Introduction

Remember the difference between Unobtainium and Handwavium:

UNOBTAINIUM: We can't build a physical example of it, but insofar as we can postulate that it can be built at all, the laws of physics say it would behave like thus and so. While Handwavium and Technobabble tell you what you CAN do, Unobtainium usually tells you what is NOT possible. Examples: gigawatt laser, antimatter weapons, ladderdown reactors.

HANDWAVIUM: It flat out violates laws of physics. We're waving our hands and saying pay no attention to the man behind the curtain. Examples: faster-than-light drive, time travel, reactionless drives.

Science fiction authors can make up handwavium on their own with no help from this website, it ain't that hard. As long as you are not scared of RocketCat and his dreaded Atomic Wedgie. Trying to keep it internally consistent enough so it does not turn around and bite you on the gluteus maximus, on the other hand, is quite difficult. There are some guidelines here.

Black Holes

The popular conception of a black hole is that it sucks everything in, and nothing gets out. However, it is theoretically possible to extract energy from a black hole, for certain values of "from."

They are just the thing to make high acceleration gravitational catapults.

Due to their extreme conditions, black holes have a thousand and one uses. A pity there doesn't seem to be any closer that a few light-centuries.

And by the way, there appears to be no truth to the rumor that Russian astrophysicists use a different term, since "black hole" in the Russian language has a scatological meaning. It's an urban legend, I don't care what you read in Dragon's Egg.

DEMYTHOLOGIZING THE BLACK HOLE

INTRODUCTION: “TRUTH IS FOR THE MINORITY.”

With the release of the Disney catastrophe, general interest in black holes has peaked. The release of this film also signals a critical overdose of misinfor- mation to which the public has been exposed. We read statements like: “The pull of a black hole’s gravity is so strong . . . time is stopped and space does not exist. . . [A black hole’s dis- covery] would unravel the mystery of both the universe’s creation and even- tual destruction.”

Such blatant idiocy induces the public conception of black holes as monsters which gobble up all the matter in the universe, as miracle workers which can solve all our energy problems, as gate- ways to other universes, and as time machines. This conception is pro- foundly misplaced. The same theory which predicts the black hole’s exist- ence also predicts that each of the pre- ceeding properties has severe limitations or does not occur at all. The very ex- istence of black holes is itself debatable; within our own galaxy only one not-yet- conclusive candidate for a black hole has been found to this date, the x-ray source, Cygnus X-1.

Thus, it strikes us as bordering on the ridiculous to use black holes as an ex- planation for every property of known space. Of course, there are mistakes and there are mistakes. Some involve subtle points, and physicists advance their own field only by making lots of them. The layman cannot be faulted for doing the same. Nonetheless, most of the non- sense written about black holes stems from an ignorant exploitation of a sub- lime idea, and a lack of interest in the pursuit of knowledge. As we will see, the theoretical properties of black holes are in themselves so remarkable that there is no need to exaggerate them in an attempt to capture the public’s atten- tion. Bearing this in mind, we now ex- amine some properties of black holes-—-without exaggeration.


CLASSICAL BLACK HOLES AND CANONICAL MISCONCEPTIONS.

Visualize a black hole. Most of us, encumbered by the limits of imagina- tion, will visualize a small, black sphere floating in space among the stars. We probably think of this ball as a highly compressed solid, somethng like cold iron but unimaginably more dense. Un- imaginably high density, we assure our- selves, produces an unimaginably great gravitational field. We further imagine the field to be so strong that all sur- rounding matter is pulled into this tiny sphere, never to escape again. Light it- self cannot avoid the same fate; fleeting, ephemeral, yet once light enters this strange object it is trapped forever by gravity. Thus, the “black hole”; ab- solutely black since light cannot be re- flected from it to show its existence.

The question is, is this picture a de- scription of anything? The answer is not straightforward but requires more pre- cise concepts, caveats, and “yes buts.” In attempting an answer, one should first keep in mind that relativists, ped- dlers of gravitational theories, distin- guish between several types of black holes. There is the basic, Schwarzschild black hole which is spherical, electri- cally uncharged, and does not rotate; there is the Kerr black hole, which ro- tates and is not spherical; and there is the Reissner-Nordstrom black hole, which is spherical and non-rotating, but contains an electric charge. (The holes are named in honor of the mathemati- cians who worked out their theoretical existence.)

These three types, without additional complications, are lumped under the heading “classical black holes” to dis- tinguish them from “quantum black holes.” A quantum black hole is any black hole, including one of the above types, in which it is necessary to take into account the fact that light, for in- stance, consists of indivisible units called quanta. For light the quanta are photons; for the gravitational field itself the quanta are gravitons. Thus, we can have quantum Kerr black holes, quan- tum Reissner-Nordstrom black holes, and quantum Schwarschild black holes. But for now limit ourselves to classical black holes.

Evidently, the above mental picture corresponds—-more or less--to the basic Schwarschild black hole. However, the emphasis in the previous sentence is on the “more or less,” specifically on the “less.” We will now begin to give a more accurate description of a classical black hole, keeping in mind that spe- cific details may vary from one category of hole to the next.


The classical, astronomical picture of a blackihole is one of a remnant left over by the collapse of a massive star; the examples typically used have about ten solar masses. The escape velocity from the surface of the black hole ex- ceeds that of light; indeed, this is the definition of both a “black hole” and its “surface.” The surface of a black hole is called the event horizon. Now, we know that no physical object can move faster than light, so nothing what- soever, having fallen across the event horizon of a black hole, can come back out through that horizon.

A ten-solar-mass black hole has a ra- dius of about 30 kilometers, roughly the size of New York City. It is this typical example of a small, collapsed object with a gravitational field so strong that not even light can escape, which has conjured up the vision of black holes as extremely dense objects which grab anything in the vicinity. In fact, the density of the ten-solar-mass hole (den- sity is the mass of the hole divided by the volume enclosed within the. event horizon) is of order l015 grams per cubic centimeter. This seems a very high den- sity by everyday standards (the density of iron is only about 8 grams per cubic centimeter) until we realize it is com- parable to the density in the nuclei of atoms. Each one of us is composed of particles of this sort of density.

In any case, a black hole does not have to be so dense. The basic black hole equations show a very simple re- lationship between the size and mass of a black hole and the density. As the radius of the hole or its mass is in- creased, the density goes down. Thus, by making a black hole large enough or massive enough, we can make the density as low as we want. Actually, there is no reason we could not make a black hole out of air. Such a hole would have a radius of about 30 billion kilometers, roughly ten times the size of our solar system. If one entered this black hole, one would hardly feel a thing, but after a few days life would become uncomfortable—as one ap- proached the singularity.

While we will not talk much about singularities in this article, we should mention that the singularity in the center of the black hole is the place where all the matter eventually ends up. The den- sity at this point is infinite, which in- troduces a “yes but” into the above remarks. The density we have been dis- cussing is the average density of the hole and, strictly speaking, one can only talk about the average density from out- side the horizon.

At the surface of the air-bag black hole, the gravitational acceleration would be about 100 times the acceleration we feel on the surface of the earth, or roughly the same as the gravitational acceleration on the surface of the sun. A larger black hole, made out of hy- drogen, would have an even lower sur- face acceleration. We see then, the gravitational acceleration of a black hole is not always overwhelmingly large.

If the gravitational field is so weak, the question immediately arises, why can’t one escape by firing a rocket en- gine. The answer is somewhat tricky. We know that by accelerating even at very low accelerations, say 0.l gee, we can eventually reach huge velocities. Similarly, even the weak acceleration produced by our air bag will eventually accelerate objects to high velocity. In fact, by the time an object has fallen to the event horizon of any black hole, it is moving at the speed of light, inward. If the falling object wants to remain even stationary at the horizon, it must then move with the speed of light, out- ward. The principle of relativity says that nothing can move faster than the speed of light. Therefore, there is no escape. Acceleration is somewhat irrel- evant to the problem; the speed of light simply cannot be exceeded.


FANCY FREE: ORBITS AROUND BLACK HOLES.

Related to the idea that a black hole possesses a strong gravitational field is the misconception that nothing can get remotely near the hole without being gobbled up. A good illustration of this nonsense is in the Disney film where the ship, the Cygnus, seems to require an antigravity field to prevent it from falling into the black hole. The film- makers ignore the fact that, at distances greater than about 10 times the radius of the black hole, ordinary orbital me- chanics—known since the time of New- ton--is applicable. For example, if the sun were suddenly replaced by a black hole of equal mass, the orbits of the planets would not change by the width of an ant’s eyebrow. Admittedly, it would get dark, but that is another story.

This brings us to the first important rule of black hole orbital mechanics: At large distances, the fact that we are in orbit around a black hole is irrel- evant. We may consider the black hole to be a spherical mass concentration producing an ordinary, Newtonian gravitational field, like that of the earth or the sun.

As the orbital radius approaches 10 black hole radii (300 kilometers for the 10 solar mass case), general relativistic effects become very important. The proverbial curvature of space and slow- ing of time come into play. Such dis- tortions of space and time manifest themselves in such effects as perihelion shifts in non-circular orbits. To under- stand perihelion shifts, we recall that Newtonian orbits are steady ellipses around the central body. The satellite’s point of closest approach, the perihe- lion, remains at a fixed point in space. We say, in this instance, space time is flat or Newtonian. (See Figure la.) When curvature of spacetime is more significant, the point of closest ap- proach pivots around the central body with each orbit of the satellite. (See Figure lb.) This pivoting is called a “perihelion shift” when speaking of orbits around the sun, a “periastron shift” when speaking of orbits around stars in general, and a “peribarythron shift” when speaking of orbits around black holes. (“Balythron" is the Greek name for a a deep pit in Athens into which condemned criminals were thrown.)

Because the shift is a cumulative, continuous effect, it can be detected even in satellites far from the central body, if a sufficiently long time is spent on the observation. For instance, Mer- cury’s perihelion shift is about 42 sec- onds of arc per century, a very small effect indeed. We can say that, as far as Mercury is concerned, the spacetime curvature caused by the sun is hardly noticeable. Spacetime is very nearly flat. Close to a black hole, on the other hand, the peribarythron shift becomes very important. At ten black-hole radii, it amounts to about 70 degrees per orbit!

Even closer to the black hole, circular orbits become unstable. A small devia- tion inward leads to a continuing spiral into the hole. For a Schwarzschild black hole, the point of instability comes at 3 black-hole radii (i.e., at 2 radii from the surface). This does not mean any- thing which falls within 3 radii of the black hole is irretrievably sucked in. One may still swoop down from a very large distance, down to 2 radii, and re- tum to infinity, just as a comet ap- proaches and then recedes from the sun. And this approach can be made without engines, again, like a comet. If rockets are employed, one can come almost all the way down to the Schwarzschild ra- dius, i.e., the horizon, and out again. Alternatively, one can continue to orbit around the hole‘ below 3 radii; but, in this instance, rockets must be fired to maintain position. What is not allowed in this region are free, uncorrected or- bits like those of satellites and skylabs around the Earth.

In the Disney film, the featured hole was not Schwarzschild, but a rotating or Kerr hole (even though the computer graphics shown during the credits were mistakenly those for Schwarzschild). For a Kerr hole, the point of the last stable orbit depends on how fast the hole is spinning, but the results are compa- rable to the Schwarzschild case; insta- bilities set in between l and 9 radii. Thus, the Cygnus should not need “an- tigravity devices" until very close to the hole indeed. On the other hand, as far as 1000 radii from the black hole, the Cygnus would be orbiting with a period of about one second. Admittedly, this may be why the antigravity device was posited in the first place——to dispense with orbits altogether. On the third hand, we doubt the filmmakers thought this far.


