lethal concentrations of the things, backed up by independently deployed energy weapon platforms, but any mine or platform left directly on top of an open warp point was inevitably sucked into it and destroyed. So although it was possible to severely constrain an attacker's freedom of maneuver, the defender was seldom able to deny him at least some space in which to deploy his fleet as its units arrived.

     And then, with the passage of time, had come what the TFN designated the SBMHAWK: the Strategic Bombardment Homing All the Way Killer—a carrier pod that was a small robotic spacecraft, capable of transiting a warp point only to belch forth three to five strategic bombardment missiles programmed to home in on defending ship types. Because they were throwaway craft, the carrier pods could and did make mass simultaneous transits, accepting a certain percentage of losses as the price of smothering a warp point's defenders with sheer numbers of missiles. With such a bombardment to precede it, the prospect of a warp point assault had become as nerve racking for the defender as for the attacker—arguably more so, because the attacker at least knew in advance when he was going in, and could prepare himself for the probability of death.

     But eventually the march of technology had provided the defense with what it had most conspicuously lacked: warning of the attack. The second-generation recon drone had been designed to allow covert warp point survey work by robotic proxy—an excellent idea in a universe that held Bugs. But it also had a more directly military use. With its advanced stealth features, it could probe through a known warp point undetected and report back on any mobilization that portended an attack . . . just as Sixth Fleet's RD2s had been doing.

     One thing, however, hadn't changed. The name of the game was to position your assets so that every unit was at its own principal weapons' optimum range from the warp point, and Alex Mordechai had done just that. His beam and missile-armed fortresses clustered around the warp point in concentric shells, prepared to pour fire into that immaterial volume of space. His six BS6Vs, each one the base for a hundred and sixty-two fighters, maintained station further out, outside direct weapons' range of the warp point. All the bases were on rotating general-quarters status, and had been ever since the RD2s first reported the Bug force building up like a thunderhead at the other end of the warp line. And in addition to the fortresses, the plot showed the lesser lights of unmanned munitions in multicolored profusion: twelve hundred patterns of antimatter mines, seven hundred and fifty laser-armed deep space buoys, twelve hundred independently deployed energy weapons (less powerful than the buoys' detonation-lasers, but reusable), and eight hundred SBMHAWK carrier pods tied into the fortresses' fire control.

     Nothing, surely, could come through that warp point and live.

     They didn't need to wait for the RD2's report. The drones were dispatched through the warp point for twenty-four-hour deployments. That represented their maximum endurance, and they returned before that time limit only if their electronic and neutrino-based senses told them one thing.
     The attack was under way.
     The general quarters call whooped through Dnepr's echoing corridors, and the other elements of Sixth Fleet were uncoiling themselves to lunge towards the warp point to support Mordechai's command. Prescott ignored it all and kept his eyes riveted on the plot and— Yes, there was the tiny light of the fleeing RD2. He watched, unblinking, for what he knew would follow it.
     He knew . . . but even so, he sucked in his breath when it happened.
     It wasn't something anyone grew accustomed to—not even someone like Raymond Prescott or Zhaarnak'telmasa, who'd seen it before.

     The Bugs had introduced the tactic, unthinkable for any other race, of mass simultaneous warp transits. Prescott knew he had no business being shocked by the phalanx of red "hostile" icons that suddenly appeared—and, in fact, he wasn't. What he felt was flesh-crawling, stomach-quivering horror at the mindset behind it: absolute indifference to personal survival.
     As if to emphasize the point, the usual percentage of those scarlet lights began going out.
     Prescott had seen actual visual imagery, not just CIC's dispassionate icons—recorded robotically from long range, of course—of a similar assault when he and Zhaarnak stood with their backs against the wall in defense of Alowan. That had been bad enough, yet he'd seen worse—and from a much closer perspective—in the final desperate stages of the Bugs' assault on Centauri. So he wasn't deceived by the peaceful way those lights flickered and then vanished, leaving a fleeting afterimage on the retina. When two solid objects tried to resume existence in the same volume, the result was of an intensity to stress the very fabric of space/time. Indeed, no one really knew precisely what happened—the phenomenon had never been studied closely enough, and doubtless never would be.
     Every TFN officer had seen imagery like that . . . in a way. The Federation had learned the hard way that there was only so much simulators, however good, could teach its personnel. And so regular deep-space drills, with real hardware, were part of the day-to-day existence of the Fleet. As part of those drills, SBMHAWKs were fired through warp points, where—as always—a certain percentage of them disappeared in those intolerably brilliant spasms of madly released energy.
     Yet there was a difference between those exercises and this. SBMHAWKs were, after all, just expendable machinery.
     But, then, so were the Bugs . . . by their own definition. And as Prescott watched those icons vanish, he realized anew that humankind and the Bugs were too alien to share the same universe.

