The Trouble With StarDrives

I wasn't going to put this section 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.

The technical term for FTL is "superluminal".

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.

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. Perversely, Ursula Le Guin has things the other way around - Ansibles, but no FTL drive. I'm going to be sexist and say that this is a woman thing: you can yak on the phone, but creeps can't get to you to break in and rape you.

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 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.

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 #2 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 stardrives 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.

Taken 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" or "stargate". 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.

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.

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


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

Your average physicist holds Relativity quite strongly. It has been tested again and again with an accuracy of many decimal places. They 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.

Therefore, they chose to jettison FTL travel.

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

  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".

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.

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.

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.

As a side note, those interested in the various ways time-travel seems to work in SF novel should run to the Guide To SF CHRONOPHYSICS.

Why have you not read about this 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 who do know enough relativity, practically no author 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.

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

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 set up a trip and the FTL drive would refuse to operate. Then the pilot would know that somehow someway the proposed trip would cause a paradox.

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, a paradox will ensue.


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)

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.

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)

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. Many novice SF novelists and game designers make the mistake of inventing a cause first and may not even try designing the effects.

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."

Effects help you avoid unintended consequences, and define the implications of your drive. Causes are fluffy technobabble explanations that a good SF story might avoid all together. As Gene Roddenberry noted, in a police TV show a policeman does not explain to the viewers how the primer of the bullet ignites the main charge propelling the lead slug down the barrel every time he shoots his handgun. Neither should Captain Kirk explain the operating principles of his phaser weapon, the fact that it is some species of sidearm is enough for the viewers.

Causes can also get you into trouble if your explanation implies new effects that you did not intend. They also give more weak points that a scientifically minded reader can use to poke holes in your theory.


The important things are the effects. 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?
  • Do the drive units require rare and hard to get materials? (the Traveller RPG required Lanthanum, H. Beam Pipers' ships required Gadolinium. Both of these are rare earth elements, emphasis on the "rare")

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.

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 thermonuclear self-destruct devices to discourage attempts at reverse-engineering. The empire takes its monopoly on stardrives very seriously.

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 fold 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.

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.

Books I will not write #4: Space Pirates of KPMG

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.

Alderson Drive

Larry Niven and Jerry Pournelle took the bull by the horns. Before they wrote their award-winning classic The Mote in God's Eye, they went to physicist Dan Alderson. Niven and Pournelle gave Alderson a list of things they wanted the proposed FTL to allow, and things to forbid. Dr. Alderson then custom designed a mostly plausible FTL drive to spec, but with additional limits. Niven and Pournelle kept within those limits, and the novel was improved as a consequence.


(interesting description of the physical basis of the Alderson drive omitted)

Travel by Alderson Drive consists of getting to the proper Alderson Point and turning on the Drive. Energy is used. You vanish, to reappear in an immeasurably short time at the Alderson Point in another star system some several light-years away. If you haven't done everything right, or aren't at the Alderson Point, you turn on your drive and a lot of energy vanishes. You don't move. (In fact you do move, but you instantaneously reappear in the spot where you started.)

That's all there is to the Drive, but it dictates the structure of an interstellar civilization.

To begin with, the Drive works only from point to point across interstellar distances. Once in a star system you must rely on reaction drives to get around. There's no magic way from, say, Saturn to Earth: you've got to slog across.

Thus space battles are possible, and you can't escape battle by vanishing into hyperspace, as you could in future history series such as Beam Piper's and Gordon Dickson's. To reach a given planet you must travel across its stellar system, and you must enter that system at one of the Alderson Points. There won't be more than five or six possible points of entry, and there may only be one.

Star systems and planets can be thought of as continents and islands, then, and Alderson Points as narrow sea gates such as Suez, Gibraltar, Panama, Malay Straits, etc. To carry the analogy further, there's telegraph but no radio: the fastest message between star systems is one carried by a ship, but within star systems messages go much faster than the ships.

Hmm. This sounds a bit like the early days of steam. Not sail; the ships require fuel and sophisticated repair facilities. They won't pull into some deserted star system and rebuild themselves unless they've carried the spare parts along. However, if you think of naval actions in the period between the Crimean War and World War One, you'll have a fair picture of conditions as implied by the Alderson Drive.

If the Drive allowed ships to sneak up on planets, materializing without warning out of hyperspace, then there could be no Empire even with the Field. There'd be no Empire because belonging to the empire wouldn't protect you. Instead there might be populations of planet-bound serfs ruled at random by successive hordes of of space pirates. Upward mobility would consist of getting your own ship and turning pirate.

From BUILDING THE MOTE IN GOD'S EYE by Larry Niven and Jerry Pournelle (1976)

     Five years. Five years ago Barbara Jean Ramsey and their son Harold were due back from Meiji. Superstitiously, Bart had waited for them before accepting his promotion... Barbara Jean had never come home from Meiji. Her ship had taken a new direct route along an Alderson path just discovered. It never came out into normal space. A scoutcraft was sent to search for the liner, and Senator Grant (Barbara's father) had enough influence to send a frigate after that. Both vanished, and there weren’t any more ships to send.

     “You got five forces in this universe we know about, ja? Only one of them maybe really isn’t in this universe; we do not quibble about that, let the cosmologists worry. Now we look at two of those forces, we can forget the atomics and electromagnetics. Gravity and the Alderson force, these we look at. Now you think about the universe as flat like this table, eh?” He swept a pudgy hand across the roseteak surface. “And wherever you got a star, you got a hill that rises slowly, gets all the time steeper until you get near the star when it’s so steep you got a cliff. And you think of your ships like roller coasters. You get up on the hill, aim where you want to go, and pop on the hyperspace drivers. Bang, you are in a universe where the Alderson effect acts like gravity. You are rolling downhill, across the table, and up the side of the next hill, not using up much potential energy, so you are ready to go again somewhere else if you can get lined up right, O.K.?”
     Ramsey frowned. “It’s not quite what we learned as middies—you’ve got ships repelled from a star rather than—”
     “Ja, ja, plenty of quibble we can make if we want to. Now, Captain, how is it you get out of hyperspace when you want to?”
     “We don’t,” Ramsey said. “When we get close enough to a gravity source, the ship comes out into normal space whether we want it to or not.”
     Stirner nodded. “Ja. And you use your photon drivers to tun around in normal space where the stars are like wells, not hills, at least thinking about gravities. Now, suppose you try to shoot past one star to another, all in one jump?”
     “It doesn’t work,” Ramsey said. “You’d get caught in the gravity field of the in-between star. Besides, the Alderson paths don’t cross each other. They’re generated by stellar nuclear activities, and you can only travel along lines of equal flux. In practice that means almost line of sight with range limits, but they aren’t really straight lines. . . .”
     “Ja. O.K. That’s what I think is happening to them. I think there is a star between A-7820 and 82 Eridani, which is the improbable name Meiji’s sun is stuck with.”
     “Now wait a minute,” Admiral Torrin protested. “There can’t be a star there, Professor. There’s no question of missing it, not with our observations. Man, do you think the Navy didn’t look for it? A liner and an explorer class frigate vanished on that route. We looked, first thing we thought of.”
     “Suppose there is a star there but you are not seeing it?”
     “How could that be?” Torrin asked.
     “A Black Hole, Admiral. Ja,” Stirner continued triumphantly. “I think Senator Grant fell into a Black Hole.”

     “Then how would Black Holes interact with—oh,” Rap Torrin said, “gravity. It still has that.”
     Stirner’s round face bobbed in agreement. “Ja, ja, which is how we know is no black galaxy out there. Would be too much gravity. But there is plenty of room for a star. Now one thing I do not understand though, why the survey ship gets through, others do not. Maybe gravity changes for one of those things, ja?”
     “No, look, the Alderson path really isn’t a line of sight, it can shift slightly—maybe just enough!” Torrin spoke rapidly. “If the geometry were just right, then sometimes the Hole wouldn’t be in the way. . . .”
     “O.K.,” Stirner said. “I leave that up to you Navy boys. But you see what happens, the ship is taking sights or whatever you do when you are making a jump, the captain pushes the button, and maybe you come out in normal space near this Black Hole. Nothing to see anywhere around you. And no way to gets back home.”
     “Of course.” Ramsey stood, twisted his fingers excitedly. “The Alderson effect is generated by nuclear reactions. And the dark holes—”
     “Either got none of those, or the Alderson force stuff is caught inside the Black Hole like light and everything else. So you are coming home in normal space or you don’t come home at all.”
     “Which is light-years. You’d never make it.” Ramsey found himself near the bar. Absently he poured a drink. “But in that case—the ships can sustain themselves a long time on their fuel!”
     “Yes.” Lermontov said it carefully. “It is at least possible that Senator Grant is alive. If his frigate dropped into normal space at a sufficient distance from the Black Hole so that it did not vanish down.”
     “Not only Martin,” Bart Ramsey said wonderingly. His heart pounded. “Barbara Jean. And Harold. They were on a Norden Lines luxury cruiser, only half the passenger berths taken. There should have been enough supplies and hydrogen to keep them going five years, Sergei. More than enough!”

(ed note: Spoiler: a rescue mission is sent. The only way to get back is to somehow generate a large nuclear reaction to create the Alderson effect. Crashing one of the trapped starships on the Black Hole will work. Unfortunately this is even more difficult that crashing a ship onto the Sun: the intense gravity will make the ship miss if you are a fraction of a degree off. Which means some brave volunteer will have to sacrifice themself to save the others, manually piloting the ship into a collision while the rescue ship is poised to jump. The rescue ship waits with their Alderson drive turned on, when the crashing ship creates the Alderson effect the drive will have something to make the ship jump.)

From HE FELL INTO A DARK HOLE by Jerry Pournelle (1973)

Jump Points

The Alderson Drive or "jump point" drive has been used in many SF starship combat games, for the same reason Niven and Pournelle used it: unlike most other FTL, it allows the possibility of interstellar battles.

Most other FTL is a "fly anywhere" kind of propulsion, which generally does not allow battles to occur except by mutual consent. Often a planet cannot even detect an enemy invasion fleet until it suddenly pops out of hyperspace. Interstellar wars only last long enough for your hyperspace bombers to fly to the enemy's planets, then a brief emergence 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. Then they fly home, only to discover that the enemy's bombers were on a similar mission. Go to The Tough Guide to the Known Galaxy and read the entry "SLAG"

These start-anyway go-anywhere 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'. Give me a setting in which the map still matters.

Please note that there is a second FTL situation that can allow interstellar combat. You need two things.

[A] Ships travel faster-than-light taking some time to travel the distance (i.e, travel is NOT instantaneous).

[B] There must exist some kind of faster-than-light radar that can detect the invading ships far enough in advance that the defenders have time to do something about it.

Something like 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).

In science fiction, jump points are generally very limited in number.

If they occur naturally, there are usually fewer than 10 in any given star system.

If they 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.

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. A starship with a fold engine 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.
Web and Starship
The Pereen web gates are teleportation devices. They can transport 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.

Defending Points

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. 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.

Vergeworlds Wormholes

Vergeworlds is a science fiction universe crafted by physicist Luke Campbell (who has been quoted extensively through this entire website).



  • Wormholes connect across space and time, not just space.

  • Nevertheless, you can't use wormholes to build a time machine.

  • A consequence of this is that interstellar wormhole networks form branching, tree-like structures with no closed loops.

  • You can try to steal nodes (worlds) from a neighboring branch by forming a closed loop. The weakest link will break, and if that link is in the other branch you will have stolen the nodes left stranded by the break. This is called a causality attack.