Since we have been speaking of or- bits, it is appropriate at this time to in- troduce the second important rule of black hole orbital mechanics: The prin- ciple of equivalence still applies. This fact seems to have escaped the attention of almost all moviemakers and writers. The principle of equivalence states that any body in a free orbit or in free fall does not experience the force of gravity. We might say, “Falling free or orbiting ’round, equivalence says gravity not found.” Examples of this are encoun- tered in everyday life: When we dive off a diving board we feel weightless. When an airplane drops suddenly, those in it feel momentarily weightless. As- tronauts in orbit around the Earth are not weightless because gravity has been tumed off above the atmosphere; rather, they are falling around the Earth, con- tinually diving off the board, if you will. Under these circumstances, the principle of equivalence says that grav- ity is not felt.

This is a very important point which applies to any situation near a black hole when rockets are not being fired: orbit- ing on a stable orbit; orbiting on an unstable orbit (when not correcting for instabilities); spiraling in; swooping down like a comet; or just falling in. In these cases, one does not suddenly feel heavy near the hole. On the contrary, one feels weightless, as if he were or- biting the Earth or diving into a swim- ming pool.

There is a complication to be intro- duced here. When an object comes close to a black hole, tidal forces can become extreme. As their name im- plies, tidal forces are those forces which raise tides on the surface of the Eaith. Because one side of the Earth is slightly closer to the moon than the other side, the near side feels a slightly greater gravitational attraction to the moon than does the far side. Thus, we get a “tidal bulge”; the Earth is stretched out in the direction of the moon. (Some readers may know there are actually two tidal bulges. We do not pause to discuss why this occurs.) We might say, with fair accuracy, that tidal forces are those which arise from the difference in the gravitational field between two points. The greater the difference, the greater the tidal forces.

Consider a man in a spaccsuit orbit- ing a black hole. He is in free fall, so by the previous discussion, feels per- fectly weightless. However, the feet of the astronaut are slightly closer to the black hole than is his head. Therefore he experiences tidal forces: his feet are being pulled toward the hole more strongly than his head. As a result, the astronaut is stretched. One might think, because a man is so small, that the dif- ference in the gravitational force be- tween his head and his feet cannot be very large. After all, gravity does not decrease so fast over a couple of meters. This is not true. Near a white dwarf, neutron star, or black hole, tidal forces can be immense. If he is orbiting a one- solar-mass body at a height of 10 kil- ometers, the tidal forces on our astro- naut are approximately ten million times the force the Earth is, at this moment, exerting on us. That is, while the Earth is pulling us to its surface with a force which, by definition, is equal to our weight, the astronaut is being ripped apart by forces about ten million times stronger. This particular example has roughly the conditions presented in Larry Niven’s story, “Neutron Star.” It is, alas, ludicrous to think the hero could save himself by curling up into a ball at the ship’s center. More likely, he would end up spread over the walls, the consistency of pink applesauce. Per- haps, we have estimated, if he initially started out as a piano wire for triple high C, he might have survived.

Still, a caveat is in order here. Near black holes which are large enough, like our air bag, tidal forces become totally insignificant, much less than even those tidal forces we feel on Earth. Thus, no shredding at all will take place near these holes until one falls close to the singularity. At the singularity, in all black holes, the tidal forces are infinite.

To sum up this section, we reiterate that it is the tidal forces which wreck spaceships near black holes, not the simple fact of strong gravity. And, as just mentioned, for very large holes, over about 105 solar masses, even this does not happen. As an astronaut orbits a black hole, he feels as weightless as if he were floating amid the clouds on a fine spring day. Near a typical black hole, though, his head is being wrenched from his feet by forces which make the bed of Procrustes amateurish by com- parison.


BEING AND NOTHINGNESS: BLACK HOLES AS THE END OF SPACE AND TIME.

Two astronauts are orbiting a ten-so- lar-mass black hole. Richard, having seen one too many bad science fiction films, decides to end it all by taking the fateful plunge. He jumps. Tony, curi- ous to see the demise of his dissertation advisor, decides to clock Richard’s fall to the‘ event horizon. “Time is on my side,” Tony chuckles to himself, but he has a surprise waiting for him. As Richard approaches the event horizon, he seems to fall more and more slowly. Tony knows this because Richard is carrying a green, flashing beacon. The time interval Tony measures between each flash of the beacon is becoming longer and longer. In addition, he is startled to find that the flashes are grow- ing much redder and dimmer “as time goes by.” Tony grows impatient, but to no avail. The fall seems to take for- ever. Tony dies of old age muttering, “Veritam dies aperit,” but Richard has still not reached the event horizon. Tsvi arrives in his space shuttle to take over the observations but suffers Tony’s fate. He too grows old watching Richard’s beacon flash ever more slowly and redly. With his dying breath, he en- treats, “Stand still you ever-moving spheres of heaven/That time may cease and midnight never come.” Tsvi’s des- cendents have no better luck. Richard fades away completely just as he reaches the horizon, after a truly infinite amount of time. The clock has stopped.

Richard, on the other hand, realizes, i “Time and tide wait for no man.” He does not notice his beacon flashing any more slowly than normal, nor does he notice it growing redder and dimmer. He reaches the event horizon after a perfectly finite number of flashes. From that point, he crosses the event horizon, although he does not realize he has done so, and continues his plunge to the sin- gularity at the center of the black hole. Of course, Richard is ripped apart by tidal forces long before he gets there, but his dispersed atoms reach the dreaded singularity in a rather short amount of time—about 10-4 seconds as measured by his flashing beacon.

As well as a mild discrepancy be- tween two clocks, there is a moral to this fable: Relativity is called relativity because relativity is truly relative. The question, “Does time stop at a black hole?” is meaningless as it stands. We can say, “To an observer in a space- ship, an object falling into a black hole takes an infinite amount of time to reach the event horizon.” But we can also say, without contradiction, “To an ob- server falling into a black hole, the time required to reach the event horizon is quite finite.” When posing relativistic questions, one must be careful to spec- ify about whom one is talking, or else one runs the risk of lapsing into gib- berish.

The slowing down of Richard’s bea- con-clock (as measured by Tony and Tsvi on the ship) and the reddening of the light are two aspects of the same effect. The curvature of spacetime as- sociated with the gravitational field around the black hole actually causes time to flow at different rates. Just as the flashing of the beacon can be thought of as a clock, so can the oscil- lations in a light beam, or the move- ments of atoms in the beacon motor. Everything is slowed down from the point of view of Tony or Tsvi on the ship. The slower oscillations of the light are interpreted by Tony’s eye as a red- dening of the light, and since light is being emitted from the beacon at longer intervals, fewer photons (light particles) reach the eye per unit time. The com- bination of these effects causes the ex- cessive dimming of the beacon.

Richard, however, falling into the hole, is subject to the principle of equiv- alence. (Falling free or orbiting ’round, equivalence says gravity not found.) He does not feel any gravity on him or on his beacon. As far as he is concerned there is no gravity to slow down his flashes and everything proceeds as nor- mal, with the exception of tidal effects.

It is important to keep in mind that all these effects occur around any grav- itating body, the sun for instance. The only difference is in the magnitude of the effects, which will be much greater around a typical black hole than near the sun or the Earth.

To conclude this brief discussion of space and time near a black hole, we would have wished to comment at length on the quotation found at the beginning of this article, to the effect that, a black hole is a place where “space does not exist.” This, unfor- tunately, has proven to be impossible because we have entirely failed to dis- cover in that statement any meaning whatsoever.


THE COSMIC WHIRLPOOL: KERR HOLES AND PENROSE PROCESSES.

Present energy dilemmas have made popular the idea of extracting large amounts of energy from black holes. The attraction of this idea is not hard to see. We are all familiar with the large flywheels used by electric companies in their power plants. These huge fly- wheels store rotational energy. By cou- pling the flywheel to a generator, we are transforming the rotational energy into electricity for use in home and in- dustry. In doing so, we have extracted the rotational energy from the flywheel and, as a consequence, it slows down.

Now, we have mentioned that Ken black holes rotate, much like the above flywheels. The rotational energy of a rapidly rotating solar mass Kerr hole is about 1054 ergs. At the Earth’s present rate of energy consumption, 1054 ergs would last approximately 1027 years, or about 1017 times the present age of the universe. This is a long time.

The question naturally arises, can the rotational energy of a Kerr hole be ex- tracted. If it could, we would expect the black hole to slow down like the fly- wheel. When no further energy could be extracted, the black hole would no longer be a spinning Kerr hole; it would be a non-rotating Schwarzschild hole. In 1969, the British relativist, Roger Penrose, showed that extraction of the rotational energy of a Kerr hole is pos- sible. Immediately after his suggestion appeared, others further proposed that the Penrose process might be used by an advanced civilization to tap the en- ergy of black holes. From there, science fiction took over. The basic idea was used in Gateway by Fred Pohl. Indeed one of us (T.R.) succumbed to the temp- tation to use the idea in his novel, The World Is Round. Unbeknownst to T.R. , T.P. and others were at the same time proving how difficult the Penrose pro- cess was to implement.

To understand the Penrose process further, we must first talk in more detail about Kerr holes. The rotation of a Kerr hole causes a “whirlpool in space.” This whirlpool is actually quite similar to an ordinary ocean whirlpool except that, instead of water whirling around, it is spacetime itself swirling around the black hole. If a space traveller is caught in this whirlpool, he is dragged around the black hole exactly as he would be dragged around the eye of the vortex if caught in an ocean whirlpool. If the space traveller wanted to remain sta- tionary, he would have to fire his rocket engines to overcome the spacetime dragging. Again, this has a marine analogy. A swimmer must swim against the current in the vortex if he wishes to remain in the same place.

We should note that this dragging is not unique to black holes but, according to relativity, occurs around any rotating body. In fact, a team of experimentalists at Stanford, led by Francis Everitt, is planning to measure the dragging force caused by the Earth's rotation. This measurement will be carried out by a satellite to be launched by the space shuttle. The dragging caused by a tiny body like the Earth is really very small. While the Stanford satellite orbits the Earth, the gyroscopes on board will be tilted a slight amount by the drag. After a full year, the cumulative angle of tilt will be less than a second of arc, about the angle subtended by a penny as seen from a distance of a kilometer.

Although the effect due to the Earth is small, around a black hole the drag- ging can become enormous. In fact, beneath a certain distance from the hole which is termed the “stationary limit,” no matter how hard one fires his rocket engines against the current, the drag- ging cannot be overcome and one is inevitably swept around the hole. This notion can be made more precise. Con- sider an observer on a “space buoy” being dragged passively around the hole; To him, someone in a rocket trying to overcome the dragging will appear to be moving in the opposite direction. At the stationary limit, this rocket will appear to the observer on the buoy to be moving at the speed of light. From a space station far above, how- ever, the rocket is just managing to fight the current and remain stationary, hence the name “stationary limit.”

We recall the famous words of the Red Queen: “ . . . it takes all the run- ning you can do to keep in the same place. If you want to get anywhere else, you must run at least twice as fast as that.” Unfortunately, one cannot run any faster than the speed of light. If she is unlucky enough to fall beneath the stationary limit, even the Red Queen will never be able to stay put and will be dragged around the hole along with space buoys, rockets, and everyone else. (See Figure 2.)

The region between the stationary limit and the event horizon is called the “ergosphere.” “Ergosphere” was coined by Wheeler and Ruffini from the Greek word “ergo” meaning “work.” It is in the ergosphere that the Penrose process takes place. (See Figure 3, for the relationship between the horizon, ergosphere, and stationary limit.)