     The deaths of Bug ships from interpenetration ceased immediately after transit. But those ships kept dying without letup, for Mordechai was clearly resolved to burn Zephrain space clean of them before they could deploy away from the warp point. Swathes of deep space buoys vanished from the sphere, committing thermonuclear suicide to focus the gathered energies of their deaths into lances of coherent X-rays that impaled the Bug ships almost too fast for their types to be identified. Almost too fast, but not quite . . . and Prescott frowned. These were all light cruisers.
     That wasn't like the Bugs. True, in the first years of the war, they'd used light cruisers for their initial assault waves. But that had changed with their introduction of the gunboat. Smaller and far cheaper than even an austere light cruiser design, gunboats were even better suited for this self-immolating form of attack, and that was precisely how the Bugs had come to use them. But today they weren't, and Prescott began to worry.
     "Raise Admiral Mordechai," he ordered his com officer. The command was barely out of his mouth when a second mass simultaneous transit appeared. These were gunboats—and Prescott's worry hardened into certainty.
     Mordechai must have seen it too. He'd let himself be drawn into expending practically all of his bomb-pumped lasers on the light cruisers of the first wave. He still had his reusable independently deployed energy weapons—but the IDEWs' puny powerplants took half an hour to power them up between shots, which meant effectively that they were good for only one shot per engagement each. He was faced with the choice of using them against the gunboats, or holding them in reserve against the big ships he knew were coming.

     Fortunately, he had another card to play: the defensively deployed SBMHAWKs. By the time the communications lag allowed Prescott to speak with him, he'd already decided to use those, rather than the IDEWs, to counter the gunboats.
     An SBMHAWK pod's fire control was normally extremely effective, but only within limited parameters. Designed to survive the addling effect of warp transit and then find and attack its designated target type, its fire control suite was extremely powerful but limited to a single target for every bird in the pod. The entire idea, after all, was for the pods' combined fire to swamp and overwhelm the defenses of their targets, so dispersing the individual pod's missiles between multiple targets was contraindicated.
     Bug gunboats were far more fragile targets than even the smallest starships. Although they did mount point defense, unlike strikefighters, they didn't have very much of it, and a single hit from any weapon was sufficient to destroy them. Which meant that just as dispersing fire against starships was an exercise in futility, concentrating the entire load of an SBMHAWK on such a vulnerable target would have been a wasteful misuse of critically valuable weapons.
     But there was a way to avoid doing that. The pods Mordechai committed were linked directly to the extremely capable fire control systems of TF 63's fortresses. The pods didn't have to find their targets; the fortresses did that for them, and the clouds of missiles they expelled were more than sufficient to compensate for the targeting problem posed by the gunboats' numbers. The space between the warp point and the nearest fortress shell began to blaze as the energies of antimatter annihilation expended themselves on the relatively insignificant masses of mere gunboats, leaving no debris. But the little craft pressed the attack with the insensate persistence humans had come to know over the last few years, and the fortress crews braced themselves for the worst: kamikaze attacks by gunboats whose crews knew they'd have no chance at a second pass.

     As it happened, they were mistaken about what constituted the worst.

     After the attack on Home Hive Three, it was no news that the Bugs had developed the close-attack antimatter missile. But no one had fully reasoned out the implications of that fact, as applied to mass assaults by gunboats which could externally mount sixteen of the things and ripple-fire twelve of them in the course of a single firing pass. They should have, but the Allies were accustomed to thinking of FRAMs as fighter munitions, and even the TFN's F-4, the most capable strikefighter anyone had yet deployed, could mount only four of them. There was an enormous difference between that weight of fire and what a gunboat was capable of putting out . . . as the Bugs proceeded to make horrifyingly evident.
     The gunboats drove in through the defensive fire of the forts. Scores of them perished in the attempt, but there were simply too many of them for the fortresses to destroy them all, and as each individual that broke through reached knife range, it salvoed twelve FRAMs. No point defense system in the galaxy could stop a FRAM once it launched, and even the mightiest fortress staggered like a galleon in a hurricane as that concentrated flail of super heated plasma and radiation smashed home.
     Prescott was as horrified as anyone by the sheer carnage a single gunboat could wreak with a full ripple-salvo, and even as he watched, the surviving Bugs departed from their standard practice by breaking off after that devastating pass rather than seeking self-immolation. Instead, they broke back towards the warp point, firing their remaining FRAM on the way out.

     Jacques Bichet, studying the readouts intently, offered an explanation.
     "It makes sense, Sir. Four FRAM hits can inflict almost two and a half times as much damage as a ramming attack by a 'clean' gunboat could."
     "So of course they're not ramming." Prescott's voice sounded far too calm to his own ears, but he nodded. "It would be better if they were," he went on, and Bichet gave him a puzzled look. But he was speaking more to himself than to the ops officer. "Their willingness to make suicide attacks has always caused us to unconsciously picture them in the mold of human religious fanatics, eagerly seeking self destruction. But they're not. The Bugs don't want to die. It's just that they also don't want not to die. They simply don't care. We'll never understand that—never understand them. And I don't think we want to understand them."