When you project a wormhole from a metropole world to a colony, you almost always exploit relativistic time dilation to reduce the perceived time to reach the colony from the metropole. For example, if the colony—metropole distance were 100 light years and the wormhole was projected at 99.9999% the speed of light, then it would take 100.0001 years for the wormhole mouth to reach its destination in the reference frame of the metropole and the colony. But due to relativistic time dilation, in the reference frame of the projected wormhole mouth it only takes 0.1414 years. Since you can look through the wormhole, you will see that 0.1414 years after launch, it arrives at its destination. At that point, you can go through and get to your new colony – you only need to wait about a month and a half to feel alien soil under your feet, rather than a century. In the metropole's reference frame, going through the wormhole takes you 100 light years away, and 99.8596 years into the future (going the other way, from the colony to the metropole, takes you 100 light years away and 99.8596 years into the past).

One might think that these time warps would let you engage in all kinds of time travel. It is easy to see that the metropole—colony situation described here doesn't allow these kinds of shenanigans. For practical purposes, you only have a time machine when you can go back to the place you left at a time before you left. And you can't do that here. Go from Colony to Metropole and you go back in time 99.8596 years. Go back to Colony through the wormhole, and you go forward in time the same amount, plus any time you spent on Metropole, so you get back after you left. If you go back through flat space-time, it will always take at least 100 years since you can't go faster than the speed of light so you also get back after you left. No paradoxes for you!

However, it is easy to imagine situations where a wormhole, or a configuration of wormholes, does make a time machine. Imagine that there are two colonies, Colony A and Colony B, each 100 light years away from Metropole, and 100 light years away from each other. The wormholes to both colonies go 99.8596 years into the future when traveling from Metropole to either colony. Now Colony A sends a wormhole to Colony B. The Colony A wormhole also goes 99.8564 years into the future when going from Colony A to Colony B. This means if a traveler at Colony B went through the Colony A wormhole he would go back in time 99.8564 years. Then going from Colony A to Metropole he would go back in time another 99.8564 years. Then he could go from Metropole to Colony B and go forward in time 99.8564 years. The net result is that he ended up back where he started nearly a century before he left.

It seems that nature really doesn't like time machines. Here's why. Think about what happens when the Colony A – Colony B wormhole has gone just far enough that a light signal going through the wormholes can get back to where it left just as it is leaving. Now, since the propagating signal and the newly transmitted signal are both leaving at the same time, you have double the intensity. So this doubled intensity signal goes around and meets itself again, quadrupling its intensity. And so on. At this point, just as the configuration is on the verge of becoming a time machine, it becomes a perfect resonator for light signals, which then build up to arbitrarily high intensities until something breaks and you don't have an incipient time machine any more.

Now clever people will try to come up with ways around this — like putting a lead shield in the way of the signal's path. It turns out these tricks don't work. When you pull quantum mechanics into the picture, what get amplified are virtual fluctuations in the electromagnetic field and those can go around and anything it is possible to go around and through anything it is possible to go through. And it's not just light. All other particles behave the same way, so even if you somehow got the wormhole past the point where light would destroy it, it would be ruined by all kinds of other quantum fluctuations. You can't beat nature. And nature doesn't like time machines.

The consequence of this is that if you have closed loops in your wormhole network, it is really hard to keep time machines from forming. There are tricks you can play on a planet, but all interstellar wormhole networks form tree-like branching patterns without closed loops for just this reason.

But you can exploit this no-time-machine property. It is called a causality attack. If you are on one branch of a wormhole network and want to expand a bit but are blocked by a neighboring branch, you beef up all your wormholes and then send a wormhole to the neighboring branch. Something will break, but if it is a wormhole connection in the neighboring branch that is the weakest link, the network will break there. Now you have just stolen all the nodes (worlds) in the network that had been cut off by the break, and you can get to them using the wormhole you just sent.

In the Human expansion into the Milky Way, these sorts of attacks were common between the Americans and Chinese, Americans and Europeans, Europeans and Indians, and Indians and Chinese. This jockeying for territory was considered just the way things were done, and generally accepted back on Earth. The American president might engage in trade negotiations with the Chinese premiere the day after a causality attack stole a dozen American worlds and all their colonists for the Chinese, with little more than lodging and official complaint. The colonists, on the other hand, usually get pretty pissed off about such things.


A description about how two wormhole networks would fight in my Vergeworlds setting


  • It is difficult for an attacker from one wormhole network to capture worlds from another network in a timely manner.
    By destroying the wormhole to a conquered world, the defender can greatly slow down the attacker.

  • The best way for an attacker to attack across a broken wormhole is to exploit any back doors that also link back to the same world.

  • The Squirm used the wormhole communication system of the Mants and Gummis to get around broken wormhole links.

  • Humans don't use wormholes for communication in the same way, so Squirm have been known to clandestinely abduct Humans, infect them with a mind-control parasite, implant a miniature wormhole in them, and set them loose to return home before beginning their invasion, in order to prevent a broken wormhole from stopping their advance.

We have already seen that when a metropole projects out wormholes to colonies, the connection from the metropole to the colony takes you considerably forward in time as well as through space. For example, if the metropole and colony are 100 light years apart, going from the metropole to the colony will take you nearly a century into the future.

Now suppose the Squirm capture the colony. The metropole will want to immediately break the wormhole to the colony. They can always project another wormhole if they want to counter-attack, which will connect across the same time-lag … from the point of view of the colony and the metropole, only as much time will have elapsed as it takes for the wormhole mouth to travel there (0.1414 years, in the above example). On the other hand, if the Squirm want to advance onto the metropole, they will need to project their own wormhole. But they're already nearly 100 years ahead in time compared to the metropole – projecting their own wormhole back the other way would result in connecting to a time coordinate nearly another 100 years ahead of the colony's time. This gives the metropole two centuries to prepare for the invasion. Two centuries of industrial output and military buildup, to fight off an invasion force which the Squirm only have a month and a half to prepare for. Therefore, the major objective of the Squirm will be to capture the wormhole before it can be destroyed, and clamp it open. Otherwise, their invasion of the metropole will almost always fail.

In the wars of the Squirm with the Zox and the Gummis, the Squirm were able to exploit a back door. Both the Zox Hierate and the Gummis used Antecessor technology, including ultra-miniaturized wormholes. These tiny wormholes were used for wormhole phones. A phone connected to a base station via a wormhole, allowing nearly instantaneous communication between the phone and the station. The station can then route your call to any other wormhole phone connected to the same station, or to other stations using wormholes between stations. The station ensures time-balancing via time dilation of either end (using miniature cyclotron-like devices based on affectors) or, in extremis, lengthening the wormhole throat. This avoids causality-related collapse in a wormhole-rich environment.

Taking a wormhole phone through another wormhole automatically avoids issues with causality and allows you to communicate instantly across interstellar distances, since the phone wormhole picks up the exact same time lag as the transit wormhole as it goes through. This made them popular with travelers. When a Squirm captured a phone a traveler was using, however, this gave them a wormhole link back to the phone's station which they could enlarge and send an invasion through.

Humans don't use wormhole phones. They use microwave transmissions and fiber-optic guided lasers. At first, this stymied the Squirm in their war with the Humans of the Indian bough. They hit upon an insidious solution, though. They developed a mind-control parasite that infected Humans and Pannovas. Before beginning an invasion, they would covertly locate a Human (Pannovas were very rare in the Indian bough) from a different world, abduct him or her, infect him or her with the parasite, and implant a miniaturized wormhole. The parasite instilled an overwhelming desire to return home. Only when the target arrived home would the Squirm invasion begin, providing them with a concealed route to different Human worlds.

In the Verge, all polities forbid taking wormhole phones through wormholes. Human technology is used exclusively for inter-world communication (usually routed through the main transport wormhole). This is one of the few Human technologies the Zox will use. Even the Gummis, with their lack of most authoritarian political organizations, form public health and safety committees that enforce this ban – usually with the enthusiastic support of the public since Gummis remember all too well the devastation of the Squirm. In the Verge Republic, Transit Law and FERA are responsible for detecting, tracking down, and neutralizing parasite-controlled travelers. Transit Law is also tasked with identifying and neutralizing covert Squirm operations before they can capture and infect citizens. Local law enforcement and health authorities also act to prevent and intercept infected people in their jurisdiction before they can become a threat.

It is worth noting that if two distinct networks connect to each other with more than one wormhole, it will form a closed loop. This initiates a causality attack, and the weakest link within that loop will break. This may well result in some of the worlds changing which network they belong to. The Gummis used this tactic extensively in their war with the Squirm. This allowed them to break pieces off the Squirm network and defeat them piecemeal, isolated from assistance of the concentrated force of the Squirm armed forces.

StarForce Alpha Centauri

Another FTL system that was carefully crafted in order to force a specific situation was the one created by Redmond Simonsen for the wargame StarForce: Alpha Centauri (keep in mind this is a paper-and cardboard tabletop game, not a computer game).

In the game, starships or "TeleShips" are jumped or "shifted" instantaneously from one location to another several light-years away by teams of women with psionic powers. Shifting cannot be done by a machine, it has to be done by a person. The supply of psionic or "telesthetic" women is limited. There is no way to genetically engineer them, they naturally occur at the rate of one First Order Telesthetic per million females (why? because Redmond Simonsen is trying to force a specific situation). Energy is cheap, any ore or element can be synthesized, any material good can be manufactured.

So the only valuable interstellar commodity are telesthetic women.

This has several implications. In interstellar warfare, there are no carpet bombings of planetary populations with mass destruction weapons. This would destroy the only valuable item the planet has: a population that can produce more telesthetic women. Obviously, there are no restrictions placed on population growth, and large families are encouraged by the planetary governments.

Since the population of telesthetics is so limited, they sort of know each other. They are also all members of the same Telesthetics Guild. Therefore, in ship-to-ship combat, weapons are not designed to kill.

Instead, the anti-ship weapon is sort of a telepathic command to the enemy teleship to make an uncontrolled interstellar shift into a random awkward location. Such a shift can be up to five times the distance of a safe shift, so a teleship will take a while to crawl back to the battle but will be essentially unharmed. And in any event, a teleship that can jump between the stars is not going to have any difficulty avoiding something as sluggish as a laser beam.

The main point to be aware of is that the telesthetics are not just the propulsion system, they are the anti-ship weapon as well.

Against planetary populations, teams of telesthetics can create the so-called Heissen Effect. This sedates the inhabitants, sending them to sleep. The ships then land squads of StarSoldiers in gravity sleds to take control. The inhabitants later wake up with migraine headaches and a newly installed government.

Teleships have a maximum safe shift limit of five light years. If a friendly teleship does nothing but sit stationary and telesthetically "enhance" its location, another friendly can do a safe shift to that enhanced location from up to ten light years.

Attempting to shift a distance greater than the safe limit is called "over-shifting." There is a small chance that the shift will go as planned. There is a greater chance that the shift will malfunction. A bad shift will be either a "mirror shift" where the teleship moves in the exact opposite vector, or a "randomization" where the teleship appears in a random location within twenty light-years of Sol (i.e., up to four safe shifts away from Sol).

A "Star Gate" is a nine kilometer ring of chanplastic, crammed with telesthetics intimately familiar with the fabric of local space. A teleship starting at a star gate and shifting to an unenhanced location has a safe range of ten light-years, fifteen light-years to an enhanced location. Shifting from one star gate to another has a safe range of twenty light-years.

Since telesthetics are at a premium, there are no warships or orbital fortresses. Instead in times of war, merchant ships and star gates are converted into warships and forts. Otherwise, in between wars, you would have part of the limited supply of telesthetics tied up as the propulsion system for idle warships. This does nothing except reducing the maximum size of the merchant fleet. And the same goes for star gates. They can get away with having no warships since the telesthetics are not just propulsion, they are also the weapon system.

You see the basic effect that flows from the FTL drive is that wars are relatively bloodless. The secondary effect is that pressures were created that caused wars. The latter effect is desirable, since a wargame simulation requires wars to simulate.