Consider a rocket orbiting in the er- gosphere. It ejects a load of garbage against the current (like the Red Queen). Although this garbage is swept around the hole——since it is beneath the sta- tionary limit—-—it is “struggling against the current.” One can imagine that an object moving on such a “counterm- tating” orbit would exert a braking force on the hole and therefore slow it down in the same manner as we slow a flywheel. Thus, some of the rotational energy is lost and is, in fact, transferred to the ship as a recoil effect. (Think of a gun shooting a bullet. The recoil is greater than normal due to the presence of the rotating black hole.) This energy would be manifested as a greater kinetic energy of the ship, that is, a higher ve- locity. The ship could then leave the ergosphere with more energy than it had to start with, to be used elsewhere.

However, the matter is not so simple. The ejected garbage will be captured by the black hole, adding its own mass to the original mass of the hole. Since E = mc2, by losing the garbage we are losing energy to the hole. If the amount of energy lost to the hole is greater than the amount of energy gained by braking the hole, we have a net loss of energy. No extraction has taken place.

Nonetheless, if certain conditions are met, the energy balance will be favor- able. That is, if the garbage is ejected at sufficiently high velocity onto a coun- terrotating orbit within the ergosphere, the net result will be an energy gain. Any orbit which meets these require- ments is termed an “energy extraction orbit.” We emphasize that they only exist within the ergosphere. Note also that it is the orbit which is important, not what we eject. T herefore. it makes sense to use garbage, since this elimi- nates waste disposal problems as well.

The Penrose process is best illustrated by the machine in Figure 4. adapted from the text Gravitation, by Misner, Thorne and Wheeler. An advanced civ- ilization builds a huge shell around a Kerr black hole. Space shuttles loaded with garbage enter the ergosphere. They eject their payloads in the manner al- ready described. receive a giant dose of energy which boosts them to huge ve- locities. and return to the surface. They are caught in the arms of a giant gen- erator which converts this kinetic en- ergy into electricity for use over the shell.

Even if our supply of garbage is lim- ited to one Earth mass, this is enough to power the Penrose process for about 1021 years, or 1011 ages of the universe, not an insignificant amount of time.


Two technical details make this ex- traordinary picture somewhat less op- timistic. The first difflculty is jettisoning the garbage onto an energy extraction orbit. The second difficulty is getting the boosted shuttle out of the ergosphere without being captured by the black hole. We can better understand these problems if we pretend we are on a shut- tle, the Penrosia, whose mission is to go into the ergosphere, dump garbage, and return to the shell with as much energy as possible. The crew is fresh out of Starfleet Academy and so learns by the dangerous method of trial and error.

We have entered the ergosphere. Be- cause fuel supplies are limited, the Cap- tain has turned our engines off. The Penrosia is now being passively dragged around the black hole’s whirlpool like a space buoy. Since we are in orbit, we feel weightless. An inexperienced space cadet attempts to eject a load of garbage onto an energy extraction orbit simply by throwing it out by hand. To our dis- may, we find that the garbage only fol- lows the shuttle along, very gradpally drifting away (exactly like what hap- pens with garbage jettisoned from a space capsule in Earth orbit). The bun- dle is certainly moving too slowly to be on an energy extraction orbit; this gar- bage would hardly brake a snail, let alone a black hole. Determined, the crew tries again, this time firing the garbage out of a cannon. Now the gar- bage vanishes into the distance, but when our sensors plot the trajectory, we find that the garbage is still not moving fast enough to be on an energy extrac- tion orbit. Many such attempts are made, each using increasing amounts of power. They all fail. Finally, the frustrated crew of the Penrosia succeeds in shooting a thimblefull of garbage onto an energy extraction orbit. They calculate the velocity of the thimble and find it to be nearly the speed of light. This has been accomplished only by momentarily diverting the full power of the shuttle’s reactor engine, just for the purpose of launching the thimble. When the energy balance is computed, the crew discovers that the energy gener- ated by the reactor on board was almost equal to that gained by ejecting the gar- bage. However, they have gained some energy and tired but happy, prepare to leave the ergosphere.

At this moment, the Captain realizes he has made a fatal mistake: He has forgotten Newton’s Third Law. When a rocket ejects fuel from its engines, the rocket is propelled in the opposite di- rection. By ejecting garbage from the Penrosia, the crew has inadvertently boosted the shuttle onto a new orbit. The ship’s computer makes a quick cal- culation. To the Captain’s horror, he realizes that the new orbit will lead the Penrosia—-and us—-directly into the black hole. The Captain guns his en- gines. After expending all the energy gained by launching the thimble, we barely escape to the surface, tired but unscathed.

What happened?

Recall our previous discussion. The “sufficiently high velocity?’ mentioned earlier for,an energy extraction orbit, turns out to be nearly the speed of light. That is, the garbage must be like the Red Queen, moving at nearly the speed of light with respect to other objects in the whirlpool. To accelerate an object to the speed of light requires stupendous amoupts of energy which, in this case, must be generated on board. It tums out that we must convert a large part of the garbage into energy in order to boost what little remains to the velocity of light.

The second problem was to get the energy out. Most orbits within the er- gosphere intersect the black hole. The Penrosia boosted herself onto one of these orbits and to escape it required also a stupendous amount of energy. In most cases, anything gained by the ejec- tion is lost in trying to escape. This sec- ond problem, as it turns out, can be overcome only by jettisoning the gar- bage exactly at the peribarythron of the orbit. Then one escapes to the surface with what little energy was initially gained by the ejection.

We have just seen that to get an ap- preciable amount of energy out of the hole requires that matter be converted on board the shuttle with essentially 100% efficiency. Then by ejecting this “energy beam” (photons), we get an additional 20% boost from the hole, for a grand total of l20% efficiency. Not bad; but since this requires almost 100% conversion efficiency to begin with, the Penrose process might not be worth all the trouble. It can, however, be used for a more efficient energy conversion process than is available on Eanh. That is, it tums out we can use a modified Penrose process to extract energy from matter with up to 10 times efficiency of the 1/2% of hydrogen bombs, the most efficient process known at present. Unfortunately, we do not have space in this article to discuss such modifica- tions, and a more detailed discussion will have to wait for another.opportu- nity.


“I EXPECT TO PASS THROUGH THIS WORLD BUT ONCE”: STAR GATES AND TIME MACHINES.

Any interstellar empire or commer- cial consortium need a means of rapid communication and transport. The smuggler Han Solo made the “jump into hyperspace” and emerged at his destination some time (l2 parsecs!?) later. Space warps and star gates are a staple of science fiction.

Relativity, as already mentioned, de- scribes gravity as a warping of space and time, and a black hole is the result of the strongest possible curvature. It is not surprising, then, that science fic- tion has latched onto black holes in an attempt to make space warps sound more plausible. To some extent, it is our own fault; in idealized situations, relativists have discovered the tantaliz- ing possibility of a “star gate” lurking in black holes. Unfortunately, the sit- uation has gotten out of hand and almost everyone has chosen to ignore work started as far back as a decade by Pen- rose and Floyd, which shows that “star gates” cannot be realized in practice.

To discuss this problem, we will need to back up and fetch some concepts not yet introduced in this article. Relativity is, in a sense, a study of geometry, but not simply the ordinary Euclidean kind which we all learn in high school. For one thing, space and time have been combined into a 4-dimensional space- time. To pursue this point briefly, let us refer to Figure 5. Here, only two spatial directions are shown, x and y (east-west and north-south if you like) and the time direction, labeled by ct. Time increases upward. From the ex- planations accompanying Figure 5, we distill four rules for understanding these diagrams: l) An object stationary in space still moves through time. Its path through spacetime, or worldline, is therefore a vertical line; 2) An ordinary, moving object, like a rocket, has a world line which is tilted at less than 45 degrees from the vertical; 3) Light travels along 45 degree lines; 4) Trav- eling on a worldline tilted greater than 45 degrees from the vertical is prohib- ited because this is motion faster than the speed of light.

This type of spacetime diagram has its defects. The most serious one is the difficulty of showing things which are very far apart——it is especially difficult to map an infinite universe onto a finite piece of paper. Nonetheless, with suf- ficiently vigorous squeezing, one can actually distort the outer edges of the universe in such a way that we can fit the entire infinite universe onto a finite piece of paper. We can even retain cer- tain features of the real universe. The one feature which is usually kept is the 45 degree angle which represents the trajectory of a light beam. A diagram like Figure 6 results.

All this is in preparation for a dis- cussion of star gates and time machines based on black holes. Recall our dis- cussion of tidal forces. We mentioned that in a simple Schwarzschild black hole, tidal forces on an infalling object (remember Richard’s plunge) become greater and greater until they become infinite at the singularity. Well, inside a rotating Kerr hole, or a charged Re- issner-Nordstrom black hole, this is not necessarily true. In fact, the theory states the following: Unless the black hale" has exactly zero charge and zero rotation, it will allow an object, say a spaceship, whose own gravitational ef- fects are negligible, to enter the black hole at a speed slower than light, avoid the singularity, and leave again by an exit diflerent from the surface through which it entered. The different exit sur- face gets around the immediate objec- tion that nothing which falls into a black hole can escape again; it can, but not through the same surface through which it entered.

If the exit surface is not the same as the event horizon by which we entered, then where does the spaceship end up? Figure 7, a spacetime diagram drawn for a Reissner-Nordstrom black hole, attempts to explain the situation. The two diamond shaped regions are like Figure 6 and thus both represent infinite universes. The diagram therefore shows two universes connected by a black hole tunnel. (Again, we are plotting space horizontally and time vertically.) The curve shows the history of the infalling- spaceship-cum-observer as it travels through the hole.

A complicated figure indeed. The in- trepid traveller falls inward. The first 45 degree line he crosses is the event horizon of the black hole; nothing can re-exit via this surface once having crossed it. The jagged lines represent the singularities, where tidal forces are infinite. (Remember, singularities are moving forward through time; therefore on this diagram they appear as vertical lines.)But the traveller can avoid these reefs; just by coasting he passes at a safe distance. When he emerges from the black hole,’ he finds himself in a normal universe like the one he just left. In fact, it may be precisely the one he left, but the black hole exit need not be near the entrance, and there is reason to think it would not be near that entrance.

We might at first worry whether the second universe is the same as ours. According to the theory, there is no rea- son it should not be, but equally no rea- son it should be either. (Parallel worlds!) If many charged or rotating black holes inhabited our universe, the possibility would exist that their exits would emerge in our own universe, or all in the same second universe, or in any number of alternate worlds (see Figure 8). More bizarrely, these various universes might be connected in such a way that, after traveling through several black holes, one returns to our own universe, but at a previous time. The theory does allow for this possibility, suggesting the use of black holes as time machines. In any case, the first pioneer to determine which of this possibilities exists, will be a very brave man, and exceedingly dedicated to the progress of science.

Unfortunately, at this point, hard sci- ence drags us back from such interesting speculation. The crucial flaw in the above discussion was the assumption that the spaceship had a negligible grav- itational effect on the hole. Can a real spaceship travel through the hole with- out disturbing its structure? In short, the answer is no.

To see this, just consider the energy content of solid space garbage, laser photons, radio and other waves, all of which a well-equipped interstellar space traveller would likely spread around during his trip. The central problem is that some of this stuff falls into the black hole too. As it falls into the hole, gar- bage, for instance, has picked up a ve- locity very close to the speed of light. We know that mass increases to infinity at these velocities. By E=mc2, this means that the energy of even the small- est amount of garbage has also become infinite. The same occurs with the en- ergy content of infalling radio waves and light signals emitted by the ship; their energy goes up to infinity also. But what has infinite matter and energy den- sities in a black hole? The singularity, of course. Where the clean black hole provided clear sailing, by allowing for garbage or radio waves we have created a singularity of infinitely destructive tidal forces, as in the Schwarzschild case.