     Bichet shivered and turned away, seeking the concrete world of facts and figures. He studied the readouts of the subsequent waves of mass simultaneous emergences from warp, and his eyes narrowed as he realized that something else was happening that was new. He started to call it to Prescott's attention, but Amos Chung was studying the same data, and he beat the ops officer to it.
     "Admiral, there are some gunboats in these latest waves, but fewer in each. Most of what's coming through now seem to be pinnaces."
     Prescott looked at him sharply. The pinnace was the largest type of small craft which could be carried internally in a starship's boatbay, and the only small craft type (other than a gunboat) that was independently warp-capable. Now that he knew what to look for, he recognized the signs in the readouts himself: the lesser mass combined with inferior speed and maneuverability, relative to gunboats. The Bugs had used them in the kamikaze role before, especially against Fifth Fleet in the original Romulus fighting, but the Allies hadn't seen much of them in the past year or two. The assumption had been that the Bugs had finally decided that pinnaces did too little damage, even as kamikazes, to make practical weapons—particularly because they were much easier to kill than gunboats were.
     "What can they be thinking?" Chung jittered as he watched the pinnaces take murderous losses from Mordechai's AFHAWKs. "Granted, they're too small for the mines to lock them up as targets, and we can't use standard anti-ship weapons against them, but still . . ."
     "We'll soon find out," Prescott muttered as the first of the pinnaces closed to attack range of the inner fortress shell.
     Part of the answer emerged instantly. The Bugs had loaded the pinnaces' external ordnance racks with FRAMs. They couldn't mount anywhere near the load a gunboat could manage, but what they could mount was devastating enough in its own right, and more shields went flat under antimatter fists, more armor vaporized and splintered, more atmosphere streamed through broken plating, and more human beings died.
     Nasty stingers when they get close enough to fire, Prescott conceded grimly to himself as he watched them attack . . . and watched the fortresses' defensive fire thresh their splintered formations with death. But not many of them will.

     He was right. Very few of them got close enough to fire, but then he watched as one of the pinnaces continued straight onward in the wake of its FRAMs, closing in on the fortress it had targeted. Unlike the gunboats, it was making a suicide run, and the range was too short and its closing velocity too high for it to be stopped. Its icon converged with the fortress's, blended . . .
     The readouts went wild, and the icon of the fortress vanished as completely as that of the pinnace.
     "Admiral!" Chung yelled. "We getting downloaded data from the nearby fortresses—we can assess the force of that explosion."
     He paused momentarily while the computers did just that, and his pale-complexioned face went bone-white as the uncaring cybernetic brains presented the numbers.
     "Sir, that pinnace must've had its cargo bay loaded with at least six hundred FRAMs! That's the equivalent of sixty times an SBMHAWK's entire missile load!"
     Prescott blanched. No fortress could take that!

     Maybe not many of them will have to take it, he thought a moment later, as he watched whole flights of pinnaces vanish like moths in the flame of defensive fire. Small craft, like fighters, could be engaged by point defense, and the fortresses' point defense crews had suddenly become very highly motivated.
     "Jacques!" the admiral snapped. "Order all standby carriers to launch their ready fighters. They can get into range faster than we can."
     Mordechai's fighter bases, further from the warp point than his innermost fortress shell and thus far unscathed, were already launching.

     But even as they did, the tactical picture became still more complicated. Bug monitors began to emerge from warp, and as they did, they began to deploy small craft of their own. These were assault shuttles . . . and they, too, had been crammed full of antimatter munitions to enhance their deadliness as kamikazes. As they came streaking in to ram, the fortresses were forced to divert still more fire from the retreating gunboats to concentrate on the incoming threat—which, of course, improved the latter's chances of completing their own firing runs and then breaking off.
     On the main plot, the spherical area of space around the warp point, inside the innermost shell, now resembled a stroboscopic ball of swarming, flashing lights. And through that maelstrom, the first monitors were advancing ponderously towards the fortresses—fewer fortresses than anyone had expected to be there at this stage of the battle.