The Solar Government was to expend several trillion Labor Credits before it discovered that...

  • (a) the discontinuity window could not reliably be produced on or near a planetary mass
  • (b) only 139 people out of 19 billion could produce the effect
  • (c) they were all women
  • (d) they were all powerfully telesthetic (i.e., clairvoyant), and mildly telekinetic
  • (e) a window could only be created between two positions in space that the Telesthetic was "comfortable" in and felt she "knew"
  • (f) a Gnostech (computer with artificial intelligence) initiated by the using Telesthetic was required
  • (g) bionic/electronic techniques could be used to amplify and refine the effect, but no pure-machine system could create it
  • (h) the range of the effect was theoretically unlimited but its accuracy was subject to degradation with the square of the distance.

Psionic linking techniques and the Telesthetics founding of the Telesthetic Guild was the response. It is probably the heavy use of empathetic bridging in these techniques that explains the remarkable fact that no member of the Guild, even while on opposing combat teams, has ever deliberately caused another member's death.) This solidarity of Telesthetics was almost totally responsible for the virtually bloodless conduct of the Intra-Specific Wars of Autonomy in the 25th Century.

In a sense the Outleap itself was responsible for the Wars of Autonomy: it dispersed and enlarged the human community into a multi-system race which was heavily dependent upon one socioeconomic factor, one resource that could not be synthesized by technology — the Telesthetics. The number of Telesthetics available to a given system was almost purely a function of how much population was contained within or controlled by that system.

The freedom from birth-controls in the colonized systems did have the desired effects of providing the population basis for "home-grown" Telesthetic crews to operate the Star Gates and the increasing number of Teleship.

It also, however, had several counter-productive side effects: (a) The vastly increased and dispersed human population became ungovernable by the institutions of the Solar Hegemony, (b) the "frontier" societies tended to produce divergent eco-political systems that either wanted independence, or worse, attempted to impose their provincial "solutions" on the rest of humanity.

All these factors conspired to produce a number of essentially pointless wars.

Redmond Simonsen

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.

From Web and Starship game manual, Greg Costikyan (1984)

Stardrives in Science Fiction

Fuller still looked puzzled. "See here; with this new space strain drive, why do we have to have the molecular drive at all?"

"To move around near a heavy mass — in the presence of a strong gravitational field," Arcot said. "A gravitational field tends to warp space in such a way that the velocity of light is lower in its presence. Our drive tries to warp or strain space in the opposite manner. The two would simply cancel each other out and we'd waste a lot of power going nowhere. As a matter of fact, the gravitational field of the sun is so intense that we'll have to go out beyond the orbit of Pluto before we can use the space strain drive effectively."

From Islands In Space by John W. Campbell, jr. (1931)

“What in blazes has that to do with your failure to obey orders?” he demanded, with explosive vehemence. “That ship must have used an interstellar space-warp drive to appear out of nowhere in the middle of the Asteroid Belt. And you deliberately let it slip away from you!”

Langford shut his eyes before replying. He saw again the myriad stars of space, the dull red disk of Mars and the far-off gleam of the great outer planets. He saw the luminous hull of the alien ship looming up out of the void. An instant before, the viewpane had been filled with a sprinkling of very distant stars with a faint nebulosity behind them. The ship had appeared with the suddenness of an image forming on a screen, out of the dark matrix of empty space.

Langford leaned forward, a desperate urgency in his stare. “Mere alienage doesn’t justify the crime of murder , sir!” he said. “Attacking an alien race without weighing the outcome would have been an act of criminal folly, charged with great danger to ourselves.”

(ed note: this is the earliest reference I've mananged to find of the term "space warp drive")

From The Miniature Menace by Frank Belknap Long (1950)

"Ladies, gentlemen! We are ready for our first Jump. Most of you, I suppose, know, at least theoretically, what a Jump is. Many of you, however—more than half, in point of fact—have never experienced one. It is to those last I would like to speak in particular.

"The Jump is exactly what the name implies. In the fabric of space-time itself, it is impossible to travel faster than the speed of light. That is a natural law, first discovered by one of the ancients, the traditional Einstein, perhaps, except that so many things are credited to him. Even at the speed of light, of course, it would take years, in resting time, to reach the stars.

"Therefore one leaves the space-time fabric to enter the little-known realm of hyperspace, where time and distance have no meaning. It is like traveling across a narrow isthmus to pass from one ocean to another, rather than remaining at sea and circling a continent to accomplish the same distance.

"Great amounts of energy are required, of course, to enter this 'space within space' as some call it, and a great deal of ingenious calculation must be made to insure re-entry into ordinary space time at the proper point. The result of the expenditure of this energy and intelligence is that immense distances can be traversed in zero time. It is only the Jump which makes interstellar travel possible.

"The Jump we are about to make will take place in about ten minutes. You will be warned. There is never more than some momentary minor discomfort; therefore, I hope all of you will remain calm. Thank you." The ship lights went out altogether, and there were only the stars left.

It seemed a long while before a crisp announcement filled the air momentarily: "The Jump will take place in exactly one minute." And then the same voice counted the seconds backwards: "Fifty...forty...thirty...twenty..."

It was as though there had been a momentary discontinuity in existence, a bump which joggled only the deep inside of a man's bones.

In that immeasurable fraction of a second, one hundred light-years had passed, and the ship, which had been on the outskirts of the solar system, was now in the depths of interstellar space.

Someone near Biron said shakily, "Look at the stars!"

In a moment the whisper had taken life through the large room and hissed itself across the tables: "The stars! See!"

In that same immeasurable fraction of a second the star view had changed radically. The center of the great Galaxy, which stretched thirty thousand light-years from tip to tip, was closer now, and the stars had thickened in number. They spread across the black velvet vacuum in a fine powder, back-dropping the occasional brightness of the nearby stars.

From The Stars, Like Dust by Isaac Asimov (1951)

The warp theory of my esteemed colleagues (and I am sure they will correct me if I am wrong) is based on the principle that two separate units of anything cannot exist in the same place at the same time; nor can they coexist without each having an effect upon the other. When the units are energy fields, the effect is supposed to be spectacular. (The effect is spectacular —I will admit that. As my esteemed colleagues have already so admirably demonstrated, the effect is certainly spectacular... though I somewhat doubt that this was the specific effect they had hoped for.)

Theoretically —at least, as their theory says —when two continuous fields are overlapped, it will cause a wrinkle in the fabric of existence. Unfortunately, the continuous energy field is only a myth —a mathematical construction. It is a physical impossibility and cannot exist without collapsing in upon itself.

Of course, there are still some members of this learned academy who insist on remaining doggedly skeptical of this fact of life. It is almost pitiful to watch them continue these attempts to generate an energy field that is both continuous and stable. So far, the only thing that they have succeeded in doing is to convert several million dollars' worth of equipment, buildings, and surrounding property into so much slag. (Oh, and incidentally, in doing so, they have also proven me correct.)

DR. J. JOSEPH RUSSELL, PH.D., M.A.. etc., comments to the Board of Inquiry into the Denver disaster

Insufferable old windbag!


Dammit! It's like trying to stack soap bubbles!

DR. ARTHUR DWYER PACKARD, remark overheard by lab. assistant and quoted by Duiy Hirshberg in "Packard —Behind the Myth"

In light of events, it would be criminal to let them continue.

DR. J. JOSEPH RUSSELL, comment to newsmen after appearing before the Board of Inquiry

Actually, they were on the wrong track to begin with. The problem was not to create a continuous and stable energy field at all —but only to overload a section of space. Once they began thinking of it in those terms, the. solution was obvious —and even practical, considering the then existing technology.

The answer lay in the use of a series of interlocking noncontinuous fields. The noncontinuous field gives the illusion of continuity, but like a strobe light, the field is actually a very rapid series of ons and offs. Several noncontinuous fields working in phase can create a stable continuous field. Each of the separate noncontinuous energy fields fills in the gaps of the others.

Three noncontinuous fields can dovetail their functions to make one continuous one, and two continuous energy fields can be overlapped to generate the much sought after warp.

When six field generators are working in phase and all on the same section of space, a great pressure quickly builds up. Something has got to give. Usually space does.

HOWARD LEDERER, Encyclopedia of 1,000 Great Inventions

Dammit! Why didn't I think of that?!!

Remark attributed to DR.ARTHUR DWYER PACKARD

Because, I did.

Remark attributed to DR. J. JOSEPH RUSSELL

The warp has no relation at all to normal space. It is a bubble, or miniature universe. Within it a ship still obeys all the known laws of physics, but it is totally separated from the outer universe.

The bubble, or warp, is made up of great energies locked together in a titanic embrace. The potential power inherent in that embrace is far greater than the sum of the component energy fields —not just because the bubble is a stable construct, but because it is a dimple in space itself. The very structure of existence is pressing against it, trying to restore itself to a condition of minimum distortion. With such an infinite store of unexpressed force to draw upon, the potential power of the system is almost unlimited. (In practice the limit is the size of the ship's generators.)

If a secondary set of fields is superimposed across this point of pressured space —that is, the warp —it acts to liberate some of this great power and simultaneously provides a focus for it. As every second sees the warp restored to stability, the bubble cannot collapse; but this continued release of energy must be somehow sublimated —and it is; the effect is the introduction of a vector quantity into the system.

Because the shape of the secondary fields can be controlled, they can be used to produce a controllable velocity in any direction. The warp can be made to move at velocities many times the speed of light.

The Einsteiniun time-distortion is neatly sidestepped, as the ship is not really traveling faster than light—only the warp is. The ship just happens to be inside it. It is the warp that moves, the ship moves within the warp and is carried along by it. Consequently, a starship has two velocities, one is the realized faster-than-light velocity; the other is the inherent normal space velocity....

... For maneuvering within a planetary system, inherent velocity is an important resource; but unless it is compensated for, it can cause havoc to a ship in warp....

JARLES "FREE FALL" FERRIS, Revised Handbook of Space Travel

From Yesterday's Chidren by David Gerrolds (1972)

"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!"

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."

"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)

Existing Drives

There are a few semi-plausible FTL methods out there. One of the most famous is Dr. Miguel Alcubierre "Warp Drive", along with Chris Van Den Broeck's improvement. Dr. Alcubierre specifically set out to make a warp drive similar to the one in Star Trek, but obeying the laws of physics. The ship is enclosed in a highly distorted bubble of spacetime. The ship technically is not moving faster than light, the warp bubble is and the ship is carried along for the ride. Problems include: it requires more energy than is contained in the entire universe to set it up, the ship inside cannot see where it is going, the ship inside cannot release the warp bubble and is thus permanently trapped without outside help, quantum mechanics says the bubble will rapidly fill up with deadly Hawking radiation and will otherwise be very unstable, and when the bubble is stopped all the interstellar particles swept up will be emitted as a planet-destroying burst of gamma-rays and high energy particles in the direction of travel.

There are others at Dr. John Cramer's Alternate View archives, Edward Halerewicz, Jr.'s Warp Physics site, Marcelo B. Ribeiro's Warp Drive Theory site, Lawrence H. Ford and Thomas A. Roman's Scientific American article Negative Energy, Wormholes and Warp Drive, David Waite's Modern Relativity site (if you can understand the math), and NASA's Warp Drive When?

More on the fringe is Burkhard Heim and his theory of everything. If the theory describes reality, it could give a form of FTL travel with an artifical gravity propulsion system at no extra charge. You can read the research paper and the expanded version here.

Luke Campbell's notes

I am going to throw my support behind scientifically plausible magitech. These are tricks like Krasnikov tubes, Alcubierre/Van-der-Broeck warp drives, and traversable wormholes. General relativity allows a number of solutions of getting from here to there faster than a photon chugging along through flat space-time, and some of these solutions can even be accomplished with less than Jupiter masses.