A moment’s thought leads to the con- clusion that the black hole star gate is a one-time affair at best. If just the radio signals transmitted by the space trav- eller can be so disruptive, the mass of the spaceship itself must certainly dis- rupt the black hole and close the gate behind him.

Assuming he makes it through in the first place. What if he is extremely care- ful not to sully theblack hole before his joumey? He maintains radio silence and stows his garbage bags. Could he make it through the tunnel?

Surely, his spaceship must have sub- stantial mass. A mass falling toward a black hole is accelerating and, conse- quently, generates gravitational waves, analogous to the generation of electro- magnetic waves by accelerating electric charges. These waves are oscillations in the gravitational field which travel at the speed of light. Again, this is in analogy to radio waves which travel at the speed of light and are oscillations in the electromagnetic field. Some of these waves travel ahead of the infalling spacecraft, are amplified to infinite en- ergy in the same way as already dis- cussed for radio waves; and the gate to the other side of the galaxy slams shut in his face. The star gate cannot even be used once.

The simple argument just given shows that the inner structure of black holes is unstable to small disturbances from the outside. Any amount of energy or debris falling in from the outside will develop an infinite energy density and destroy the inner structure of the hole. In a perfectly clean universe, we could not know a priori whether a given Kerr or Reissner-Nordstrom black hole con- tains a tunnel to another part of the universe. But we do know that, if we probe the black hole by trying to reflect radiation off it, we automatically de- stroy the star gate, because some ab- sorption of radiation is inevitable. In the real uniyerse, of course, the situation is even worse because radiation and matter are everywhere present to some degree and must be falling into any ex- isting black holes.

So it seems, for instance, the collap- sar transpon system used in Joe Halde- man’s Forever War will not work; nor does the physics at the end of the Disney film hold water (not to mention the metaphysics); and, in fact, the syphon- ing of extra matter from another uni- verse mentioned at the conclusion of T.R.’s own novel will not go through either. At least these works were re- leased as science fiction. Books such as Adrian Berry's The Iron Sun, which purport to be science are either flagrant rip-offs or bad science fiction. As either rip-offs or science fiction, they deserve no further serious consideration.


BIG SURPRISES COME IN SMALL PACKAGES: PRIMORDIAL BLACK HOLES.

Until now, we have concentrated our attention on large black holes, from l0 solar masses to over 1010 solar masses. In this section, we turn our attention to the other end of the spectrum: mini black holes. At the very beginning of the universe, at times much less than one second after the Big Bang, the den- sity of matter was comparable to what is found in typical black holes. It is con- ceivable, then-—but by no means proven—that a slight fluctuation in den- sity would “snap” the matter into black holes. Such “primordial” black holes would range in size from the very large, about 100,000 solar masses, to the very small, about 10-5 grams. The small holes would be formed first, when the density was highest, followed by suc- cesively large holes, until the density was too low to form any at all.

Large primordial black holes would behave in exactly the same way as the other large holes which we have already discussed. There is nothing to be added here. At the other extreme, holes of 1015 grams and below are remarkable ob- jects. The density of 1015 gram black holes is so high that one cubic centi- meter of them would contain the known mass of the universe! Holes smaller than this mass would exhibit extraordinary quantum properties, specifically the fa- mous Hawking radiation named after its discoverer. Space does not permit us to discuss these amazing properties. Suf- fice to say, there is no observational evidence to indicate that holes smaller than 1015 grams exist or existed. More- over, theoretical upper limits placed on such holes by Page, Hawking, Novikov et al., and two of us (R.M. and T.R.), indicate that, if they ever existed, they were few and far between. For instance, there cannot now be more than about 10 black holes of 1015 grams per cubic parsec, each with the mass of a moun- tain but the size of a proton.

Primordial black holes with masses greater than 1015 grams have negligible quantum properties and can be treated classically. Such black holes have also received attention in science fiction and popular folklore and therefore their share of misrepresentation. Perhaps the most famous—or notorious—suggestion was put forth by Al Jackson and Mike Ryan, then at the University of Texas, that the 1908 Tunguska blast in Siberia was caused by the collision of a 1021 gram black hole with the Earth.

We may first ask, “What are the odds of such a collision taking place?” Not bloody likely. Assuming all the observ- able mass in the universe to be concen- trated into 1021 gram black holes, one can calculate that one collision should occur about every ten ages of the Uni- verse, or 1011 years. Marauding black holes do not seem an overwhelming threat to U.S. security. Nonetheless, it is possible that Tunguska was the col- lision. Although a 1021 gram black hole is small in radius, about 10-7 centi- meters, its mass is large, about one million small mountains. Jackson and Ryan proposed that the gravitational attraction of this hole caused the sur- rounding air to be yanked inward, re- sulting in a compact ball of air whose shock effects produced the destruction seen in well-known photographs. There was, however, substantial debate on whether a black hole of this mass would have the Claimed effect when interacting with the solid earth. Most physicists believe the ground shock would have been tremendous, much more so than what actually occurred. So in scientific circles the matter is considered dead and buried. In any case, Al Jackson and Mike Ryan have on occasion confided that the suggestion was not entirely se- rious in the first place.*

(*We have recently learned that a report in Sotsialisticheskaya Industriya, 1/24/80, in- dicates that ordinary meteoric debris was re- cently found at the Tunguska site.)

Detailed statements about the inter- action of smaller black holes (about 1015 grams) with matter are difficult to make. Nonetheless, simple calculations give the following general picture, which should not be too far wrong: Recall, a 1015 gram black hole has the diameter of a proton. This is too small a size to rapidly accrete (gobble up) surrounding matter. Even if one considers that any nearby particle in random motion falls in when nearing the hole, one finds an accretion rate such that the black hole will not even double its mass in the life- time of the universe. Talk of eating a planet becomes absurd. Thus, the black hole posited by Larry Niven in “The Hole Man” would certainly never gob- ble up Mars in less than extreme cos- mological times, meaning millions or billions of ages of the universe.


WHERE DO WE GO FROM HERE?: PROSPECTS FOR THE FUTURE.

We have talked about many types of black holes and many properties but have omitted discussion of many other interesting properties as well. We have not spoken about Hawking radiation, nor about black hole collisions, nor about superradiance, nor about astro- physical accretion, nor about photon trajectories and imaging properties, nor about the influence of primordial black holes on nucleosynthesis after the Big Bang. We have also shied away from direct discussion of the famous singu- larity which occurs within all black holes. The singularity, as already men- tioned, is the center of the black hole where all the matter has fallen. It is a place where the density of matter is in- finite, as well as gravitational and tidal forces. When people speak of space and time ending at black holes, they are perhaps thinking of the singularity. But it may be a mistake to say space and time end at the singularity; what ends is our present knowledge of physics.

Much work is currently underway to remedy the situation. Many physicists believe that true singularities do not ex- ist, that at such small distances the quantum properties of spacetime itself come into play. They suggest that mat- ter cannot be compressed to a smaller size than the so-called Planck length, about l0-33 centimeters, where the quantum effects become dominant. Ac- cording to this view, the singularities of classical black holes are nonexistent in reality and are only the temporary nuisances of defective mathematics.

At least two Russian physicists, Fro- lov and Vilkovisky, have recently claimed to have proven that black holes, in some sense, do not exist at all. Proper use of quantum field theory, they argue, shows that as matter collapses to form a black hole, it misses the singularity, “rebounds," and eventually re-expands beyond the event horizon. This process, for even Tunguska-sized black holes, will take longer than the age of the universe. Nonetheless, in a strictly»log- ical sense, a black hole is no longer a black hole, but only temporarily out of sight. We are not yet sure whether Fro- lov and Vilkovisky are correct, but we are certain that the full merger of rela- tivity and quantum theory will reveal many answers and even more ques- tions.

From DEMYTHOLOGIZING THE BLACK HOLE by Richard Matzner, Tsvi Piran, and Tony Rothman (1980)
NAKED SINGULARTIES

First, let me establish something. When I go to Cal Tech I do not expect an experience out of H. P. Lovecraft. Horror may be interesting at the proper time and place, but it's not very pleasant as a total surprise.

It started peacefully enough. Dr. Robert Forward, the Hughes Research gravity expert you've heard of here and other places, called to ask if I would be interested in meeting Stephen Hawking. Since Hawking is thought by important physicists possibly to rank alongside Newton and Einstein, it took perhaps five milliseconds to think over the proposition. I didn't even need to look at my calendar; nothing I had planned could be that important.

A week later Larry Niven and I drove over to the California Institute of Technology. It was a bright spring afternoon. . .

The lecture was in a small modern slant-floored room of the type sometimes called lecture theaters; the sort of classroom lecturers like. The tiered seats let everyone have a good view of the speaker and his demonstration materials, and give the speaker a good view of the audience.

It was only partly filled: graduate students, several undergraduates, a sprinkling of faculty, one or two of the top names in theoretical physics. It was a room of serious women and men, mostly younger than I, all expectantly quiet. At the bottom of the well, the focus of attention on the stage, was an incredibly thin, very young-appearing man seated in a high-backed motorized chair of Victorian design; the chair had no flavor of the hospital about it. He wore a light suit, dark shirt, and flowered tie, and he kept his hands folded carefully in his lap as he was introduced.

The chairman gave his credits and spoke wonderingly of how privileged we were to hear a man of this stature. No one disagreed. Not, of course, that anyone would have said anything no matter what he thought, but the total silence in the room was an obvious sign of unanimous assent.

Hawking began to speak Everyone leaned slightly forward, straining to hear. Except for the heavily slurred voice there was absolutely no sound; you could quite literally hear a pen drop, for I dropped mine and it clattered loudly on the cement floor.

This is the scene, then: a lecture room partly filled with very bright people, a few extremely well known in theoretical physics, others students at one of the world's most prestigious institutions. They all strain to hear a wizened young man who makes awkward gestures and speaks with a thick slur that keeps his words just at the edge of intelligibility.

He grins like a thief. He's obviously not in pain, and he doesn't feel sorry for himself. And he tells that room of bright people that everything they thought they knew is nonsense. And he chuckles.

He tells us that the pudding that ate Chicago may someday exist; that duplicates of each one of us may one day wander the universe; that anything can, and probably will, happen. He tells us that the universe isn't lawful, never will be lawful, never can be lawful; that we cannot ever know enough to predict the totality of events in this universe; that at best we study local phenomena that may be predictable for an unspecifiable time.

And he laughs.

He tells us that Cthulthu may exist after all.

As I said, it was an afternoon of Lovecraftian horror.

Larry and I escaped with our sanity, after first, in the question period, making certain that Hawking really did say what we thought he'd said.

He had.


Stephen Hawking's lecture had originally been entitled "The Breakdown of Physics in the Region of Space-Time Singularities." The title was flashed on the screen; then another slide took its place, and Hawking chuckled. The new slide said:

THE BREAKDOWN OF PHYSICS PHYSICISTS

IN THE REGION OF SPACE-TIME SINGULARITIES

He began simply enough. The principle of equivalence, he said, is well established. This is the principle that states that inertial mass, that is, the resistance of objects to being moved by an outside force, is exactly equivalent to gravitational mass, that is, the gravitational force a given mass will exert. There are not two kinds of mass.

This was Galileo's principle, and there's the famous apocryphal story of his dropping a cannon-ball and a musket-ball from the Leaning Tower of Pisa and observing their striking the ground at the same time. Obviously if gravitational and inertial mass were different, heavy objects would not fall at the same speed as light ones.

So far so good. Next, gravity affects light. It can bend light rays, as predicted by Einstein and observed several times in solar eclipses.

Now in short order: the energy-momentum tensor of gravity is positive; gravity is universally attractive, not repellent. Therefore, enough mass will create a field from which no light can escape.

The Special Theory of Relativity says that nothing can travel faster than light.