     "My fighters are fully engaged," Mordechai reported, as Dnepr and her consorts drew into position to reinforce the decimated fortresses and a conversation without time lags became possible. "But the ready squadrons were configured to engage ships and gunboats. None of them are armed with gun packs. Most of the BS6Vs don't even have the packs in stores!"
     Prescott's face tightened in understanding. Against targets as small, fragile, and nimble as small craft, "guns" were far and away the most efficient close-in weapon. They weren't actually anything a pre-space human would have considered a "gun," of course, but they were the closest thing twenty-fourth-century humanity had, and their clusters of individually powered flechettelike projectiles covered a far greater volume than the focused pulse of any energy weapon.
     "They'll just have to use their internal lasers, Alex," Prescott told the fortress commander grimly. "And at least my fighters are joining in, as well."
     "Thank God for that!" Mordechai's face was smoke-blackened, and behind him Prescott glimpsed a scene of desperate damage-control activity. "Are you arming the next wave with gun packs?"
     Prescott hesitated some fraction of a heartbeat.
     "Negative, Alex. Their battle-line's main body is bound to come through any time. I'm going to need them in the anti-ship role. They'll launch with FRAMs, not guns."
     "But, Admiral—"

     "Incoming!" The scream from somewhere behind Mordechai interrupted the task force commander. His head snapped around towards the shout, and . . . . . . Prescott's com screen dissolved into a blizzard of snow, then went dark.
     Prescott closed his eyes and waved the young com rating silent.
     "I know, son," he said. "I know."
     He didn't need to hear the "Code Omega" from Mordechai's command fortress. He'd seen its icon blink out of existence on the plot.

     Yet he had no time to grieve, for the Bugs' final surprise appeared on the plot with soul-shaking suddenness.
     By now, everyone was inured to mass simultaneous warp transits of Bug gunboats and even light cruisers, however incomprehensible the mentality behind them might be. But suddenly Raymond Prescott was back at the "Black Hole of Centauri," face-to-face with something no human being, no Orion, could ever become inured to. Not gunboats, not cruisers—superdreadnoughts.
     Twenty-four of them appeared as one, lunging through the invisible hole in space between Zephrain and Home Hive Three. He watched them come, watched them pay the inevitable toll to the ferryman as five of them interpenetrated and died, and a part of him wanted to flatly deny that any living creature could embrace such a tactic.
     But these living creatures could do just that, and they had. It was a smaller wave than they'd thrown through at Centauri, yet "smaller" was a purely relative term which meant nothing. Not when any navy was prepared to sacrifice so many personnel, so many megatonnes of warships, so casually.
     People wonder why the Bugs have never developed the SBMHAWK. There's no technological reason for them not to have it. But the problem isn't technological. It's . . . philosophical, if the word means anything as applied to Bugs. They probably can't imagine why anyone would want to use technology to minimize casualties.

     The surviving superdreadnoughts began to fire. They were using second-generation anti-mine ballistic missiles, sweeping away the minefields and the independently deployed energy weapons—and as seconds turned to minutes, the latter didn't fire back.
     "Why are the IDEWs just sitting there?" Prescott demanded.
     "Admiral Mordechai's fortress was the one tasked to control them," Mandagalla replied. "Admiral Traynor is shifting control now, but it takes time for the standby to gear up to order them to fire."
     Something that will have to be rectified in the future, Prescott thought behind his mask of enforced calm.
     "Are Force Leader Shaaldaar's second-wave fighters ready to launch?" he asked aloud.
     "Yes, Sir," Bichet said. "In fact—"
     "Good. Tell him to launch them."

     Three minutes had ticked by before the seriously reduced volley of energy-weapon buoy fire lashed out at the Bug capital ships. But now Prescott's battle-line was moving inward, pouring in long-range missile fire to support the fighters that were already beginning to engage, and there was something odd about the fire coming to meet it.
     "What's the matter with the Bugs' fire control?" the admiral asked, and Bichet looked up from his console.
     "We've been able to identify the classes of those superdreadnoughts, Sir. And they don't have as many Arbalest command ships as they should for that many Archers. Their interpenetration losses must've included a couple of Arbalests."
     "Thank God for that," Prescott said with feeling. About time we got a break, he added silently as he watched Shaaldaar's fighters slash in.

     The battle was stunning in its intensity, but not as long in duration as it seemed at the time. Afterwards, Prescott and Zhaarnak would freely admit that the Bugs might have broken through if they'd used all their superdreadnoughts in mass waves. But the remaining SDs and monitors began coming through the warp point in a more conventional fashion. There wasn't a single undamaged fortress in the inner shell left to receive them, but Prescott's battle-line was there. And the second wave of fighters from the BS6Vs arrived, armed with primary packs and eager to hunt monitors. After six of those titanic ships had died, the Bugs broke off the attack.
     Prescott was left staring at a plot that was far less colorful than it had been. Few of the fortresses of the inner shell remained, and virtually all of those were critically damaged. The stardustlike lights of mine patterns and weapon buoys were largely gone. And Sixth Fleet had lost six superdreadnoughts, three assault carriers, two battleships, nine battlecruisers and over six hundred fighters.

     But, he thought wearily, we held.