The fun thing about scientifically plausible magitech is that it leads you in all sorts of unexpected directions. You get interesting restrictions on what is possible and often your setting takes delightful unexpected twists when you consider the implications. Sometimes, you end up having to ditch cool ideas — much like ditching space fighters. For example, why take a rocket ship through a wormhole to Zeta Reticuli rather than getting on a tram through the Spokane wormhole gate directly to Port Kato, Zeta Reticuli Prime?

I'll haul out my PhD in physics and the work I've done in general relativity to mention that wormholes, warp drives, and Krasnikov tubes are viable solutions of Einstein's equations of general relativity. They require some rather odd conditions, namely regions of space-time with negative energy densities. We know this is not unphysical, since there are odd cases we know or strongly suspect exist with negative energy densities (black hole event horizons, the Casimir effect between nearby conducting surfaces). The fun stuff tends to require an awful lot of negative energy, but the amount needed tends to keep getting smaller with more research.

A few highlights of the various space-warping methods:

Wormholes are shortcuts through space-time. One end of a wormhole connects on another end, and going through takes you somewhere else in space and time. Wormholes are two way — you can go back again, and going through a wormhole may (or may not) involve strong tides but is otherwise just like traveling through any other region of space (none of this shimmery barrier like you see in StarGate).

It is strongly suspected, but not yet proven, that a wormhole cannot take you farther back in time than it would take for a light signal to propagate from where you are going to where you left — in otherwords, wormholes can be used for FTL but not time travel (in relativity jargon, they only connect space-like intervals). Trying to move a wormhole around so as to make a time machine is thought to result in the destruction of the wormhole (or possibly just large forces that prevent the wormhole from entering into configurations that let you travel into your own past).

All conserved quantities are conserved locally at wormholes — if a wormhole end has a given mass, pushing something with extra mass through the wormhole from that end will add its mass to the wormhole end, while if something comes out of that end, its mass will be subtracted from that end of the wormhole. The same goes for electric charge and (in a vector sense) momentum. If wormholes cannot have negative mass, this limits the amount of stuff you can send one-way through a wormhole before needing to send more mass back the other way.

Many Sci Fi authors posit wormholes orbiting around stars in the vacuum of space, but there is no real reason I can think of not to have them located some place more convenient, such as in the aforementioned Spokane, WA. You would probably want to put them in an airlock to keep all the air from whooshing through from high pressure to low, and if you have more than one wormhole you will need to be careful that that there are no round trips you can take that bring you back into your own past (because if there was, some wormhole leg of that trip would collapse to prevent this).

Warp drives let you take a spacecraft and warp space-time around it so that a bubble of space-time around the spacecraft surfs through space-time at an apparent superluminal rate. The spacecraft, however, is at rest inside its bubble and is not actually moving.

The most plausible form yet devised is the Alcubierre/Van-der-Broek geometry, which pinches the spacecraft off into a pocket universe connected by a microscopic wormhole to our universe through a region smaller in volume than a proton. Then you warp the microscopic wormhole end rather than the huge volume of the entire spacecraft. Clearly, the spacecraft would be blind while warping.

There are unresolved issues with a warp drive — when moving at super-luminal speeds you get a singularity "bow shock wave" at the front of the bubble, which may not be physical (we are not sure yet). Also, when going super-luminal, the spacecraft is causally disconnected from the rest of the universe, so it could not maneuver while warping, only travel on a pre-planned course. These last two limitations go away if you only use the warp drive for sub-luminal journeys (making a warp drive a sort of reactionless drive). The conservation laws still hold — if you warp close to a planet, the planet's gravity will pull on the warping craft and change its velocity, building up momentum toward the planet.

Krasnikov tubes are not well researched yet, but they seem to work. You prepare a path through space-time along which material objects can move back and forth at apparent super-luminal speeds. This is sort of like an interstellar rail line.

Note that none of these tricks allow local faster than light motion through space-time — you only seem to move faster than light to distant observers.

I will mention that we already know of at least two cases which are experimentally verified as having negative energy density — the Casimir vacuum between conductive surfaces and so called "squeezed states". If black holes exist, then the event horizon of a black hole will also have a negative energy density.

One nice thing about wormholes is that they let you adventure in a universe filled with interesting aliens that are naturally neither so god-like in their technology that they completely out-class you nor mere stone-age primitives.

Consider — suppose we humans invent a way to split off a pair of connected wormhole mouths from the vacuum and keep them open. We can use them for interstellar transport by charging up one of the mouths and putting it in a particle accelerator to shoot it out toward an interesting looking star at ultrarelativistic speeds (make sure to discharge it in flight, or it may be deflected by interstellar magnetic fields). When it reaches the destination star, slow it down by shining an intense laser through it and using the light beam as a photon rocket. Once you stop, gobble up some mass so you can send things through.

Now, the thing about wormholes is they do not connect points in space, they connect events in space-time. That ultrarelativistic wormhole you shot out will have a very high time dilation while it is in motion. From the point of view of the wormhole mouth in motion, it might only take a month to make a 100 light year journey due to time dilation. Since the wormhole mouth back home is connected to the wormhole mouth in transit both in space and time, the people back home only need to wait one month before they can look through the wormhole and see the virgin star system, ripe for colonization. We'll call our new conquest Terra Nova.

Of course, in our reference frame that is not looking through the wormhole, it takes somewhat over 100 years for the wormhole mouth to travel those 100 light years (for the listed time dilation, it takes 100 years, 18 minutes). This means the wormhole is a time machine that takes you (roughly) 99 years, 11 months into the future if you go from Earth to Terra Nova, or 99 years, 11 months into the past if you go from Terra Nova back to Earth.

Now there are certain details we will need to follow if we have wormholes to many star systems, to prevent the creation of time machines (which will probably break the wormholes involved before we can make the time machines). The main idea, though, is that an expansion front of earth civilization sweeps through space at almost the speed of light — and due to time dilation, as the expansion front overtakes regions of space, they are linked back to human civilization at a time (and thus level of technological advancement) not too far beyond what is needed to make wormholes.

Now, suppose there is another technological civilization in a distant galaxy. Maybe they have not even evolved by the time we start sending out wormholes (in some galaxy centered reference frame). Maybe (in that galaxy centered reference frame) they were ancient long before our distant ape-like ancestors came out of the jungles to gaze across the African savanna. Nevertheless, due to time dilation effects of wormhole transport, when our expansion front meets their expansion front, we will both have only recently invented wormholes (well, maybe within a few hundreds of years — but not millions of years).

Perhaps a timeline would help. I will use GMT to refer to the Greenwich Mean Time coordinate frame. Keep in mind that the actual time coordinate depends on your frame of reference.

Jan 1, 00:00:00.00 2050 AD GMT

Mankind launches a wormhole mouth toward Nova Terra. The other mouth remains on earth. Nova Terra is 100 light years distant from earth. The launched wormhole mouth has a time dilation factor of 1200 — for every second of proper time experienced by the mouth, 1200 seconds pass in the GMT coordinate frame. To make this explicit, a motor is placed inside the wormhole. The motor turns a drive shaft that connects to an analog clock face on each side of the wormhole. Since the shaft turns at the same rate for both clock faces, anyone looking through the wormhole sees the same time on both the clock face on Earth and the clock face on the other side of the wormhole. The clock drives the shaft at a rate such that the clock faces turn at one second mark per second of proper time. A time dilation factor of 1200 corresponds to a speed of 0.999999653 c.

Jan 1, 00:18:15.75 2150 AD GMT

The wormhole mouth arrives at Terra Nova. 100 years, 18 minutes and 15.75 seconds have passed in the reference frame at rest with respect to Earth. This is 3,155,761,095.75 seconds. Due to time dilation, the projected wormhole mouth experiences only 1/1200 of this of its own proper time (equivalently, time in its own inertial coordinate frame). This means the proper time of the projected wormhole mouth is 2,629,800.91 seconds, or 30 days, 10 hours, 30 minutes, and 0.91 seconds. Anyone who had been drifting along with the wormhole mouth would have experienced a passage of time of 30 d, 10 h, 30 m, 0.91 s. If she were watching the clock, she would have seen it tick off that amount of time. Since the clocks on both sides of the wormhole are ticking along at the same rate from the point of view of someone looking through the wormhole, anyone sitting back on earth watching the clock would have seen it tick off 30 d, 10 h, 30 m, 0.91 s. This means that 30 d etc after launching the wormhole, people on earth experience the wormhole's arrival as viewed through the wormhole. This then means —

Jan 30, 10:30:00.91 2050 AD GMT

People on Earth experience the arrival of the Terra Nova wormhole. They can start sending explorers and colonists through.

Of course, our time-line is a bit out of order. Putting it in order, we have

Jan 1, 00:00:00.00 2050 AD GMT — wormhole launched

Jan 30, 10:30:00.91 2050 AD GMT — Earth wormhole mouth experiences arrival of Terra Nova mouth.

Jan 1, 00:18:15.75 2150 AD GMT — Terra Nova mouth arrives.

An explorer going through the wormhole the moment it arrives would go from a time coordinate of Jan 30, 10:30:00.91 2050 AD GMT to a time coordinate of Jan 1, 00:18:15.75 2150 AD GMT. This is a jump forward in time of 99 y, 334 d, 19 h, 48 m, 14.84 s. If one of the little green native inhabitants of Terra Nova were to jump through the wormhole the moment it arrives, he would go from a time coordinate of Jan 1, 00:18:15.75 2150 AD GMT to a time coordinate of Jan 30, 10:30:00.91 2050 AD GMT, a jump backwards in the time coordinate of 99 y, 334 d, 19 h, 48 m, 14.84 s.

First, keep in mind that a wormhole is, by its nature, a general relativistic object. The reference frames in flat spacetime from special relativity should not be expected to hold in the highly curved spacetime of a wormhole. I've tried, as much as possible, to avoid the curvature of the wormhole and use only observers located in spacetime that is mostly flat (i.e., on one side of the wormhole or the other) so as to be able to use special relativity to analyze the motion. However, you do need a coordinate patch at the wormhole — although spacetime across the wormhole is continuous, the specific coordinates that you use in flat spacetime will become discontinuous across the wormhole (alternately, you can choose continuous coordinates across the wormhole, but then you need to patch your coordinates together someplace else, creating a discontinuity in the coordinate representation between Earth and Terra Nova.

The key point is that the wormhole mouth en route to Terra Nova is both at rest with respect to Earth (through the wormhole) AND moving at relativistic speeds with respect to Earth (through flat spacetime). Likewise Earth is both at rest with respect to Terra Nova (through flat spacetime) AND moving at relativistic speeds with respect to Terra Nova (through the wormhole). The perceived speed is path dependent in this particular spacetime geometry.

Note that for just one wormhole causality is not broken. At Terra Nova, you can go back in time by 99 years, 11 months by going through the wormhole to Earth. However, you can never get back to Terra Nova before you started. If you go back through the wormhole, you will go forward in time by 99 years, 11 months, so when you add in however long you spent on Earth, you get back after you left. If you try to go back to Terra Nova the long way through flat spacetime, it will take at least 100 years since Terra Nova is 100 light years away — even if you sent yourself a lasercom signal to Terra Nova as soon as you got to earth, the message would not arrive until a month after you left. We maintain time ordering, and causes always precede their effects.

Out of convenience, it is often useful to consider a specific kind of wormhole called a Visser wormhole (after its inventor, Matt Visser). A Visser wormhole is essentially supported by a "cage" or "circle" of negative energy stuff, and paths through the wormhole that do not touch the cage only go through flat spacetime. Thus, any trip through a Visser wormhole is no different from traveling through flat spacetime. Visser wormholes are valid solutions of Einstein's equation for the geometry of spacetime in general relativity. This makes them convenient for analyzing cases like this — the flat spacetime through the wormhole no more impedes the flow of matter or information than any other region of flat spacetime, like the spacetime between my library and my living room.