And therefore sufficient mass must create a space-time singularity, a place which cannot be observed.

A singularity is therefore inevitable; that is, at least one singularity must exist, provided only. (1) that Einstein's general relativity is correct; (2) gravity is truly attractive and never repellent; and (3) enough mass has ever been collected together.

And therefore at least one singularity exists in our universe, since at the time of the Big Bang all the conditions certainly prevailed; and also, it's very likely that other singularities have been created by collapse of stars, since many stars have more than enough matter and don't have enough energy to throw that matter away as they die.


OKAY so far? Nothing startling here. Bit dry, but all we've shown is that singularities must exist, and nearly everyone accepts the idea now. They're hidden away inside black holes, of course, and observers are now very nearly certain that we can observe a black hole.

Well, not observe the hole itself; but Cygnus X-l, an x-ray emitting star in the constellation Cygnus, has an invisible companion and the pair of stars, the one we can see and the one we can't, together act very like what Gal Tech's Kip Thorne predicted such a pair would act like if one were a black hole.

So what else is new? We've proved black holes can exist, and lo, the observers think they've found one. What's scary about that?

Nothing, so far. Holes aren't scary unless you're about to fall into one. We even understand them. We know they "have no hair," that is, that they can be completely described given their mass, M; angular momentum, J; and electric charge, Q, Given these data we can describe their shape, and predict what effect they'll have on nearby objects, and play all kinds of fascinating scientific-theory games.

We can talk about black hole bombs, and toy with ideas on how to extract energy from them: take one rotating black hole, throw garbage into it, and you not only get rid of the garbage, but can get useful energy back out. There are speculations (not SF; just plain science) about extremely advanced civilizations using black holes for precisely that purpose.

There's just no end to the nice things you could do with black holes, and although not many years ago they were no more than toys for theoreticians to play mental games with, black holes have become household-word objects now.

Black holes don't make us nervous.

Ah, but inside each black hole there lurks a singularity. This is the little beastie that breaks down physics in the nearby regions. By definition they do things we can't predict. They behave in strange ways. Up close to them time reversals can happen. How, then, can we avoid this breakdown of our nice predictable universe?

Hawking discussed several theoretical alternatives, and dismissed each. A couple of the cases seemed to startle one of the big-name theoreticians listening to the lecture. When Hawking was finished, though, the singularities were back and inevitable. I won't pretend to have understood all of this part of the lecture; and I wouldn't bore my readers with it if I had. If you appreciate that sort of thing you'll read Hawking's paper when it comes out.

For the rest of us I sum up by saying that he found no good alternatives; eliminating General Relativity doesn't eliminate the singularities, or else lands you in an even worse theoretical soup.

Therefore, let us look at General Relativity; but let us add quantum theory to it. Hawking recently published that work, and I described it here.

The important fact is that the quantum effects violate cosmic censorship. The Law of Cosmic Censorship, you may recall, states that there shall be no naked singularities; every singularity shall be decently clothed with an event horizon that prevents us from ever being able to observe it directly, and thus prevents us from observing the region in which physics breaks down.

Thus we needn't fear the singularity. It can't affect our lives, because nothing it does can get out of that black hole "around" it.

But adding quantum effects to General Relativity repeals cosmic censorship. Black holes evaporate. Big ones slowly, small ones rapidly, all inevitably. And what of the singularity that MUST have been created by the Big Bang of creation?

Evaporation of black holes produces naked singularities. We may play about with the concept of quantizing relativity, and Hawking did; but the conclusion was inescapable. Again I don't pretend to have followed every step, nor did most of the rest of us in that room; but several did, and they weren't pleased.

Because now comes the punchline. The singularities emit matter and energy. And "they emit all possible configurations with equal probability. Thus, perhaps, this is why the early universe from the Big Bang singularity was in thermal equilibrium and was very nearly homogeneous and isotropic. Thermal equilibrium would represent the largest number of configurations."

But since that time the universe has changed, and we have stars and planets and nematodes and comets and people; but the singularity must still be around. It emits. And what comes out is completely random, absolutely un-correlated. This fundamental breakdown in prediction—Hawking is saying not only that we can't predict now, but that in principle we can never predict, no matter how much we know or how smart we get or how large a computer we build—is a "consequence of the fact that General Relativity allows fundamental changes in the topology of space-time; that is, allows holes.

"Matter and information can fall into these holes—or can come out. And what comes out is completely random and uncorrelated."

The hole can emit anything. Anything at all.


"No," I thought. I looked to Niven. "No," he was thinking. Surely we misunderstood.

And the thin chap grinned ever more broadly. "Of course we might have to wait quite a while for it to emit one of the people here this afternoon, or myself, but eventually it must—"

Hawking chuckled and waited expectantly, and after a long and very silent pause first one, then another joined him in laughter; but it had a rather hollow sound, or so I thought. Larry agreed when we could talk about it later.

So far as we can tell, we've just heard one of the top people in theoretical physics tell us that we don't know anything and can't know anything; that causality is a local phenomenon of purely temporary nature; that time travel is possible; that Cthulthu might emerge from a singularity, and indeed is as probable as, say, H. P. Lovecraft.

Hawking concluded by reminding us that Albert Einstein once said "God does not play dice with the universe."

"On the contrary," Hawking said, "it appears that not only does God play dice, but also that he sometimes throws the dice where they cannot be seen!"


Lovecraftian horror indeed. Our rational universe is crumbling. Western civilization assumes reason; that some things are impossible, that's all, and we can know that; that werewolves don't exist, and there never was, never could be, a god Poseidon, or an Oracle that spoke truly; that the universe is at least in principle discoverable by human reason, is knowable.

That, says one of the men we believe best understands this universe, is not true. It's not very probable that Cthulthu will emerge from the primeval singularity created in the Big Bang, or that Poseidon will suddenly appear on Mount Olympus, but neither is impossible; and for that matter, this world we think we understand, which seems to obey rational laws we can discover, isn't very probable either—isn't, in fact, in the long run any more probable than a world that includes Cthulthu, or the pudding that ate Chicago.

From IN THE BEGINNING by Jerry Pournelle (1975)

Gravitational Catapults

This is sort of like a gravitational Slingshot, but turbo-charged.

In case it wasn't obvious, these are all ultra-high tech. The closest known black hole is about 3,000 light-years away, neutron stars and close orbit white dwarfs are not much closer (for practicality's sake you'll need a faster-than-light starship). And creating ultra-dense objects is a little beyond our ability.

GRAVITATIONAL MACHINES

      The difficulty in building machines to harness the energy of the gravitational field is entirely one of scale. Gravitational forces between objects of a size that we can manipulate are so absurdly weak that they can scarcely be measured, let alone exploited. To yield a useful output of energy, any gravitational machine must be built on a scale that is literally astronomical. It is nevertheless worthwhile to think about gravitational machines, for two reasons. First, if our species continues to expand its population and its technology at an exponential rate, there may come a time in the remote future when engineering on an astronomical scale will be both feasible and necessary. Second, if we are searching for signs of technologically advanced lite already existing elsewhere in the universe, it is useful to consider what kinds of observable phenomena a really advanced technology might be capable of producing.

     The following simple device illustrates the principle that would make possible a useful gravitational machine (see Figure 1). A double star has two components A and B, each of mass M, revolving around each other in a circular orbit of radius R. The velocity of each star is

V = (GM/4R)1/2     (1)

where

G = 6.7 × 10-8 cm2/sec2g     (2)

     is the gravitational constant. The exploiters of the device are living on a planet or vehicle P which circles around the double star at a distance much greater than R. They propel a small mass C into an orbit which falls toward the double star, starting from P with a small velocity. The orbit of C is computed in such a way that it makes a close approach to B at a time when B is moving in a direction opposite to the direction of arrival of C. The mass C then swings around B and escapes with greatly increased velocity. The effect is almost as if the light mass C had made an elastic collision with the moving heavy mass B. The mass C will arrive at a distant point Q with velocity somewhat greater than 2V. At Q the mass C may be intercepted and its kinetic energy converted into useful form. Alternatively the device may be used as a propulsion system, in which case C merely proceeds with velocity 2V to its destination. The destination might be a similar device situated very far away, which brings C to rest by the same mechanism working in reverse.

     It is easy to imagine this device converted into a continuously operating machine by arranging a whole ring of starting points P and end points Q around the double star, masses C being dropped inward and emerging outward with increased velocity in a continuous stream. The energy source of the machine is the gravitational potential between the stars A and B. As the machine continues to operate, the stars A and B will gradually be drawn closer together, their negative potential energy will increase, and their orbital velocity V will also increase. The machine will continue to extract energy from their mutual attraction until they come so close together that orbits passing between them are impossible. For a rough estimate one may suppose that the machine can operate until the distance between the centers of the two stars is equal to 4a, where a is the radius of each star. The total energy extracted by the machine from the gravitational field is then

E = GM2/8a     (3)

     If A and B are ordinary stars like the sun, the radius a is of the order of 1011 cm. The energy E is then equal to the luminous energy radiated by the stars in a few million years. Under these conditions the available gravitational energy may be exploited, but it is of minor importance compared with the luminous energy of the system. A technically advanced species would presumably put its main efforts into harnessing the luminous energy.

     If the stars A and B are typical white dwarfs, the situation is entirely reversed. In that case the optical luminosity is less than that of the sun by a factor of about a thousand, while the available gravitational energy is increased by a factor of a hundred. It is therefore logical to expect that around a white-dwarf binary star a technology based on gravitational energy might flourish. For purposes of illustralion, let us assume

M = 1 solar mass = 2 × 1033g     (4)

a = 109 cm     (5)

R = 2a = 2 × 109 cm     (6)

     Then we find

V = 1.3 × 108 cm/sec     (7)

E = 3 × 1049 ergs     (8)

     The orbital period of the binary star is

P = 100 sec     (9)

     A search for eclipsing binaries of such short period among the known white dwarfs was suggested many years ago by H. N. Russell. The search was subsequently made by F. Lenouvel, with negative results. The negative result is not surprising, since the total number of identified white dwarfs is very small.

     A white-dwarf binary star with the parameters (4) to (9) would have the interesting property that it could accelerate delicate and fragile objects to a velocity of 2000 km/sec at an acceleration of 10,000g, without doing any damage to the objects and without expending any rocket propellant. The only internal forces acting on the accelerated objects would be tidal stresses produced by the gradients of the gravitational fields. If the over-all diameter of the object is d, the maximum tidal acceleration will be of the order of

A = GMd/a3 = ⅛d     (10)

     For example, if A is taken to be l earth gravity, then d = 80 m. So a large space ship with human passengers and normal mechanical construction could easily survive the l0,000g acceleration. It may be imagined that a highly developed technological species might use white-dwarf binaries scattered around the galaxy as relay stations for heavy long-distance freight transportation.

     An important side effect of a short-period white-dwarf binary would be its enormous output of gravitational radiation. According to the standard theory of gravitational radiation, which is not universally accepted, a pair of stars of equal mass moving in a circular orbit radiates gravitational energy at a rate

W = 128V10/5Gc5     (11)

     where c is the velocity of light. It would be extremely valuable if we could observe this radiation, both to verify the validity of the theoretical formula (ll) and to detect the existence of white-dwarf binaries. Inserting the value of V from (7) into (ll), we find

W = 2 × 1037 ergs/sec     (12)

     which is 5000 times the sun’s optical luminosity. Comparing (12) with (8), we see that the gravitational radiation itself will limit the lifetime of this white-dwarf binary to about 40,000 years. However, since the dependence of W on V is so extreme, a binary with V = 5 × 107 cm/sec could live for many millions of years. A technologically advanced species might then choose the value of V to suit its particular purposes.