From THE SHIVA OPTION by David Weber and Steve White (2002)

      Twelve years before, when I was ten years old, they had discovered the collapsar jump. Just fling an object at a collapsar (black hole) with sufficient speed, and out it pops in some other part of the galaxy. It didn't take long to figure out the formula that predicted where it would come out: it travels along the same "line" (actually an Einsteinian geodesic) it would have followed if the collapsar hadn't been in the way—until it reaches another collapsar field, whereupon it reappears, repelled with the same speed at which it approached the original collapsar. Travel time between the two collapsars … exactly zero. (in other words they are jump points, but with jump links to lots of other points)
     It made a lot of work for mathematical physicists, who had to redefine simultaneity, then tear down general relativity and build it back up again. And it made the politicians very happy, because now they could send a shipload of colonists to Fomalhaut for less than it had once cost to put a brace of men on the moon. There were a lot of people the politicians would love to see on Fomalhaut, implementing a glorious adventure rather than stirring up trouble at home.

     The ships were always accompanied by an automated probe that followed a couple of million miles behind. We knew about the portal planets, little bits of flotsam that whirled around the collapsars; the purpose of the drone was to come back and tell us in the event that a ship had smacked into a portal planet at 0.999 of the speed of light.
     That particular catastrophe never happened, but one day a drone limped back alone. Its data were analyzed, and it turned out that the colonists, ship had been pursued by another vessel and destroyed. This happened near Aldebaran, in the constellation Taurus, but since "Aldebaranian" is a little hard to handle, they named the enemy "Tauran."
     Colonizing vessels thenceforth went out protected by an armed guard. Often the armed guard went out alone, and finally the Colonization Group got shortened to UNEF, United Nations Exploratory Force. Emphasis on the "force."

     There was a general movement toward the coffee machine. I got in line behind Corporal Potter.
     "What do you think, Marygay?"
     "Maybe the Commodore just wants us to try out the shells once more."
     "Before the real thing."

     "Maybe." She picked up a cup and blew into it. She looked worried. "Or maybe the Taurans had a ship way out, waiting for us. I've wondered why they don't do it. We do, at Stargate."
     "Stargate's a different thing. It takes seven cruisers, moving all the time, to cover all the possible exit angles. We can't afford to do it for more than one collapsar, and neither could they."
     She didn't say anything while she filled her cup. "Maybe we've stumbled on their version of Stargate. Or maybe they have more ships than we do by now."

     I filled and sugared two cups, sealed one. "No way to tell." We walked back to a table, careful with the cups in the high gravity.

From THE FOREVER WAR by Joe Haldeman (1975)

(ed note: the Sh'daar empire showed up one fine day and told the Earth confederation that the confed had to become enslaved by the Sh'daar or die. Earth takes exception to that. Admiral Koenig has lead a large task force (CBG-18) deep into Sh'daar space to take some of the heat off Terra. At the star Texaghu Resch they discover a huge artifact that is quickly identified as a modified Tipler cylinder (TRGA). Basically it is a stargate. Which means it is probably a bridghead, i.e., a trap)

      The Sh’daar fleet, if those had been Sh’daar warships, had given in far too easily. Their maneuvers had suggested that they’d been being guided by software, not organic intelligence . . . and rather low-grade software at that. After taking heavy losses, every one of those gray and silver ships had vanished down that rotating tube. The smart money said they would now be on the other side, probably heavily reinforced, waiting for the Confederation fleet to follow them.

     And if the CBG did so, it would be a slaughter.

     The problem was the tactical situation in which the battlegroup would find itself after traversing the TRGA cylinder—a situation analogous to a primitive warrior faced with entering an enemy’s tent, with the only access provided by a low and narrow door that required that he stoop and crawl. The interior of the tunnel was only about a kilometer wide, as wide as America was long. The ships of the battlegroup, all but the smallest frigates and destroyers, would have to go through in single file, and they wouldn’t be able to see what was waiting for them on the other side. The enemy would be in position to swarm in on each vessel as it emerged and destroy it, annihilating one ship at a time. An alerted enemy could be expected to have the far end of the tube covered by a hellstorm of nuclear warheads and high-energy beams, as well as those deadly weapons that appeared to collapse matter into neutronium. Unable to shield or to maneuver, unable even to fight back, the battlegroup would not have a chance against that concentration of firepower.

     But there might be a way. . . .

     He’d dismissed the fleet conference earlier, giving orders to the tactical departments throughout the fleet to work on possible approaches to the problem and report back to him by 1030 hours.

     It was time to initiate “Trigger Pull.”
     That was the operation name with which the battlegroup tactical departments had come back. Koenig had given them a problem: Was there a way to get through the TRGA bottleneck without subjecting the fleet to devastating and concentrated fire?
     And his staff had come back with an unqualified . . . maybe.