The ends of wormholes follow the same paths that any object would. They have mass, and if you exert a force on them they accelerate in accordance with Newton's second law. If you have one in a star system, it will follow a Keplerian orbit around that star just as would any bit of inert matter. If you keep your wormhole on a planet, you will need to support it against gravity (perhaps just resting on the ground will do this, we do not know). Each end moves independently on its own trajectory, regardless of what the other end is doing. The main complication is that a wormhole absorbs the momentum as well as the mass of anything going through, and gives up the momentum as well as mass of anything coming out. Thus, traffic through a wormhole will generate forces that can alter its trajectory.

All of the wormhole geometries I am familiar with don't have the ends moving with respect to each other through the wormhole, as much as they might move with respect to each other through flat space-time. That is, look through the wormhole and the other end is a constant distance away, always. Look at the other end through flat space-time through a telescope and you might see the other end moving quite a bit.

You can see how a wormhole is useful for travel by considering our previous example — one end on Earth and one on Terra Nova. I am on Earth and I want to visit Terra Nova. I step into the wormhole end on Earth, jump across the wormhole tunnel (we'll make this one have a short tunnel, just because we want to, but you can have a long tunnel, or just a vanishingly thin portal if you prefer), and you will be on Terra Nova, 100 light years away. When you get bored of life on the frontier, you can go back to the wormhole, jump through, and be back on Earth. So long as the wormhole does not take you further backward or forward in time than 100 years, it is impossible to violate causality (we say that they have a space-like separation). So long as the separation is space-like, it is thought that the wormhole mouths exert no forces on each other, and the wormhole is stable.

However, what happens if Terra Nova orbits a heavier star than Earth, so it is orbiting faster and deeper in a gravity well. It is also farther into the galaxy's gravity well. Uh oh! The Terra Nova end of the wormhole is continuing to experience extra time dilation not felt by the Earth end. Eventually, more than 100 years of time lag will build up. Perhaps Terra Nova's sun (and thus Terra Nova itself) is drifting toward Earth, so the distance is getting closer. As soon as the time lag (in years) is more than the distance (in light years), you can use the wormhole to go back in time and then send a lasercom signal to yourself before you left. (Terminology: when the time lag is exactly equal to the distance, we say the separation is light-like. When the time lag is more than the distance, we say the separation is time-like.) It is thought that as soon as you get a light-like separation, the path back in time through the wormhole and then returning through flat-space forms a perfect amplifier for radio, light, and any other electromagnetic signal (not to mention gravitational waves). Fluctuations in these waves spontaneously appear and build up to such huge amplitudes that they either destroy your wormhole or exert a force that pushes the wormhole ends apart so as to keep them from forming a time machine.

Fortunately, there is a way to prevent this. Charge up your wormhole, shrink it back down to what it was when it was traveling, and put the Earth end in a cyclotron. Spin it up to ultrarelativistic speeds. The time dilation on the Earth end decreases your time lag across the wormhole. Stop spinning the earth end when the time lag gets small enough, discharge the wormhole, inflate it back up to usable dimensions again, and open it back up for travelers.

Citizen Joe said: Putting wormhole mouths on the surface of worlds seems like there would always be a huge conservation of momentum issue.

Citizen Joe: There is no conservation of momentum issue. Momentum is automatically conserved locally. Here's an example:

Suppose we have a stationary wormhole mouth with mass M. It has a maglev train track going through it. A maglev trolley with mass m and velocity v floats along the track and through the wormhole. Before the trolley goes through, the total momentum of the system is

M * 0 + m * v = m * v

After the trolley goes through, the wormhole mouth has a mass of

M + m

and a velocity of

v * m / (M + m)

drifting along the track.

The total momentum of the system is

(M + m) * v * m / (M + m) = m * v

the same as before. Momentum and mass (energy, actually, and also angular momentum and electric charge) are conserved locally, with no reference at all to what is going on at the other end. (In practice, the wormhole end will probably be braced if it is on a planet's surface, not free floating along the track. In this case the wormhole exerts a force on the braces, which in turn push back on the wormhole via Newton's third law of motion. This transfers the momentum between the planet and the wormhole as the trolley goes through which keeps the wormhole stationary with respect to the planet).

But let's look at the other end for a moment. This end has a mouth with a mass M', also initially at rest. The initial momentum of the system is

M' * 0 = 0

When the trolley comes out of the mouth at velocity v, the mass of the mouth decreases to

M' - m

and it acquires a velocity of

- v * m / (M' -m)

backwards along the track such that the total momentum is still

[m * v] + [(M' - m) * (- v * m / (M' - m))] = 0

Again, momentum and mass are conserved locally. There is no dependence on the dynamics of the other end of the wormhole.

However, now we have an interesting question. What if the mass of the trolley is larger than the mass of the wormhole mouth that the trolley comes out of? The conservation of mass tells us that the wormhole mouth ends up with a negative mass! Negative mass is weird — if you push on it, it comes toward you! It seems unphysical. Perhaps it is — some relations in quantum mechanics indicate that regions with negative energy (mass) density must be bounded with regions of positive energy (mass) density and with more positive energy (mass) than negative energy (mass). If this holds, a wormhole will never acquire negative mass. Perhaps it collapses before this can happen (shearing off anything inside of it that is about to give one end negative mass). Perhaps some sort of force develops which bounces back anything in it that is about to give one end negative mass. Or maybe you really can have negative mass general relativistic (as opposed to quantum mechanical) objects. We do not know.

Personally, I think it is more interesting if you have to keep the mass of both ends positive. Now you need to be careful to balance the mass going through, which adds an interesting and novel constraint on our wormholes that is not generally seen in FTL used in fiction. But my preference is not certain, you can write stories with negative mass wormholes in them and still have them be hard science fiction if that is what you prefer.

Francesco said...

If I understand the description of wormholes correctly, once you sent a wormhole from Earth to Terra Nova, you could not send back a different wormhole from Terra Nova to Earth without destroying one of them (if you did, you could use the Earth-TerraNova-Earth bridge to go 200 years in Earth future and return with precious informations about who won the World Cup of 2051...).

In fact, once you opened a wormhole route to a destination, you could not send a new wormhole from that destination anywhere inside the light-cone of the original source point.

What kind of effect would take care of so conveniently saving causality?

Francesco: Exactly right. Well, not quite inside the future light con — if you send the wormholes slowly so that they only built up a time lag of, say, 6 months, you could have a wormhole from Earth to Terra Nova, and another from Terra Nova to anywhere further than a light year of Earth.

There is a way around this. I mentioned taking the Earth end of the wormhole, putting it in a particle accelerator, and letting it go around in circles at ultrarelativistic speeds to reduce the time lag. If you do this for long enough, you can completely get rid of the time lag, or even reverse it. For the Earth — Terra Nova wormhole, it will require the wormhole to go around and around in the accelerator for at least 100 years, although you could always stop it every so often to let people and equipment through. Note that on Terra Nova it will seem to be much less than 100 years, since the wormhole end on earth is undergoing time dilation. This trick would allow you to build round trip wormhole networks, but you will need to be careful to keep them all synchronized to prevent time machines.

Also, the powers on Earth might not want this. Suppose we Earthlings send a wormhole to Tera Nova. And then we send another to New Carolina, 100 light years away in another direction. And maybe other wormholes to Homestead, and Johnsworld, and Zemynia, and perhaps a few other colonies. In order to trade with each other, these colonies must route their traffic through Earth, since they cannot send wormholes to each other without making a time machine. The colonies can extend their wormhole networks away from earth, but you end up with a branching tree-like network in which Earth is at the nexus, the root node, and thus all trade between major branches will come through Earth. You can see how there would be those on Earth who would be making a lot of money off of this.

One minor detail — remember that mass must be conserved locally (well, energy must be conserved locally, but to our approximation it would be mass). So if uncle Ernie wants to put his super-heavy home made ship into orbit (and assuming net negative masses are impossible), he will need to find an equal mass of stuff in orbit to bring back. The sequence might go something like this:

  1. Ernie launches a 10 nanogram wormhole mouth up into orbit. The corresponding mouth stays at home with him (also 10 nanograms).
  2. The orbiting wormhole mouth finds a 1,000,000 ton asteroid up there, and "eats" it. The asteroid is now inside the wormhole. The orbiting wormhole mouth now has a mass of 1,000,000 tons (plus ten nanograms, but I'll ignore that for now).
  3. Uncle Ernie puts his 400,000 ton Ernietopia habitat through the wormhole. The wormhole end back at home has a mass of 400,000 tons and the orbiting end has a mass of 600,000 tons.
  4. Ernie still has 1,000,000 tons of stuff inside his wormhole.

It's this minor detail that makes getting to empty space difficult, but it certainly makes getting to other planets easier.

There is one simple way of connecting far flung reaches of a wormhole network that automatically gets you the right "time lag" for that connection to prevent its collapse.

Suppose that the colony on the planet of Homestead matures into its own industrial world, and they want to trade directly with the world of Zemynia. Unfortunately, Zemynia is on another main branch of the wormhole network, with lots of time lag from Homestead.

The engineers on Homestead can spin off a wormhole pair, keep one end on Homestead, shrink the other down small enough to fit into a packing crate, and then mail it to Zemynia through the existing wormhole network. When it gets to Zemynia, the time lag of the new wormhole pair will exactly match that of going through the pre-existing wormhole network, so that Homesteaders can trade directly with Zemynites through the new wormhole without needing to get routed through Earth, but both worlds can still use the pre-existing network to trade with Earth and all the other worlds connected to the network.

There is a risk, though.

Now that you have a closed loop, you will need to be much more careful of relative changes in time lag between the wormhole ends. You will need to take much more care with such a loop in your network than you would if your network only had a branching tree-like architecture. Just a little time slip between the ends can leave you with the beginnings of a time machine that would break the weakest wormhole link in the loop.

One way to mitigate this is for the Homesteaders to put their end of the newly created wormhole some several light seconds or light minutes away, to give a bit more leeway for time slop.

Of course, this means that to complete this leg of the loop, you will need a robust surface to orbit infrastructure and powerful space rockets to commute to the wormhole end, rather than just trams or maglevs going through surface stations.

While it would undoubtedly be an annoyance for the folks making the Homestead-Zemynia trip, many authors and setting designers may be secretly gleeful about this solution.

(When dealing with wormhole transit networks on the same planet, regarding accumulated time lag between wormhole ends due to elevation differences or differences in rotational speed due to north-south distance)

A quick calculation shows that a wormhole connecting North Bend, WA with Renton, WA (which have significantly different elevations, but nearly the same speed) would be able to last 266 years if it was initially synchronized.

A wormhole that connected Renton, WA with Kent, WA (which are nearly the same altitude, but are in a more-or-less north south line so their different latitudes give different speeds with a minimal distance between them) would last 1690 years. The Public Works Department might take them down for time balancing after about 1/10th to 1/20th of this time, just for safety purposes — so every few decades.

The current barometric pressure in Richland, WA is 103386 Pa and the temperature is 0 degrees C. In Rochester, NY, it is 101693 Pa and -16 C. The difference in air pressure will drive winds of 43 m/s through the wormhole.

Between Richland and Davis, CA you would get 46 m/s windspeed with current conditions. Between Richland, WA and Kenai, AK, 63 m/s.

Wind speeds between 43 m/s and 50 m/s are a category 2 hurricane wind speeds; between 50 m/s and 58 m/s is a category 3; and between 58 m/s and 70 m/s is a category 4. Not only does this make transit more difficult, at 1.2 kg/m3 it will shift a lot of mass around as well.