     Assuming the value (12) for the intensity of a source of gravitational waves at a distance of 100 parsecs, we find that the signal to be detected on earth has the intensity

I = 2 × 10-5 erg/cm2/sec     (13)

     Unfortunately the period of the radiation is 100 sec, which is not short enough to be observed with the existing apparatus of J. Weber. However, it is quite likely that a detector could be built which would be sensitive to the incident flux (13) at a period of 100 sec. This would then allow us to detect by its gravitational radiation any white-dwarf binary of period 100 sec within a volume of space containing over half a million stars.

     According to astrophysical theory, a white dwarf is not the most condensed type of star that is possible. A still more condensed form of matter could exist in “neutron stars," which would have masses of the same order as the sun compressed into radii of the order of 10 km. Whether neutron stars actually exist is uncertain; they would be very faint objects, and the fact that none has yet been observed does not argue strongly against their existence. (since this was written neutron stars have been observed)

     If a close binary system should ever be formed from a pair of neutron stars, the consequences would be very interesting indeed. Consider for example a pair oi stars of solar mass, each having radius

a = 106 cm     (14)

     and with their centers separated by a distance 2R = 4a. According to (1) and (11), each star moves with velocity

V = 4 × 109 cm/sec     (15)

     in an orbit with period 5 msec, and the output of gravitational radiation is

W = 2 × 1052 ergs/sec     (16)

But by (3), the gravitational energy of the pair is at this moment

E = 3 × 1052 crgs     (17)

     Thus the whole of the gravitational energy is radiated away in a violent pulse of radiation lasting less than 2 sec. A neutron-star binary beginning at a greater separation R will have a longer lifetime, but the final end will be the same. According to (ll), the loss of energy by gravitational radiation will bring the two stars closer with ever-increasing speed, until in the last second of their lives they plunge together and release a gravitational flash at a frequency of about 200 cycles and of unimaginable intensity.

     A pulse of gravitational radiation of magnitude (17) at a frequency around 200 cycles should be detectable with Weber's existing equipment at a distance of the order of 100 Mparsecs. So the death cry of a binary neutron star could be heard on earth, if it happened once in l0 million galaxies. It would seem worthwhile to maintain a watch for events of this kind, using Weber's equipment or some suitable modification of it.

     Clearly the immense loss of energy by gravitational radiation is an obstacle to the eflicient use of neutron stars as gravitational machines. It may be that this sets a natural limit of about 108 cm/sec to the velocities that can be handled conveniently in a gravitational technology. However, it would be surprising if a technologically advanced species could not find a way to design a nonradiating gravitational machine, and so to exploit the much higher velocities which neutron stars in principle make possible.

     In conclusion, it may be said that the dynamics of stellar systems, under conditions in which gravitational radiation is important, is a greatly neglected field of study. In any search for evidences of technologically advanced societies in the universe, an investigation of anomalously intense sources of gravitational radiation ought to be included.

From GRAVITATIONAL MACHINES by Freeman Dyson ()
DYSON SLINGSHOT

Let’s start the week by talking about gravitational assists, where a spacecraft uses a massive body to gain velocity. Voyager at Jupiter is the classic example, because it so richly illustrates the ability to alter course and accelerate without propellant. Michael Minovitch was working on this kind of maneuver at UCLA as far back as the early 1960s, but it was considered even before this, as in a 1925 paper from Friedrich Zander. It took Voyager to put gravity assists into the public consciousness because the idea enabled the exploration of the outer planets.

Can we use this kind of maneuver to help us gain the velocity we need to make an interstellar crossing? Let’s consider how it works: We’re borrowing energy from a massive object when we do a gravity assist. From the perspective of the Voyager team, their spacecraft got something for ‘free’ at Jupiter, in the sense that no additional propellant was needed. What’s really happening is that the spacecraft gained energy at the expense of the planet. Jupiter being what it is, the change in its own status was invisible, but it lent enough energy to Voyager to prove enabling.

According to David Kipping (Columbia University), the maximum speed increase equals twice the velocity of the planet we’re using for the maneuver, and when you look at Jupiter’s orbital speed around the Sun (around 13.1 kilometers per second), you can see that we’re only talking about a fraction of what it would take to get us to interstellar speeds. But the principle is enticing, because traveling with little or no propellant is a longstanding goal, one that drives research into solar sails and their fast cousins, beamed lightsails. And it has been much on Kipping’s mind.

For gravitational assists from planets are only one aspect of the question, there being other kinds of astrophysical objects that can help us out. Depending on their orbital configuration, some of these are moving fast indeed. In the early 1960s, Freeman Dyson went to work on the physics of gravitational assists around binary white dwarf stars — he would ultimately go on to consider the case of neutron star binaries (back when neutron stars were still purely theoretical). Such concepts obviously imply an interstellar civilization capable of reaching the objects in the first place. But once there, the energies to be exploited would be spectacular.

While I want to begin with Dyson’s ideas, I’ll move tomorrow to Kipping’s latest paper, which addresses the question in a novel way. Kipping, well known for his work in the Hunt for Exomoons with Kepler project, has been pondering Dyson’s notions but also applying them to what would seem, on the surface of things, to be an entirely different proposition: Beamed propulsion. How he combines the two may surprise you as much as it did me, as we’ll see in coming days.

Nature of the Question

If we talk about manipulating astrophysical objects, a natural objection arises: Why should we study things that are impossible for our species today? After all, we can get to Jupiter, but getting to the nearest white dwarf, much less a white dwarf binary, is beyond us.

But big ideas can be productive. Consider Daedalus, conceived in the 1970s as the first serious design for a starship. The idea was to demonstrate that a spacecraft could be designed using known physics that could make a journey to another star. The massive two-stage Daedalus (54,000 tonnes) seems impossible today and doubtless will never be built. Was it worth studying?

The answer is yes, because once you’ve established that something is not impossible, you can go to work on ways to engineer a result that may differ hugely from the original. Breakthrough Starshot is built around the idea of using lasers to propel a different kind of spacecraft, not of 54,000 tonnes but of 1 gram, carried by a small lightsail, and designed to be sent not as a one-off mission but as a series of probes driven by the same laser installation.

Once again we’re stretching our thinking, but here the technologies to do such a thing may (or may not, depending on what Breakthrough Starshot’s analyses come up with) be no more than a few decades away. The current Breakthrough effort is all about finding out what is feasible.

Again we’re designing something before we’re sure we can do it. The challenges are obviously immense. Consider: To go interstellar with cruise times of several decades, we need to ramp up velocity, and that takes enormous amounts of energy. Kipping calculates that 2 trillion joules — the output of a nuclear power plant running continuously for 20 days — would be needed to send the Breakthrough Starshot ‘chip’ payload to Proxima Centauri. And that’s just for one ‘shot’, not for the multiple chips envisioned in what might be considered a ‘swarm’ of probes.

Working with Massive Objects

Are there other ways to generate such energies? Freeman Dyson’s extraordinary white dwarf binary gravitational assist appears in “Gravitational Machines,” a short paper that ran in a book A.G.W. Cameron edited called Interstellar Communication (New York, 1963). Conventional gravity assists aren’t sufficient because to be effective, a gravitational ‘machine’ would have to be built on an astronomical scale. Fortunately, the universe has done that for us. So we should be thinking about the principles involved, and what they imply:

…if our species continues to expand its population and its technology at an exponential rate, there may come a time in the remote future when engineering on an astronomical scale will be both feasible and necessary. Second, if we are searching for signs of technologically advanced life already existing elsewhere in the universe, it is useful to consider what kinds of observable phenomena a really advanced technology might be capable of producing.

Dyson’s considers the question in terms of binary stars, specifically white dwarfs, but goes on to address even denser concentrations of matter in neutron stars. Now we’re talking about a kind of gravitational assist that has serious interstellar potential. A spacecraft could be sent into a neutron star binary system for a close pass around one of the stars, to be ejected from the system at high velocity. If 3,000 kilometers per second appears possible with a white dwarf binary, fully 81,000 kilometers per second could occur — 0.27 c — with a neutron star binary.

Hence the ‘Dyson slingshot.’ (As an aside, I’ve always wondered what it must be like to have a name so famous in your field that everything from ‘Dyson spheres’ to ‘Dyson dots’ are named after you. The range of Dyson’s thinking on these matters certainly justifies the practice!).

The slingshot isn’t particularly effective with stars of solar class, where what you gain from a gravitational assist is still outweighed by the possibility of using stellar photons for propulsion. But as Dyson shows, once you get into white dwarf range and then extend the idea down to neutron stars, you’re ramping up the gravitational energy available to the spacecraft while at the same time reducing stellar luminosity. An advanced civilization, in ways Dyson explores, might tighten the orbital distance until the binary’s orbital period reached a scant 100 seconds.

Now a gravity assist has serious punch. In other words, there is the potential here for a civilization to manipulate astrophysical objects to achieve a kind of galactic network, where binary neutron stars offer transportation hubs for propelling spacecraft to relativistic speeds. As you would imagine, this plays to Dyson’s longstanding interest in searching for technological artifacts, and we’ll be talking about that possibility as we get into David Kipping’s new paper.

For Kipping will take Dyson several steps further, by looking not at neutron stars but black hole binaries and coming up with an entirely novel way of exploiting their energies, one in which a beam of light, rather than the spacecraft itself, gets the gravitational assist and passes those energies back to the vehicle. Kipping calls his idea the ‘Halo Drive,’ and we’ll begin our discussion of it, and a novel insight that inspired it, tomorrow.

The Dyson paper is “Gravitational Machines,” in A.G.W. Cameron, ed., Interstellar Communication, New York: Benjamin Press, 1963, Chapter 12.

From PONDERING THE ‘DYSON SLINGSHOT’ by Paul Gilster (2019)
GRAVITY CATAPULT 1

      The important thing to remember about the unconventional space travel techniques is that they are based on known laws of physics extrapolated to the extreme. A gravity catapult—in other words, a machine that actually pushes a body with gravitation instead of just attracting it—is possible. As shown in Figure 8, there are three ways to do it. First, we could find a spinning black hole and travel around it very near the equator, which would give us a substantial increase in velocity.5 Of course, we’d have to be very careful about the tides. But there are tricks using dense masses in a space vehicle to cancel the tides which I’d be glad to tell anyone who wants to use the idea in a story (Forward went into detail about this in his novel Dragon's Egg).

     A more conventional gravity catapult technique which would also give us a change in velocity is to use a contact binary and come very close to the binary stars. Here, we are getting not only the Newtonian gravity whip that we use in our present space probes when we go by a moving planet, but, in addition, if these stars are moving relativistically and are very dense, we get extra forces due to the gravity nonlinearities.5

     Or we might use inside-out whirling dense mass smoke rings as a propulsion technique or gravity catapult.9


5 R. L. Forward, American Journal of Physics, Vol. 37, p. 166 (March 1963).

9 G. P. Field, Galaxy, Vol. 21, No. 2 p. 78 (December 1962).

From FAR OUT PHYSICS by Robert Forward (1975)
GRAVITY CATAPULT 2

      It wasn’t until 1930 that Pluto was found. The radius, eccentricity and period of the orbit were almost exactly as Lowell had predicted. Because the orbital calculations were so closely verified, there was no reason to doubt Lowell’s prediction that Pluto had a mass of six times the earth’s mass, except that the size of the planet was impossibly small. It was so small that it still looked like a point through the telescope. It wasn’t until 1950, using the 200-inch Palomar telescope, that Pluto’s diameter was measured. It was roughly 3600 miles, or about as big as Mercury. This would make the density of the planet hundreds of times greater than water! The earth is only 5.5 times denser than water and osmium, the densest known material, is only 22 times denser. Thus Pluto seems to be made of collapsed matter, except such matter should only be stable in the interior of dwarf stars. Such a planet should not exist.