     The actual idea had come from General Joshua Mathers, in command of the fleet’s Marines. “What we need,” Mathers had said, “are some door-kickers.”
     The Marines of MSU-17 were there to seize enemy orbital fortifications, bases on moons or planetoids, or even, if necessary, grab a beachhead on an alien planet. Trained in CCBT—close combat boarding tactics—they could also be employed to storm enemy hard points, capture weapons positions, secure landing zones, or rescue prisoners. “Door-kicker” was a term from centuries before, referring to the man on point who would take down a locked door so the rest of the assault team could storm through. Tactics varied with the situation and the door; historically, they included the use of explosives, a shotgun, a battering ram, or a low-tech application of shoulder or foot.

     What Mathers had suggested was the use of explosives—specifically of high-yield nuclear explosives. CBG-18 possessed three ships designated as heavy missile carriers, or bombardment ships. The Ma’at Mons was a veteran of the battles of Arcturus and Alphekka, under the command of Captain John Grunmeyer.
     The other two had joined the fleet after the confrontation with Grand Admiral Giraurd at HD 157950. There was the Pan-European missile carrier Gurrierre, Captain Alain Penchard in command.
     And there was the Chinese Hegemony vessel Cheng Hua, officially designated as a cruiser, but in fact designed as a missile bombardment ship. She was under the command of Shang Xiao Jiang Ji.
     A typical missile bombardment vessel was a third the length of the America—around 350 meters long and massing perhaps 100,000 tons. The Chinese cruiser was a little smaller—312 meters in length. All had the same general layout dictated by the physics of high-velocity travel—a forward cap filled with water that served both as reaction mass and as a shield against particulate radiation—and a relatively slender spine mounting drives and a set of rotating habitation modules tucked into the cap’s shadow. Each ship housed massed batteries of launch tubes and carried some hundreds of nuclear-tipped missiles. The Confederation arsenal included both VG-92 Krait space-to-space missiles and the larger, more powerful, and heavily shielded VG-120 Boomslang, for space-to-ground bombardment. The Hegemony had their own versions of nuke-tipped smart missiles that filled the same niches.
     Each missile possessed a limited-purview AI, making it smart enough to evade enemy defenses and choose the best moment for detonation. They carried variable-yield nuclear warheads—up to a megaton for Kraits, and a hundred times that for Boomslangs. And the bombardment vessels’ fire control suites could fire, track, and direct hundreds of missiles simultaneously.
     The Ma’at Mons had used up much of her missile inventory at Alphekka, but reloads had been cranking through from the fleet’s manufactories on board the various stores and munitions ships with the fleet. The Ma’at’s tubes were up to 70 percent readiness, now, while the Gurrierre and the Cheng Hua both were at 100 percent.

     Usually, a bombardment vessel had plenty of room in which to operate. Her missiles had a range of anywhere up to 100,000 kilometers, and were designed to steer themselves on wide sweeps around the flanks of battlespace, in order to come in on the enemy from as many different directions as possible. This time, however, they would be firing their warloads while hurtling down the narrow confines of the tunnel.
     There’d be precious little room for error. The bombardment vessels would have to guide their missiles ahead of them into the tunnel’s opening, keep them tightly corralled as they traversed the tunnel’s length, then detonate them with absolutely precise timing instants before the ship emerged at the other end.

     “Attention all hands,” he said. “This is Admiral Koenig.
     “We are about to take a blind leap into the unknown. The alien artifact we’ve been calling the Texaghu Resch gravitational anomaly, the TRGA, or ‘Triggah,’ will lead us to the heart of a star cluster, which we believe to be over eighteen thousand light years from Earth. We’re not sure what will be waiting for us on the other side, but we can assume the enemy will be waiting for us, and in large numbers.
     “We are employing what General Mathers has called ‘door-kickers,’ our three bombardment vessels, which will shepherd their nukes through the tunnel and detonate them at the far side of the tunnel just before they emerge. We believe that massed thermonuclear detonations will both confuse any waiting enemy ships and seriously reduce their numbers . . . but I must emphasize that we do not have a tactical view of the far side, and we will have to pass through the tunnel and emerge before we can track and target the enemy.
     “We believe that if we succeed, we will find ourselves inside the enemy’s backyard, quite close to the homeworld of the Sh’daar, and at the very least deep inside the central regions of Sh’daar space. From there, we hope to negotiate a settlement with the Sh’daar government, and end the war that has threatened our worlds and the lives of our families for the past nearly four decades.
     “It is a terrible risk, and we will be facing terrible odds. But I believe it is a risk worth taking, because we have here a golden chance to end the war within the next few hours.
     “All ships of the assault formation! Acceleration in three . . . two . . . one . . . initiate, ahead slow. . . .”
     And the carrier battlegroup began moving forward, toward the waiting maw of the tunnel.