Better put airlocks on all your portals, even on the same planet.

The Canonical List of StarDrives

Landis List

If you want to roll your own, you might find the following useful. Noted physicist and Hugo & Nebula award-winning SF author Geoffrey A. Landis has created a catalog of every kind of StarDrive that has ever existed in science fiction. It appears here with Dr. Landis' permission.

  • [1.0] Discontinuous Drives ("teleport-like"). Discontinuous drives are ones in which the traveler does not traverse the space between origin and destination.
    • [1.1] Flash gates. Devices in which the object transported disappears from point X and reappears at point Y.
      • [1.1.1] Transmitter to receiver. Teleport in which a discrete transmitter and a receiver are needed. May require a ship, or may not.
      • [1.1.2] Transmitter to anywhere. Teleport in which a transmitter is needed, but a receiver is not; the transporter can select the target location ("Beam me down" is the most well-known example)
      • [1.1.3] Anywhere to receiver. Teleport in which a receiving unit is needed, but a transmitter is not. ("Beam me up" is an example of this.)
      • [1.1.4] Distant transmitter. A teleport system in which a fixed unit is needed, but this unit can teleport you from a place to another place. (The "point to point" use of the transporter in Trek is an example.)
    • [1.2] "Door" gates. Gates in which an opening is made between point X and point Y which exists for some finite time; the object transported then moves though the gate.
      • [1.2.1] Portal to portal. A transmitting device to act as the "out" door and a receiving device to act as the "in" door are both required. (e.g. Poul Anderson, The Enemy Stars.)
      • [1.2.2] Portal to anywhere. Here the transmitting door opens a receiving door without requirement for any device at the receiving end. ('Tak Halus' (pseud. of Steven Robinette) did a series of stories in Analog in early 70s with this premise)
      • [1.2.3] Anywhere to portal. The same as [1.2.2] "Portal to anywhere", but traveling in the opposite direction.
      • [1.2.4] Distant portal. Anywhere to anywhere, device located elsewhere. Here "door" opens from X to Y by use of a device at a third location C. The 'door' equivalent of [1.1.4] "Distant transmitter".
    • [1.3] "Permanent" gates (Wormholes). "Permanent" here means that these stay open without the requirement of a device, that is, they are a path from X to Y without being energized. There are a wide variety of subsets of this. Recently the most talked-about are Lorentzian wormholes, which are apparently allowed by the general theory of relativity if the presence of negative matter is permitted. General relativity variants include Morris-Thorne spherical wormholes, Visser portals, Kerr ring-wormholes, Einstein-Rosen bridges (nb: which actually collapse before allowing you to traverse them), Tippler rotating cylinders (nb: which don't actually serve as bridges, but at least one SF writer, Poul Anderson, wrote a book which assumed that they did). A non-relativity version is the "mirrors" used in Wolfe's New Sun series of books.
    • [1.4] Teleportation (aka "jump"). Here I use "teleportation" to imply something that can transport itself without a fixed transmitter or receiver. Reference to quantum "tunneling" is often made. Some books imply that humans can do this unassisted (Tyger, Tyger/The Stars My Destination). Many more use ships which can "jump" with some device. Here I use 'jump' or 'teleportation' only for the case that physical travel is not required in some alternate version of space, in distinction to some SF writers who use the term or a variant for cases where a ship 'jumps' to some 'hyperspace' (jumpspace, subspace, etc) where it can travel FTL.
      • [1.4.1] Single jump. A ship (or person) who can jump from place to destination in a single step, and can select the target.
        • [] Single jump/variant. In the variant, this only works at selected places, and takes you only to selected spaces (The Mote in God's Eye). This type of variant in general can be considered a version of the [1.1] "Flash-gate" discussed above.
      • [1.4.2] Multiple-connection. The ship can engage a "jump" drive, which will connect your location in space-time with another location in space-time that is fixed by the universe (may depend on your state of motion in some variants). The connection will vary from place to place, so to go to a given destination you need a "map" of where to go in space to find the place that jumps to the right spot. The analogy is of the universe to a crumpled sheet of paper. An ant can cross from one place on the paper to another where the paper touches itself. (Heinlein, Starman Jones). For some locations, a long trip moving from one place to another to take multiple jumps may be necessary.
      • [1.4.3] Multi-jump (Stutter). A ship can jump from place to place, but not far enough to travel in a single jump. Thus, the ship travels by a series of short jumps. In the limit of very short jumps, the ship "appears" to be traveling through space at a "pseudo" velocity without actually having any momentum. (This shades into [1.4.1] "Single jump" as the length of jump gets longer).
      • >
      • [1.4.4] Hopscotch drive. Use of any version of a gate or portal to accomplish self-motivated teleportation by having a transmitter transmit a transmitter, so that a ship "bootstraps" across space by continuously beaming itself incremental distances. (Such a drive is somewhere in the fuzzy region between a [2.0] "Continuous" and a [1.0] "Discontinuous drive").
      • [1.4.5] FTL by time travel. In FTL by time travel, faster than light travel is achieved by traveling to the destination at ordinary slower-than-light speed, then teleporting backward in time to arrive at the same time you started (e.g. Roger MacBride Allen, The Depths of Time).
    • [1.5] "Fold" drive ( Telportation/variant ). A "fold" drive appeals to the "folded space" concept of [1.4.2] "Multiple-connection", but now assumes that the ship can intentionally "fold" space to produce the direct connection between point X and point Y required. Since this categorization is by how the drive appears, and not how it functions, "fold" variants are identical to actual teleport (or "portal") variants, cf. [1.2] "Door gates")
  • [2.0] Continuous Drives. Continuous drives are ones in which the traveler does traverse the space between start and finish. A ship gets from point X to point Y by traveling rather than by an instant "jump", although the travel is not necessarily in "real" space. The word "ship-like" is a little fuzzy, since many SF writers use 'ships' to accomplish what is actually teleportation-like travel. This is, I think, because ships are such a great story device.
    • [2.1] "Railroad" drives
      • [2.1.1] Fixed trail. A "railroad" drive is one in which it is assumed that some physical structure connects two points, and that FTL travel is possible, but only traveling along this structure (as railroad travel is only possible along a railroad). One might appeal to the concept of a cosmic string, or some other astrophysical object. The railroad is in some ways a conceptual link between wormhole-like drives and ship-like drives. If the travel is actually instantaneous, with an object leaving one end appearing at the same time at the other end, the railroad drive becomes a variant of [1.3] "Permanent gate". (e.g. Glen Cook, The Dragon Never Sleeps.)
      • [2.1.2] Consumable trail. In a consumable trail, some structure must be put in place between a and b, and the drive consumes this material as it travels in order to produce FTL. Some versions of the Alcubierre drive, for example, require that a structure of negative energy be put in place along the path from x to y, and the ship can then travel between the two points, but destroys the structure as it travels.
    • [2.2] "Non-railroad" drives. This section covers continuous drives (that is, drives where the ship traverses space to get to the place desired) which do not require a structure in place in space.
      • [2.2.1] Real space drives. Real space drives assume that faster than light travel is possible in physical space. In terms of appearance, all of these drives apparently operate the same way (you go faster than light), and so if I were to keep to my strict classification, these would all be in the same category. The main difference between the drives is how they talk around relativity.
        • [] Newtonian space drives (EMF classification: fakedrive). This version of a FTL drive simply ignores relativity. The ship goes faster than light merely by speeding up to a velocity which is faster than light. (e.g. E.E."Doc" Smith, The Skylark of Space.)
        • [] Post-relativistic space drives (EMF classification: fakedrive). This is a minor variant [] "Newtonian space drive"; the drive assumes that there is some (yet unknown) "correction" to relativity such that the speed of light is not, in fact, a barrier. Often this correction will be some added term which applies only very close to the speed of light.
        • [] Tachyonic travel. Tachyonic travel notes that faster than light speeds are in fact permitted by relativity for bodies of imaginary rest mass, and assumes that there is some way to reach the faster than light state (often invoking "tunneling") from slower than light states without leaving "real" spacetime. (nb: tachyonic FTL travel still has causality paradoxes in special relativity).
        • [] Modified local speed of light. Drive assumes that the speed of light in the vicinity of the ship can be modified by the drive system in some way, so that although the ship does not exceed the speed of light, it nevertheless can travel faster than 300,000 kilometers per second.
        • [] Modified regional speed of light. Assumes that the speed of light is greater than 300,000 kilometers per second in some places in the universe. Faster speeds can be achieved in other places in the universe.
        • [] Modified universal speed of light. A scientist discovers a way to change the speed of light in the entire universe, and does so. Now any ship can go faster than (what used to be) the speed of light.
        • [] Tachyonic teleportation. The ship and/or person is converted into a stream of tachyons and beamed across space, then reconstituted at the receiver. Actually a variant of [] "Tachyonic travel" and/or [] "Hyperspace with transmitter and receiver"; listed separately because it is significant that the ship does not travel as a cohesive unit. Other variant names can be used for the particles, which can travel either through real space or some alternative space.
        • [] Other real drives. This covers other ways of dealing with relativity problems without leaving real space. (Usually this involves employing doubletalk and bafflegab.)
        • [] "Bubble" drives (EMF classification: warpdrive). "A bubble of different space is projected around the ship so that the ship can travel faster-than-light while still in realspace." This is listed last, since it is an intermediate step between "real space" drives and alternative space drives, with some nature of both. (This seems to be the FTL system used on Star Trek.)
      • [2.2.2] Alternative space (non-real space drives). In SF parlance, often called hyperspace, hyper, jumpspace, FTL space, and other such words. EMF classification: "Type I; hyperdrive: The ships enters some different space during the trip, whether or not time passes for the crew while in this space."
        • [] Alternative space with fixed nodes. Like teleport systems, a alternative space drive may require a fixed station.
          • [] Hyperspace with transmitter and receiver. A fixed station boosts the ship into hyperspace; another station is needed to retrieve the ship out of hyperspace. In some variants, only specific locations are nodes which can be used to access hyperspace.
          • [] Hyperspace with transmitter. A fixed station boosts the ship into hyperspace. (Babylon-5?)
          • [] Hyperspace with receiver. A ship can enter hyperspace on its own, but needs a receiver to get back into real space. Another one I've never seen in SF.
          • [] Hyperspace with distant transmitter. In this variant, a fixed machine is needed to access hyperspace, but the machine need not be at either the original location or the destination. I've never seen this in SF; included for completeness.
        • [] Alternative space without fixed nodes.These are the variants of the classic SF hyperdrive. There are probably more examples of this in SF than all other of the drive types combined, and hence it is possible to make very fine divisions within the type. EMF classification: "Type I; hyperdrive: The ships enters some different space during the trip, whether or not time passes for the crew while in this space." The space is often explained away as being a dimension different from the four dimensions we currently can perceive (this explanation typically advanced by people who seem to have only a foggy idea what a "dimension" is). There are many variants based on the supposed "theory" of how the drive works, including entering a space where the speed of light is faster, entering a space which maps onto real space with a mapping such that points far apart in real space are closer in the alternative space, entering a space where the ship expands and then contracts to a different place, entering a space where everything moves at the same FTL speed, etc. Likewise, there are a long list of "conditions" which hyperspace drives are imagined to require. A common one is that the FTL space cannot be entered when "in the gravitational well of a massive body," (Niven, Ringworld series) or that your ship must have a high velocity in real space before you can enter FTL space (Niven, World of Ptavvs, O'Donnell, Fire on the Border) These two are convenient for sf writers, because they explain why spaceships are required. Important questions for hyperspace concepts are whether ships can see and/or dock with each other in hyperspace, whether all ships travel the same speed, and whether a ship can navigate while in hyperspace. These questions can also be asked of [] "Hyperspace with fixed nodes". I will take this last to be the question used for subdivisions.
          • [] "Jump" hyperspace. The destination is fixed when the ship enters the alternative space, either as a function of its position and velocity entering, or else by some settings in the drive. After a ship enters the alternative space, there is no way for it to change the destination. (e.g. GDW's "Traveller" RPG)
          • [] Direction hyperspace. A ship's direction is fixed when the ship enters hyperspace (often, but not always, fixed by the direction the ship was traveling when it entered). How far it travels, however, is a variable that can be changed. Usually the distance is proportional to time spent in hyperspace, but may be a more complicated function. The ship may or may not be able to calculate its position in real space while in hyperspace.
          • [] Navigable hyperspace. The ship is able to completely navigate in hyperspace. It may or may not be able to calculate its position in real space while in hyperspace. Sometimes the hyperspace may have geography or dangers which must be navigated around.
  • [3.0] Modifying the Universe. A final category of FTL, not precisely fitting in elsewhere, requires modifying the universe. Some items in this category also could be made to fit other categories.
    • [3.1] Modify distance in space. Remove or shrink the space between two points.
    • [3.2] Modify the speed of light. Change the value of the speed of light in the region where travel is desired (see [] "Modified universal speed of light")
    • [3.3] Universal parameter change. Gain access to the parameters that describe the universe, possibly by hacking into the operating system that the universe runs. Find the parameters which describe your location. Rewrite these parameters to put you in the place you want to be. (e.g. Greg Bear, Moving Mars)
Geoffrey A. Landis