     But it does!

(ed note: after this article was written this was found not to be the case. Astronomers assumed Pluto had a mass comparable to Terra to account for its effect on Neptune's orbit. As it turns out Pluto had no effect on Neptune's orbit, and its actual mass was 1/459th of Terra. So Pluto's mean density is actually less than Terra)

     One of the most spectacular possible solutions to the mystery is to assume that it really is a visitor from outside the solar system. Not just a wandering frozen planet that happened to be collected by the sun long ago in its wanderings through space, but a device, a “gravity catapult” made by intelligent beings and placed in orbit around the sun ... a “gravity catapult” being a generator of gravitational fields that is used to accelerate spaceships to velocities near the speed of light. It has only been recently realized that such a “gravity catapult” could exist. We can describe how it should be made, but we couldn’t even begin to construct it with our present technology.

     It has long been known that Einstein’s theory of gravity predicts many unusual properties of gravitation. These effects are not well known since they are unobservable with our presently available instruments. So there was little reason to talk about them. The most interesting effect is that a rotating mass, such as a planet, not only attracts an object toward it with its regular gravitational field, but it also “drags” the object around it in the same direction as its rotation. Thus a spaceship in orbit near the earth is helped along in its orbit by the earth’s rotation. In order to have any appreciable dragging effect on a space ship, a rotating planet has to be very heavy, and rotating rapidly; also the spaceship should be as close as possible to the planet’s center. This calls for planets with high density, since they have all their mass concentrated in a small radius and the spaceship can get close to the center without hitting the surface.

     Using these ideas of Einstein, we can envision how such a gravitational catapult could be made. It would require a large, very dense body with a mass larger than the earth, made of collapsed matter many times heavier than water. It would have to be whirling in space like a gigantic, fat smoke ring, constantly turning from inside out. The forces it would exert on a nearby object, such as a spaceship, would tend to drag the ship around to one side, where it would be pulled right through the center of the ring under terrific acceleration and expelled from the other side. If the acceleration were of the order of 1000 g’s, then after the minute or so that it would take to pass through, the velocity of the ship on the other side would be near that of light. The amazing thing is that because these are gravitational forces, a person in the space ship would feel nothing. He would actually be in free fall all the time! This is because gravitational forces act independently on each atom of the body at the same time and give each atom the same acceleration. Because there are no differences in motion of different parts of the body, there is no feeling of weight.

     A network of these devices in orbit around interesting stars would allow an advanced race to have an energetically economical method of space travel. Because, even though the ring would whirl a little slower after the spaceship had taken away some of its energy, it would gain that energy back when it decelerated an incoming ship. There, of course, would be no way to aim such a massive object, so to make sure that it can be used for more than one direction, it would be set to cartwheeling slowly (say with a 154 hour period?) so as to cover all parts of the sky.

     Such a device could even be made elsewhere by some unimaginable technology and shot through space by a much larger device. It could halt itself by pushing against a massive planet (such as Neptune?).

     Maybe when we get to Pluto, we will find a small artificial satellite around it. Inside will be a message from the Galactic Federation welcoming us to its membership now that we had interplanetary flight, and presenting us with the gravity catapult for our use until we know enough to make one ourselves — a sort of “coming out” present!

From PLUTO - DOORWAY TO THE STARS by G. P. Field (Robert Forward) (1982)
COMPENSATOR MASSES 1

(ed note: Dragon's Egg is a fast rotation neutron star a bare 2,300 AU from Terra. It was formed 500,000 years ago at a distance of 50 light-years from Sol. It managed the trip in such a short time due to its relatively large proper motion of 30 km/sec. As it passed nearby, it was visited by a human scientific expedition. They want to make observations at an insanely close orbit of 400 kilometers. Ultra-dense compensator masses were constructed to counteract the gravitational tides that would otherwise shred the ship and crew.)

Pierre Carnot Niven floated in front of the console on the science deck of the interstellar ark, St. George. The thin young man pulled thoughtfully at the corner of his carefully trimmed dark brown beard as he monitored the activities out in the asteroid belt surrounding the still-distant star, Dragon's Egg.

The expedition was still six months away from Dragon's Egg, but it was time to start the activities of the automated probes that had been sent ahead by St. George. There would be a lot of work to do in preparation for their close-up view of the star. Now that they had found and identified the asteroidal bodies around the neutron star that they would need, the work could be done as easily by robot brains as human ones.

The largest of the probes was really an automated factory, but its single output was very unusual—monopoles. It had some monopoles on board already, both positive and negative types. These were not for output, but the seed material needed to run the monopole factory. The factory probe headed for the first of the large nickel-iron planetoids that the strong magnetic fields of the neutron star had slowed and captured during its travels. It started preparing the site while the other probes proceeded with the job of building the power supply necessary to operate the monopole factory, for the power that would be needed was so great that there was no way the factory probe could have carried the fuel. In fact, the power levels needed would exceed the total power-plant capability of the human race on Earth, Colonies, Luna, Mars, asteroids, and scientific outposts combined.

Although the electrical power required was beyond the capability of those in the Solar System, this was only because they didn't have the right energy source. The Sun had been—and still was—very generous with its outpouring of energy; but so far the best available ways to convert that radiant energy into electricity, either with solar cells or by burning some fossilized sun energy and using it to rotate a magnetic field past some wires in a generator, were still limited.

Here at Dragon's Egg, there was no need for solar cells or heat engines, for the rapidly spinning, highly magnetized neutron star was at one time the energy source and the rotor of a dynamo. All that was needed were some wires to convert the energy of that rotating magnetic field into electrical current.

The job of the smaller probes was to lay cable. They started at the factory and laid a long thin cable in a big loop that passed completely around the star, but out at a safe distance, where it would be stable for the few months that the power would be needed. Since a billion kilometers of cable was needed to reach from the positions of the asteroidal material down around the star and back out again, it had to be very unusual cable—and it was. The cables being laid were bundles of superconducting polymer threads. Although it was hot near the neutron star, there was no need of refrigeration to maintain the superconductivity, for the polymers stayed superconducting almost to their melting point—900 degrees.

The cables became longer and longer and started to react to the magnetic field lines of the star, which were whipping by them ten times a second—five sweeps of a positive magnetic field emanating from the east pole of the neutron star, interspersed with five sweeps of the negative magnetic field from the west pole. Each time the field went by, the current would surge through the cable and build up as excess charge on the probes. Before they were through, the probes were pulsating with displays of blue and pink corona discharge—positive, then negative. The last connection of the cable to complete the circuit was tricky, since it had to be made at a time when the current pulsating back and forth through the wire was passing through zero. But for semi-intelligent probes with fractional-relativistic fusion-rocket drives, one-hundredth of a second is plenty of time.

With the power source hooked up to the factory, production started. Strong alternating magnetic fields whipped the seed monopoles back and forth at high energies through a chunk of dense matter. The collisions of the monopoles with the dense nuclei took place at such high energies that elementary particle pairs were formed in profusion, including magnetic monopole pairs. These were skimmed out of the debris emanating from the target and piped outside the factory by tailored electric and magnetic fields, where they were injected into the nearby asteroid. The monopoles entered the asteroid and in their passage through the atoms interacted with the nuclei, displacing the outer electrons. A monopole didn't orbit the nucleus like an electron. Instead, it whirled in a ring, making an electric field that held the charged nucleus, while the nucleus whirled in a linked ring to make a magnetic field that held onto the magnetically charged monopole.

With the loss of the outer electrons that determined their size, the atoms became smaller, and the rock they made up became denser. As more and more monopoles were poured in the center of the asteroid, the material there changed from normal matter, which is bloated with light electrons, into dense monopolium. The original atomic nuclei were still there; but, now with monopoles in linked orbits around them, the density increased to nearly that of a neutron star. As the total amount of converted matter in the asteroid increased, the gravitational field from the condensed matter became higher and soon began to assist in the process, crushing the electron orbits about the atoms into nuclear dimensions after they had only been partially converted into monopolium. After the month-long process was complete, the 250-kilometer-diameter asteroid had been converted into a 100-meter-diameter sphere with a core of monopolium, a mantle of degenerate matter of white dwarf density, and a glowing crust of partially collapsed normal matter.

After the first asteroid had been transformed, the factory turned to the next, which had been pushed into place by a herder probe that had started its task many months ago. The process was repeated again and again until finally there was a collection of eight dense asteroids circling the neutron star: two large ones and six smaller ones, dancing slowly around each other as they moved along in orbit. They were kept in a stable configuration with thrusts from the probes, which used the magnetic fields from a collection of monopoles in their noses to exert a push or pull from a distance on the hot, magnetically charged, ultra-dense masses.

The probes, herding their creations along, now waited patiently for St. George to arrive. As the humans approached the neutron star, the herder probes became more active. They pushed, pulled, and nudged the two larger asteroids until they approached one another. As the ultra-strong gravitational fields of the two asteroids interacted, they whirled about one another at blinding speed and then took off in opposite directions on highly elliptical orbits that would meet again many months later at a point much closer to the nearby neutron star.


"How much longer?" she asked the group gathered in front of consoles at the other end of the room.

Pierre glanced at the flickering numbers on the right of his screen. "Fourteen minutes, and everything looks fine."

Carole looked at a display across the room. The field of view of the monitor camera contained the glowing sphere of one of the larger condensed asteroids in the lower corner, and a small white speck representing the other large asteroid in the upper corner. As she watched, the smaller speck moved slowly across the screen, getting brighter as it came. Carole looked at another console, the picture there was almost the same, but reversed. The geometry of the elastic collision of the two large ultra-dense asteroids was almost exactly symmetric.

Pierre stared at his console. There were no pictures on his screen, just a computer-generated plot of two curved lines that were slowly approaching each other in a collision course. Numbers in boxes along the side of his screen changed rapidly. "Thirty seconds to last abort point," he announced. "Any problems?"

     Jean spoke from another console. "Video monitors operating."
     "Computer control well within margins," another voice said.
     "Herder probe propulsion units all operational," said another.
     "I'll let it go, then," Pierre said, lifting his finger from the abort toggle and snapped shut the safety cover.

Carole watched one of the screens as the smaller blob grew larger and larger. Angry tongues of fire burst rapidly in seemingly random directions from positions near the two spheres as the computer directed the herder probes to keep the asteroids on their correct paths. Then suddenly, in a sequence that was too fast to follow, an ultra-dense asteroid flashed around between its twin and the camera probe, and the screen was empty.

Pierre flicked on another camera that was off at a different angle, but that view was only good for a few seconds before the rapidly shrinking spot faded from the screen.

They all turned to Pierre's screen, which showed the orbits of the two asteroids. The trajectories had approached so close to each other that the tight curlicues in their respective paths due to their mutual gravitational attraction seemed to be placed one on top of the other. They now watched as one line headed outward toward the asteroid belt again, while the other seemed to be dropping straight into the neutron star. Actually, the falling massive asteroid would miss the star by a slight margin and was now in a highly elliptical orbit, with its aphelion near the 100,000 km circular orbit of St. George and its perihelion at just over 400 km from Dragon's Egg.

Their elevator was in place.


Commander Carole Swenson was floating above the console, watching over Pierre's shoulder as the outward-going asteroid met the first of the compensator masses still waiting far out in the asteroid belt. In the same manner as it had dropped the deorbiter mass toward the neutron star, the large asteroid overtook the first of the smaller masses and dropped it inward toward the star. It then went on to the next one. After watching the first two, Carole went back to the bridge. Nothing was more boring than the inevitability of the Newtonian law of gravitational attraction.