     Captain John Grunmeyer sat on the Ma’at’s bridge, his acceleration chair overlooking the navigational systems station, the helm, and the weapons stations, as the hazy dark blur of the tunnel’s interior wrapped itself around them. Deck, bulkheads, and overhead currently all projected imagery gathered from the shield cap forward, creating the illusion that the bridge was open and exposed to empty space. “Release Volley One,” he said.
     This was the tricky part . . . well, the first of several tricky parts, the biggest of which would be simply surviving the next few minutes. But it was the first step.
     The Ma’at Mons possessed four rotating modules evenly spaced about her spine. Two were hab modules for the ship’s crew of eighty-four. The other two were missile stores and launch bays. Like the fighters dropped from America’s rotating bays, missiles could be released gently from the cruiser, set free into open space with an outward velocity of about five meters per second—the impulse derived from a rotational acceleration of half a gravity. With one complete rotation, a string of Boomslang missiles was put into place, a necklace encircling the bombardment vessel like a ring.
     Data sent back from the hapless America fighter pilot who’d already fallen through the tunnel and reported back by message drone had told the mission planners what to expect—the strange apparent elongation of the tunnel as the Ma’at accelerated down its length, approaching at last the speed of light. The tightly clustered stars ahead had gradually smeared out into a high-velocity starbow, and still the tunnel seemed to go on and on and on. The boomslangs reached optimum separation from the ship, and their onboard AIs took control of their flight programs, arresting their outward drift, then beginning to move them forward, sliding past Ma’at Mons’ forward shield and into the space ahead. According to the data from Lieutenant Gray, they still had another ten subjective seconds.

     At seven seconds, the missiles’ AIs punched it, accelerating at fifty thousand gravities, which, since they were already moving at near-c, meant they slowly dragged their way forward one kilometer . . . ten kilometers . . . fifty kilometers ahead of the bombardment vessel.
     Then they hit the programmed screen engagement point, with five seconds to go, and the ship’s screens slammed to full.
     Despite the fact that all incoming electromagnetic radiation was now being blocked by the vessel’s electromagnetic screens, the image of the tunnel’s weirdly distorted interior remained. Telescoping antennae mounted around the shield cap’s rim and extended above the hull-hugging flow of the ship’s defensive screens continued to send in visual images from outside, distorted by the high velocity.
     Grunmeyer didn’t expect that to last for much longer, however. In another few seconds . . .

     Four VG-120 Boomslang missiles approached the far end of the tunnel and detonated in perfect unison, mutiple fireballs erupting within the kilometer-wide confines of the TRGA opening while they were still traveling at within a percent or so of the speed of light. The blast—radiant heat and hard radiation, together with the plasma that originally had been the eight-meter-long hulls of the missiles themselves—emerged from the tunnel in a star-hot eruption of apocalyptic white fury. The detonation was like a shotgun blast, and any Sh’daar ships or facilities in front of the TRGA opening would have been vaporized in an instant.
     Those first four warheads had been precisely timed to explode just inside the TRGA cylinder’s entrance, before they could be crumpled by the enemy’s matter-compression weapons. The next twelve missiles emerged in a ring just less than a kilometer across, entering a searing storm of high-energy plasma that in effect masked them from the enemy’s momentarily blinded sensors. Much of a Boomslang’s mass was in its shielding, which was designed to let it penetrate planetary atmospheres from orbit at high velocity without burning up and disintegrating. That shielding, along with their electromagnetic screening, protected their internal circuitry and the resident AIs from the surrounding firestorm for the precious second or two necessary for each missile to swing onto a new course, swinging around through 90 degrees and traveling out at right angles from the length of the rotating cylinder.

     Koenig and his tactical staff had decided that the likeliest location of any Sh’daar warships, fortresses, or guardian monitors protecting the Omega Centauri end of the TRGA would be beyond and even behind the opening. As each missile emerged from the expanding cloud of radiation, their sensors picked up the nearest potential military targets and accelerated, hard. They’d lost much of their velocity as they emerged from the tunnel into normal space, a phenomenon similar to the velocity bleed-off of ships emerging from the bubbles of the Alcubierre Drive. The course change and high-grav boost sent them streaking into the clouds of waiting alien starships faster than organic senses could have recorded it.
     The missile AIs, operating far more swiftly than organic nervous systems, located and identified the enemy targets, homed in on them, and detonated. Fresh nuclear firestorms erupted in empty space, blotting out the star-packed sky and etching in the TRGA cylinder in harsh, actinic radiance.
     And alien warships began dying in the thousands, the tens of thousands, before they could react and trigger their own weapons.

     Grunmeyer and his officers could only wait and watch from the bridge of their missile cruiser, able only to glimpse what was happening through the signals relayed back from the Boomslangs ahead. They saw the flashes, glimpsed massed hosts of enemy vessels . . . and then Ma’at Mons had passed through the tunnel opening and plunged into the expanding nuclear fireball engulfing a fifty-kilometer sphere of space beyond.
     “Multiple targets!” Commander Hugh Conrad called. But the imagery surrounding the ship’s bridge was already failing, flickering out in large sections, as the antennae mounted on the ship’s shield cap burned away in the fireball.
     “Volley fire!” Grunmeyer yelled in response, and missiles, dozens of them, spilled from rotating weapons bays, or lanced into darkness from launch tubes mounted beneath the shield cap and radiating from the vessel’s spine. The bridge projection screens were completely dark, now, the ship in effect cut off from the universe outside.