EMF Classification

The EMF (Erik Max Francis) classification

  • Type 0; realdrive: A drive which uses tricks of spacetime geometry (a la general relativity) to travel faster than light.
  • Type I; hyperdrive: The ships enters some different space during the trip, whether or not time passes for the crew while in this space.
  • Type II; warpdrive: A bubble of different space is projected around the ship so that the ship can travel faster-than-light while still in realspace.
  • Type III; jumpdrive: The ship travels from one point to another, possibly in multiple jumps, without occupying the intervening space and without the use of a different space to assist the travel.
  • Type X; fakedrive: Assume that special relativity or general relativity are incorrect in part or in whole, or just ignore them. Now you can just accelerate at constant gravity until you go faster than light.
Erik Max Francis

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.

First Lensman

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.

Stranger in a Strange Land

     “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)
Skylark of Valeron

“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)
Starman Jones

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)
A Wrinkle in Time

"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 die 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)

The Universe Between

"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)

FTL Communication

Some faster-than-light communication methods in science fiction include:

  • Hainish Cycle by Ursula K. Le Guin: Ansible (name comes from "anserable"). The term has also been used by Terry Bisson, Orson Scott Card, L. A. Graf, Elizabeth Moon, Dan Simmons, Vernor Vinge and Jason Jones.
  • Singularity Sky and Iron Sunrise by Charles Stross: causal channels communicates using entangled particles. Each particle can send one bit of information then becomes worthless. In theory the communication is impossible to be eavesdropped. In a fascinating twist there does exist FTL spacecraft, but if such spacecraft transport entangled particles they become unentangled and worthless. The causal channel particles have to be shipped slower than light by Starwisp at great expense.
  • The Quincunx of Time and others by James Blish: The Dirac communicator was named after Paul Dirac who predicted antimatter. It communicates instantly and has infinite range. So all sentient creatures in all the galaxies can listen in to what you say. As it turns out it is even worse than that. Each transmission starts with a "beep" noise. As it turns out, the beep is the sum total of all Dirac messages ever sent in all the past and all the future. By demultiplexing you too can receive messages from the future and violate causality.
Forbidden Planet

{In the movie Forbidden Planet} I'm reminded of the efforts of poor Chief Engineer Quinn in building a FTL communications device, primarily by disassembling the United Planets Cruiser C-57D's hyperdrive.

This has implications.

It means that the United Planets have FTL communication, but not their starships. At least not while they are in space.

It's also faster than a starship, as it was implied that they would be able to send a message back to Command and receive a reply in a short period of time.

So that implies that other star colonies in the UP have these "ansibles" either by scraping a hyperdrive or hauling the parts to build one with them. However, Commander Adams' remarks about Quinn building one also implies that this is not a trivial task or that the parts are readily available.

"I'll bet any quantum mechanic in the service would give the rest of his life to fool around with this gadget." — Chief Engineer Quinn, C-57D

Because of this fact, these ansibles are rare, hard to maintain, and require a dedicated staff to operate and repair. And if one breaks, the only place to get spare parts is Earth. That pretty much means one per colony, and it's not instantaneous communication, but it's faster a ship.

CHIEF: Commander.
COMMANDER: What is it, Chief?
CHIEF: If you'd like to check my assembly for the monitor unit of the Klystron transmitter...
COMMANDER: What, already?
CHIEF: Yes, sir.
COMMANDER: Excellent. Are... are these condensers out of my accelerator circuits?
CHIEF: Yes, sir. I borrowed some solenoids from your gyrostabilizers too.
CHIEF: Here's the big deal, sir. I'll bet any quantum mechanic would give his life for a chance to fool around with this gadget.
COMMANDER: Get this in the ship by dark. It won't do any good to have some fool fall on it before we transmit tomorrow.
{ invisible monster snuck into the ship last night, killed the officer who looked lustfully at Dr. Morbius' daughter, and beat the living snot out of the klystron frequency modulator }
CHIEF: Half of this gear we can replace and the rest we can patch up somehow except this special Klystron frequency modulator. With every facility of the ship, I think I might be able to rebuild it, but frankly, the book says no. It came packed in liquid boron in a suspended grav...
COMMANDER: All right, so it's impossible. How long will it take?
CHIEF: Well, if I don't stop for breakfast...
COMMANDER: Get on it, Quinn.
CHIEF: Thank you, sir.
From John Reiher

"You've got your own causal channel?" Frank asked, hope vying with disbelief...

..."Tiny — it's the second memory card in my camera." She held her thumb and forefinger apart. "Looks just like a normal solid state plug. Blue packaging."...

...Alice looked over the waist-high safety wall, then backed away from the edge. "I'm not climbing down there. But a bird — hmmmm. Think I've got a sampler head left. If it can eject the card . . . you want me to have a go? Willing to stake half your bandwidth with me if I can liberate it?"

"Guess so. It's got about six terabits left. Fifty-fifty split." Thelma nodded. "How about it?"

"Six terabits —" Frank shook his head in surprise. He hated to think how much it must have cost to haul those milligrams of entangled quantum dots across the endless light years between here and Turku by slower-than-light starwisp. Once used they were gone for good, coherence destroyed by the process that allowed them to teleport the state of a single bit between points in causally connected space-time. STL shipping prices started at a million dollars per kilogram-parsec; it was many orders of magnitude more expensive than FTL, and literally took decades or centuries of advanced planning to set up. But if it could get them a secure, instantaneous link out into the interstellar backbone nets..."

From IRON SUNRISE by Charles Stross (2004)

Quantum Entanglement

About every six months or so, some science writer stumbles over a reference to "quantum entanglement" or "Bell's Inequality" or "spooky action at a distance", then immediately writes an article or blog post about OMG! Quantum Mechanics can send radio messages faster than light!

Short answer: No, it won't work.

Slightly longer answer: When you send the message, it will technically arrive faster than light. But the message will be in two parts: a scrambled sequence of numbers at the source, and a second scrambled sequence at the destination. The only way to decode the message is with both sequences. So the source has to send the first scrambled sequence to the destination over conventional just-as-fast-as-light radio. Which sort of defeats the purpose.

After receiving both parts of the message at a rate equal to the speed of light, you can find out after the fact that yes indeed there was some faster-than-light communication. Oh, my, wasn't that pointless?

Longest answer:

Back in 1930, several physicists in general and Albert Einstein in particular were quite upset when Quantum Mechanics was invented. Everything about QM was offensive to those who like their physics logical, deterministic, and non-weird. Einstein and co-authors Boris Podolsky and Nathan Rosen wrote a paper in 1935 demonstrating that Quantum Mechanics had to be utterly wrong, or at the very least quite incomplete. The paper set forth a paradox. The two solutions were [a] Quantum Mechanics is wrong or incomplete or [b] there exists bizarre spooky action at a distance which travels faster than light (actually it is instantaneous). Since [b] was obviously impossible, Einstein and his co-authors smugly sat back and waited for Quantum Mechanics to be discarded into the dust-bin of history.

Unfortunately for Einstein et al, in 1964 some clown named Dr. John Stewart Bell wrote a paper showing how to test the paradox (called "Bell's Inequality"), and to the horror of the foes of quantum mechanics it turned out that bizarre spooky action at a distance which travels faster than light actually happens.

This saved quantum mechanics from the EPR paradox, but now all the physicists had to deal with this obnoxious FTL action at a distance. As mentioned above, physicists hate FTL because it destroys causality and thus makes the entire structure of Science collapse into a flaming ruin.

As it turns out: yes, the FTL effect is real but no you can't use it for anything useful. Physicists heaved a sigh of relief (and science fiction writers became quite angry).

Why can't you use it for anything useful? Well that's complicated. Here is how Heinz R. Pagels puts it:

(ed note: when he says "Local Causality" he means "there is no such thing as a spooky action at a distance". When he says "Objectivity" he means "Quantum Mechanics is false". When he says "Nonlocality" he means "spooky action at a distance exists")

Imagine that we have a special nail gun that shoots nails two at a time in exactly opposite directions along a fixed line. Unlike most nail guns, which shoot nails like arrows, this one shoots them sideways—a pair of nails flies away from the gun with their long axis perpendicular to the direction of motion. Although each nail in a pair has the same orientation, different pairs, shot off successively, have completely random orientations relative to each other. The reason for all these peculiar requirements will become apparent when we consider a corresponding quantum system.

The flying nails are aimed at two metal sheets, A and B, each with a wide slot in it. These slots behave like real polarizers—devices which let objects with a specific orientation pass through them while blocking the passage of identical but improperly oriented objects. For example, polarized sunglasses let waves of light which are vibrating with a vertical orientation go through them while blocking light which vibrates horizontally. Since most reflected light, in contrast to direct light, is vibrating horizontally, the effect of the polarized sunglasses is to cut out glare. The slots we will call polarizers, because they only let flying nails which are aligned with the slot pass while blocking all others. We can adjust the orientation of these polarizers in the course of the experiment. At sheets A and B there are two observers who keep records of the nails that get through and those that don't. If a nail gets through the slot a "hit" is recorded as a 1 and if it fails a "miss" is recorded as a 0.

Initially the two polarizers are both oriented in the same direction as the gun fires its pairs of nails. Since each member of a pair has precisely the same orientation and the polarizers at A and B are aligned, each member of the pair either gets through the slot or it fails—hits and misses are exactly correlated at A and B. The record at A and B might look like

Each sequence of 0s and 1s is random, because the gun fires the pairs out at random orientations. But note that the two random sequences are precisely correlated.

The next step is to change the relative angle between the two polarizers by rotating the slot at A clockwise by a small angle θ and holding B as a fixed standard. With this configuration a nail in a pair will sometimes get through at A but fail at B and vice versa. The hits and misses at A and B are no longer exactly correlated but since the slots are wide it is still possible to have two hits. The record might look like

where the mismatches are indicated. These mismatches we can call "errors," for they may be thought of as errors in A's record relative to B's, which is the standard. In the above example there were 4 errors out of 40, so the error rate E(θ) for the angle set at θ is E(θ) = 10%.

Suppose that we had left the polarizer at A untouched but rotated the one at B counterclockwise by the angle θ. Now we might say the "errors" are in B s record and A's acts as the standard. The error rate will clearly be the same as before, E(θ) = 10%, because the configuration is identical.