From SINGULARITY (Star Carrier Book Three) by William H. Keith, Jr. (under pseudonym Ian Douglas) (2012)


Though it does become difficult and fuel intensive for the defenders, since Alderson points do not orbit their primary star, while planets, orbital fortresses, anti-ship mines and blockading tasks forces have to. The defending forces must constantly be thrusting for the entire tour of duty just to maintain their position. In The Gripping Hand, sequel to The Mote in God's Eye, there is some mention of a constant stream of tanker ships travelling between the defending forces and the gas giant fuel sources. And there are only blockading spacecraft, orbital fortresses and mines are impractical.

Well, maybe not totally impractical. For mines a possibility is Dr. Robert Forward's statite concept. This uses a carefully angled solar sail to generate the constant thrust required to keep the mine stationary. I haven't done the math, but my gut feeling is that if the jump point is too far from the primary star the solar flux will be so low that even for low mass miles the sails will have to be huge. However, I am quite proud of making the jump point/statite connection, since this is actually an original idea by me (unlike almost all of the rest of this website).

While I haven't done the math on statites, David Harris did! Here is his analysis:

There is actually a very simple method to find the "thrust" on an object due to the solar flux radiating on it. The intensity of light per square meter divided by the speed of light has the same units (after some manipulation) as a pressure. So, very simply, to find this solar pressure, divide the intensity of light (in Watts per meter squared) by c (in meters per second). You get a pressure (in Newtons per meter squared). This pressure equates to light impacting on a surface, but if you have a mirror, the light also bounces off. This actually doubles the pressure on a mirror.

At 1 AU from the sun, the solar intensity is 1400W/m2. Dividing by c = 3x108 m/s and multiplying by two, we find that the pressure on a 1 square meter mirror should be 9.3x10-6 Newtons.

Now, if you want your mirror to float stationary at a certain point in space (like a non-orbiting "Jump Point"), the light pressure must counterbalance the gravitational force of the sun at that point. A quick check through a high-school physics book (bring a calculator) will show that the force on a 1 kg object at 1AU from the sun is a mere 0.00590 N. With this, it is easy to show that a 1 kg statite needs a solar sail 632m2 in area, or a square 25m on a side.

Now here cones something interesting: Solar intensity falls off as a 1/r2 law (inverse square), meaning if you increase the distance by a factor of three, the intensity falls by a factor of nine. Gravity also follows a 1/r2 law, meaning if you increase the distance by a factor of three, the gravitational force falls by a factor of nine. The math is easy, but it is excruciating to type, so I will leave it as an exercise for the reader to show that, since both forces are governed by a 1/r2 law, the size of the sail does not change as you change your distance from the sun. No matter how far you are from the sun, a 1 kg statite will always need a sail 25m on a side.

Now, what fun things can we go and do with this? Perhaps we can start with a simple minefield. We can arbitrarily assume that each mine is 1 megaton. Adding on detonators, sensors, etc., assume that the whole mine is one tonne. A one tonne mine needs a sail 794 meters on a side, or 632,000m2. Since the statite mine field will be located away from a planet, let us also arbitrarily decide that we will be defending a volume of space equal to the volume of the Earth. I really do not know how big the Jump Points or Crazy Eddie Points are, so this is pure guess work.

Assume we set our mines to detonate when a ship is 1km away. If a ship flew straight through the center of our minefield, I would hope that it would get within 1 km of at least one mine. If we assume one mine per 37,680 cubic kilometers, this gives us a 50/50 chance of a ship traveling through the center of our minefield coming within 1 km of a mine. Again, the tedium of algebra manipulation in ASCII prevents me from showing how I came to this figure. At one mine per 37,680 km3, we need 24 million (!) mines. That's 15 million square kilometers of solar sails!

With that many mirrors, you could do more damage with the reflected light than with the nuclear mines themselves! 15 million kilometers of solar sails adds up to 2.1x1016 watts of reflected light at 1 AU. That's 5 megatons of energy every second. In less than two months, the solar energy delivered by these mirrors would do more than the nuclear mines they are supporting.

David Harris

ClaysGhost's points out that the magnitude of the constant thrust problem depends upon how far the jump points are from the primary star.

The acceleration due to the Sun's gravity acting on a mass at the orbital distance of Jupiter is about 0.2mm/sec2. Even for a 100 tonne vehicle you need a counter-force of only 20N to keep your station.


This will make stealth difficult for a minefield. Even such low thrust from a rocket will be readily detectable, and a statite sail will be large enough to be hard to hide.

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