The final step is to rotate As polarizer by an angle θ clockwise so that the total relative angle between the two polarizers is now doubled to 2θ. What is the error rate for this new configuration? This is easy to answer provided we assume that the errors at A are independent of the situation at B and vice versa. In making this assumption we are assuming local causality. After all, what does a nail getting through its polarizer at A have to do with the situation at B? Since the errors produced at B were previously E(θ) we must add to this the errors produced by rotating the polarizer at A, which is also E(θ). So it seems that the error rate with the new setting should be the sum of the two mutually exclusive error rates, or E(θ) + E(θ) = 2E(θ). But by shifting A by the small angle 6 we have lost the standard record for B's record, and likewise by shifting B we have lost A's standard. This means that from time to time an error will be produced at both A and B — a double error. But a double error is detected as no error at all. For example, suppose a pair of nails would have registered a 1 and 1 at A and B if the polarizers were perfectly aligned. But because A's polarizer is shifted the nail then misses and a 0 is registered. This shows up as an error. But since we have also shifted B's polarizer it is possible that the nail there also misses. This is a double error in which two hits, a 1 and 1, has been changed to two misses, a 0 and 0. The two misses are seen as no error. Because of the impossibility of detecting a double error, the error rate with an angle 2θ between the two polarizers — E(2θ) — will necessarily be less than the sum of the error rates for each of the separate shifts. This is expressed mathematically by the formula

E(2θ) ≤ 2E(θ)

which is Bell's inequality.

No doubt if this odd experiment were performed, Bell's inequality would be satisfied. For example, with an angle of 2θ the record might look like

or 6 errors out of 40 so E(2θ) = 15% ≤ 2 × 10% = 20%. Bell's inequality is satisfied for this classical physics experiment.

Let us examine closely the crucial assumptions that have gone into obtaining Bells inequality. We have assumed that the nails are real objects flying through space and that the orientation of pairs of nails is the same. We aren't actually observing that the nails have a definite orientation because they fly by us so quickly. This seems like a safe assumption for nails, but we have indulged in the fantasy of objectivity. We are assuming that the nails exist like ordinary rocks, tables, and chairs. Suppose we are the observer at A. Then we are assuming that a nail flying toward B, even if B is on the moon, has a definite orientation. The notion that things exist in a definite state even if we do not observe them is the assumption of objectivity—and of classical physics. (ed note: this means Quantum Mechanics is false)

The second crucial assumption in obtaining Bell's inequality was that the errors produced at A and at B were completely independent of each other. By shifting the polarizer at A we did not influence the physical situation at B and vice versa—the assumption of local causality. (ed note: this means there is no such thing as a spooky action at a distance)

These two assumptions—objectivity and local causality— are crucial in obtaining Bell's inequality. What happens if we now replace flying nails with photons—particles of light? (ed note: replace classical physics objects with quantum mechanical objects)

Instead of a nail gun we will use positronium atoms as our source of particles. Positronium is an atom consisting of a single electron bound to a positron (anti-electron), and this atom sometimes decays into two photons traveling in opposite directions. The important features of this positronium decay is that the two photons have their relative polarization precisely correlated—like the flying nails. The polarization of a photon is the orientation of its vibration in space. If one photon has its polarization in one direction, its companion flying off in the opposite direction has its polarization in the same direction. The absolute direction of the polarization of the two correlated photons changes from decay to decay in a random way, but the relative polarization between any pair of photons is fixed. That is the important feature of this source—it is like the nail gun.

The photons fly off in opposite directions and pass through separate polarizers at A and B, located far apart with observers stationed there. Behind the polarizers are photomultiplier tubes that can detect single photons. If a photomultiplier tube detects a photon, the event is recorded by a 1, and if it detects no photon the event is recorded by a 0. In the initial configuration the two polarizers at A and B are perfectly aligned relative to each other. Let the polarizer at B be fixed while the one at A is free to rotate and call the relative angle between the two polarizers θ so that in this initial configuration θ = 0.

If a photon hits the polarizer it has a certain probability of getting through and being detected. If the photons polarization happens to align parallel to that of the polarizer it gets through to the detector, and a 1 is registered. If the polarization of the photon is perpendicular to the polarizer, then it won't get through and a 0 is registered. With other orientations there is only a probability that it gets through.

The polarization of the photons relative to the polarizers is completely random, so that each detector, in the initial configuration with θ = 0, will register a series of 0s and 1s. Suppose the series looks something like this at each detector.

This is just like the records with the nail gun. The series are identical because each pair of photons is polarized identically and the angle between the polarizers is zero. Further, each series has on the average an equal number of zeroes and ones, since it is as likely for a photon to get through the polarizer to the detector as not.

Next we rotate the polarizer at A, slightly, so the angle θ is not zero. Set θ = 25°. This slight shift means that the two photons in each pair have a slightly different probability of going through the polarizers and being detected. The series are not precisely identical but instead disagree from time to time. However, on the average, both the series at A or B have an equal number of zeroes and ones because the probability of getting through the polarizer is independent of its orientation. The new series looks like

where we have indicated the mismatches. In the above example the rate of errors, since there are 4 errors out of 40 detections, is E(θ) = 10%.

So far this experiment done with photons resembles that with the nails. Photons are behaving just like the perfectly visualizable experiment with the flying nails. If we assume the state of polarization the photons have at A and B is objective (objectivity assumption) and that what one measures at A does not influence what happens at B (local causality assumption), then Bell's inequality, E(2θ) ≤ 2E(θ), ought to hold for this experiment. If we double the angle to 2θ = 50°, the following records are found:

This is 12 errors out of 40, so that E(2θ) = 30%. Now let us compare this result with the requirement of Bell's inequality, since E(θ) = 10% we have 2E(θ) = 20%; but Bell's inequality requires that E(2θ) ≤ 2E(θ), so that 30% is supposed to be less than 20%—completely false—30% is greater than 20%! We conclude that Bells inequality is violated by this experiment, as it is for real experiments with photons. Consequently, either the assumption of objectivity (ed note: quantum mechanics is false) or locality (ed note: no such thing as spooky action at a distance) or both are wrong. That is very remarkable!

We have described the experiment and Bell's inequality in some detail because it is rather elementary and illustrates the crux of quantum weirdness. Bell was motivated to find a way of testing if there were hidden variables that exist out there in the world of rocks, tables, and chairs. He showed that the violation of the inequality by quantum theory did not necessarily rule out an objective world described by hidden variables but the reality they represented had to be nonlocal (ed note: there IS such a thing as spooky action at a distance). Behind quantum reality there could be another reality described by these hidden variables and in this reality there would be influences that move instantaneously an arbitrary distance without evident meditation. It is possible to believe the quantum world is objective—as Einstein wanted—but then you are forced into accepting nonlocal influences—something Einstein, and most physicists, would never accept.

To get an intuitive sense of how objectivity implies nonlocality, compare the records for the angle θ = 25° and θ = 50°. There are just too many errors (12) for the 50° setting as compared to the number of errors (4) for the 25° setting. It seems that by moving A's polarizer we must have influenced the polarization of the photons about to be detected at B and that produces all those "extra" errors that violate Bell's inequality. Observer B could be on the earth and A light-years away, on another galaxy. A, by moving the polarizer, it seems, is sending a signal faster than the speed of light, thus instantaneously changing B's record. That certainly seems like action-at-a-distance and the end of locality.

Now that we see what we have been forced into we might want to look at this a bit further. Either alternative—a nonobjective or nonlocal reality—is a bit hard to take. Some recent popularizers of Bell's work when confronted with this conclusion have gone on to claim that telepathy is verified or the mystical notion that all parts of the universe are instantaneously interconnected is vindicated. Others assert that this implies communication faster than the speed of light. That is rubbish; the quantum theory and Bell's inequality imply nothing of this kind. Individuals who make such claims have substituted a wish-fulfilling fantasy for understanding. If we closely examine Bell's experiment we will see a bit of sleight of hand by the God that plays dice which rules out actual nonlocal influences. Just as we think we have captured a really weird beast—like acausal influences—it slips out of our grasp. The slippery property of quantum reality is again manifested.

Bohr would be the first to point out an alternative interpretation of the experimental violation of Bell s inequality. In order to conclude that the photons were subject to nonlocal influences we have indulged in the fantasy that they exist in a definite state. Try and verify that, Bohr would insist. If we can verify that the photons actually exist in a definite state of polarization without altering that state, then indeed we must conclude from Bell's experiment that we have real nonlocal influences.

For the flying nails this verification is easy—we set up a high-speed camera and take pictures of them just as they arrive at the polarizers. This won't disturb their state. But then the experiment with the flying nails did not violate Bell's inequality as did the experiment with photons.

If we now try to verify the state of polarization of a photon we find that this is not possible without altering the requirement that both members of a pair of photons have identical polarization. In measuring the polarization of the photon we put it into a definite state, but this alters the initial conditions of the experiment. This is identical to the problem we faced in the two-hole experiment with the electron. By observing with light beams which hole the electron went through we changed the detected pattern. Likewise, the very act of establishing the objective state of the photon alters the conditions under which Bell's inequality was derived. The attempt to experimentally verify the objectivity assumption has the consequence that the conditions of the experiment are altered in just such a way that we can no longer use the violation of Bell's inequality to conclude that nonlocal influences exist.

Suppose then that we do not try to verify the state of the flying photons. After all, we have the records of hits and misses at A and B and these are part of the macroscopic world of tables, chairs, and cats and are certainly objective. Cannot the observer at B read his record, see that Bell's inequality is violated, and conclude that local causality has also been violated? The answer is no, because the God that plays dice has a trick to show us. Remember that the source of photons emits them in pairs with random polarization. This means that the records at A and B, no matter what the angle is, are completely random sequences of 0s and 1s. And that fact is what lets us slip out of the conclusion of real nonlocal influences.

At first you might think that by changing A's polarizer we have directly influenced the number of errors produced at B. Hence by altering A's polarizer to various settings in a sequence of moves, B could, by observing the alteration in the number of errors produced at B, get a message from A—a telegraph that would violate causality. But no information can possibly be transmitted from A to B using this device because holding a single record of events at either A or B would be like holding the message of a top-secret communication in a random code—you can't ever get the message. Because the sequences at A and B are always completely random there is no way to communicate between A and B. That is how real nonlocality is avoided by the God that plays dice; He is always shuffling the deck of nature.

Random stereograms, which we already discussed, illustrate this trick. Each half of the stereogram is completely random, but two random sequences of dots if compared can yield nonrandom information. The information is in the cross-correlation gotten by comparing the two sequences. It is the same with the records at A and B—the information about the relative angle between the polarizers at A and B is in the cross-correlation of the two records; it is not in either record separately. All that happens when the polarizer angle is changed is for one random sequence to be changed into another random sequence, and there is no way to tell that happens by looking at only one record. Because such real random processes actually occur in nature—as they do in this experiment— we avoid the conclusion of real nonlocality.

What a marvelous trick nature has used to avoid real nonlocal influences! If we asked out of all things in this universe which one, if altered in a random way, would remain unchanged, the answer is: a random sequence. A random sequence changed in a random way remains random—a mess remains a mess. The random sequences at A and B are like that. But by comparing these sequences we can see that there has been a change due to moving the polarizers—the information is in the cross-correlation, not in the individual records. And that cross-correlation is completely predicted by the quantum theory.

We conclude that even if we accept the objectivity of the microworld then Bell's experiment does not imply actual nonlocal influences. It does imply that one can instantaneously change the cross-correlation of two random sequences of events on other sides of the galaxy. But the cross-correlation of two sets of widely separated events is not a local object and the information it may contain cannot be used to violate the principle of local causality.

From The Cosmic Code: Quantum Physics as the Language of Nature by Heinz R. Pagels (1982)

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