One after another, the six glowing compensator masses were dropped from their far-flung orbits to a spot near St. George, where they were met by the deorbiter mass, which stopped them in their tracks and left them dancing randomly about each other in a 100,000-kilometer circular orbit not too far from St. George. Their huge bulk dwarfed the long, thin mother ship, and the heat generated during their formation made them glow like new stars in the black sky.


Most of the crew of the interstellar ark were floating in front of the viewports on the bridge as St. George approached the site of the compressed asteroid collection. The rest were at various observation posts where the telescopes and scanners gave them a better view.

Pierre looked up from the screen and rotated to face the Commander of the expedition.

"I know it's safe, but I still don't like it, Carole," he said. "Those red-hot asteroids are not only too hot to touch, but they would crush us with their gravity tides if we ever got too close. And we are going to live within 200 meters of six of them for over a week!"

Carole smiled reassuringly and replied, "You know perfectly well that, if it were not for the toasty embrace of those friendly asteroids, the gravity tides of Dragon's Egg would crush you instead! Let's get them down there where they will do you some good."


When the deorbiter came up this time, there was going to be a spectacular show. Commander Swenson was again in the port science blister, watching the action on the console screens.

"Check position of compensator masses!" Pierre called out.

Six confirmations flashed instantly on his screen and were echoed by voices floating through the air from six nearby consoles, where each compensator mass was being monitored by a crew member.

Pierre looked up at Carole as he shrugged and lifted his finger from the abort toggle. "I really don't know why we insist on monitoring the computer on these close encounters. Things are going so fast I doubt we could do anything about it even if something did go wrong with the computer."

"Still," Carole said, "it lets us get in on the fun." She watched as a tiny speck in one corner of the screen slowly grew bigger and approached the six glowing spheres in the center of the screen. Then, in a complex wiggle and flash, the deorbiter mass pulled its disappearing act. The six glowing compensator masses were gone, and the screen was empty.


"The compensator masses are down," Carole said, turning to Pierre. "Now it is Dragon Slayer's turn."

It was twenty minutes to separation and the crew of Dragon Slayer gathered in the small lounge at the base of the ship.

The time for separation approached, and they all went up to the main deck where each would have a viewport. The breakaway was quiet and uneventful. The procedure consisted of opening the hatch doors of the huge mother ship, unlocking the attachment fittings, and slowly backing the larger ship away from the freely falling sphere. Pierre had been right—no one went to quarters as the small sphere floated away from the immense side of the interstellar ark.

     Cesar spoke. "It is always awe-inspiring to be outside, and up this close. The last time for me was when I came on board two years ago."
     "I've been out a dozen times on antenna maintenance," Amalita said. "But you're right—no matter how often you see it, it is still impressive."
     Pierre spoke into the communications console. "You look good, St. George. See you in a week."
     "Good hunting, Dragon Slayer," came Carole's throaty reply.

They drifted away from the ark. As it grew smaller and smaller in the distance, the crew members gathered around the port facing the retreating mother ship. Finally Pierre went to one of the consoles and rotated the sphere so that the port faced the neutron star that they would soon be orbiting at close quarters.

"The deorbiter will arrive in six hours," Pierre said to the crew. "Everyone into the high-gravity protection tanks." He closed the metal shields over the viewport windows, turned off the console, and started opening the hatches in the six spherical tanks clustered around the exact mass center of Dragon Slayer.

The crew went to suit lockers, where they stripped down to briefs and put on tight-fitting wet suits with a complex array of hydraulic tubing, pressure bladders, and a full underwater breathing apparatus. They then climbed, one by one, into the spherical tanks. Abdul was ready first and climbed into the tank with the hatch that opened downward into the lounge. Pierre helped him in, closed the lid, checked the breathing air once more, got a final nod from Abdul and then purged all the air out of the tank, filling it completely with nearly incompressible water. He then checked out all the ultrasonic driver circuits that would send powerful currents to the piezoelectric drivers that would produce rapidly varying pressure waves from different sides of the tank to counteract the differential gravity fields that the water alone did not take care of.

Once he had Abdul safely in the tank, he turned and visited the rest of the crew. Amalita had checked out her equipment and was climbing into her tank, while Seiko Kauffmann Takahashi, with her typical Germanic thoroughness, was still checking out her air system. Jean was already in her tank and Doc had carried out the final checkout with her. Pierre floated by Seiko, and double checked Jean's tank for good measure. He took no chances, for if Jean's tank failed during the deorbiting maneuver and any of the water leaked out, then the beautiful body of Jean Kelly Thomas would be literally torn to shreds by the powerful tidal forces from the deorbiter that would yank at head and feet with a pull of 10,000 gees, while simultaneously compressing her about her waistline with 5000 gees. "We would have to bottle her and pour her into the crematorium when we got back to St. George," he thought to himself. Pierre shook his head at the grisly thought and proceeded to climb into his own tank.

Pierre flashed a smile at all the screens. "I'll push the button for the down elevator," he said, touching a panel and flicking the screen controls to bring in a view of a large, rapidly spinning star in one corner and a glowing speck in another. The speck flashed occasionally as powerful rocket motors trimmed its course.

Through the long wait they could feel vibrations and slight accelerations that leaked through their water shields and pressure suits. These were vibrations from the ship's rockets, as the computer brought the spacecraft and the ultra-dense asteroid closer together.

"Down we go!" Pierre whispered into his throat mike, but he was only part way through the first phoneme when the asteroid passed by them. In a blink, they whirled half way around the massive sphere and found themselves falling down toward the neutron star, the ship's engines firing at full blast to remove the angular momentum that had been imparted by the gravity whip.

The drop down into the fierce gravity well of Dragon's Egg only took two and a quarter minutes. All was quiet for most of the fall, but in the last few seconds—as they began to approach the neutron star—Pierre could feel the differential pressures of the tidal forces on the water in the tank. Then in a last instantaneous burst of feeling, Pierre's head was jerked about by a fierce acceleration. His ears ached and his hands and legs were jerked about by the second and third order tidal effects, as the piezoelectric drivers sang their ultrasonic cloak of protection into the water that surrounded him.

His eyes failed to see the glow of the deorbiter mass as it flashed again across his screen, leaving Dragon Slayer motionless in the center of the six compensator masses that were whirling about the neutron star and the spacecraft five times a second. "What a ride!" a female voice said over the intercom, masked by the excitement and the breathing mask.

After exiting the tanks, the crew of Dragon Slayer gathered on the main console deck. The outside metallic micrometeorite shields had been pulled back from the six darkened viewing ports and they stared out. It was a dizzying sight, although they could feel no motion.

They were in a synchronous orbit 400 km out from the neutron star. To counteract the 41-million-gee gravitational pull from the nearby star, their spacecraft had to orbit about the star at five revolutions per second. Yet despite the rapid rotation they felt nothing because Dragon Slayer was stabilized to inertial space and did not try to keep a port facing the neutron star. It was good that it did not, for the centrifugal force in a spacecraft spinning around at five revolutions per second would have been enough to crush their bodies to a pulp against the outer bulkhead.

Since the spacecraft was orbiting but not spinning, this meant that the large, brilliant image of the neutron star flashed by each of the viewing ports five times a second, shining a flickering white glow on the walls of the central deck. Also visible through the ports was a ring of six, large, red ultra-dense asteroids only 200 meters away. They too whirled about the spacecraft five times a second, their glow alternating with the flashes from the distant neutron star.

Seiko took in the scene at one view port with a quick professional glance. She then shut her eyes and went limp in the air. Her arms and legs were stretched out in all directions.

"What's the matter!" Cesar exclaimed, looking over at her with concern.

Seiko slowly opened one eye. "Don't be concerned, Doctor Wong, I was merely checking the tidal compensation," she said, slightly annoyed at being interrupted. "At 406 kilometers from the neutron star, the tidal gravity gradient should be 101 gees per meter. Even though my middle is in free-fall, my arms, legs and head try to go in different orbits. My feet are one meter closer to the star and should feel a pull of 202 gees. My head is one meter further than my middle and should also feel a pull of 202 gees, while my arms should feel a push of 101 gees.

"The six compensator masses also make tidal forces of the same magnitude, only they make tides of the opposite sign. I was just trying to see how accurately the two tides were compensating by using my hands and feet as crude accelerometers. I am surprised at how small the residual tide is. Only very near the hull can I sense any forces on my arms as the ship rotates." She closed her eyes again and continued to feel the play of the minute gravitational tugs coming twenty times a second on her hands and feet as the compensator masses and the neutron star whirled about the ship five times a second, rotating their four-lobed gravity pattern about the nonspinning ship.


ST. GEORGE

The spaceship that took the humans to Dragon's Egg was a primitive monopole-catalyst fusion rocket. Its basic structure was a cylinder 500 meters long and 20 meters in diameter, with large spherical external tanks of liquid deuterium fuel. The mass ratio was about 10. St. George accelerated at 0.035 gees, and reached a speed of 0.035 the speed of light at its turnover point. The total trip time out to the neutron star was 1.94 years.

The scientific spacecraft used for the close approach to the neutron star was a seven-meter sphere with a spinning tower 1.6 m in diameter and 2.5 m tall, containing the microwave sounder, infrared telescope, laser radar, star image telescope mirror, and other star-oriented instruments. When in synchronous orbit about the star, the science instrument tower on the top of the ship was aligned in the direction of the north spin pole of the neutron star. The bottom end of the science sphere had a viewing point that looked southward toward the distant Solar System.

Around the equator of the ship were six viewing ports that looked out at the neutron star whirling about the ship. The ship was inertially stabilized, so that the distant stars stayed fixed in the viewing ports. The ship, being in orbit around the neutron star with a period of 0.1993 seconds (5.018 rps), rotated with respect to the neutron star at 5 times a second. The science turret was de-spun at the orbital rate so that the instruments pointed to the star at all times. (The entire space ship could not be rotated at those speeds; had it been, the crew would have been thrown against the outer wall with a force of 350 gees).

Figures 9 through 12 are diagrams of the three decks and a side view of the scientific spacecraft, Dragon Slayer. The steady component of the residual gravitational tidal fields around and inside the ship are shown by arrows. In addition to the steady component, there is an alternating acceleration component of about the same magnitude as the steady component, which varies twenty times a second as the four-lobed gravity pattern of the neutron star and tidal compensator masses rotates about the ship five times a second.

DEORBITER AND COMPENSATOR MASSES

The human explorers of Dragon's Egg used gravitational techniques to move into and survive in a synchronous orbit around the neutron star. The prime mover for all of the gravitational maneuvers near Dragon's Egg was the large deorbiter mass. Originally a small planetoid about 1000 kilometers across, it had been picked up (along with other asteroidal debris) by the neutron star in its wanderings. The planetoid was condensed by the humans into an ultra-dense mass one kilometer in diameter by injection, of magnetic monopoles.

There were actually two large condensed asteroids made at the same time. One was used in a close-encounter gravity whip to drop the deorbiter down from its original orbit out in the "asteroid belt" of the neutron star into the desired orbit. This orbit was a highly elliptical one with a perihelion at 406 km and aphelion at 100,000 km, where the human interstellar ship, St. George, moved in a 12.82-minute circular orbit.

The elliptical orbit of the deorbiter mass (called Bright's Messenger by precontact cheela) had a period of 4.56 minutes or 9.53 greats of turns of the neutron star. It thus took it only 2.28 minutes or 4.77 greats of turns to drop from the safe circular orbit of St. George to the dangerous synchronous orbit at 406 km above Dragon's Egg.

The gravity field of the neutron star is 40 million gees at the 406 kilometer altitude of Dragon Slayer. However, since the spacecraft was in orbit around the star, most of that 40 million gees was canceled by the fact that it was in a "free-fall" orbit. However, an object is only in free fall at its exact center of mass. When the middle of your body is in a free-fall orbit around a neutron star at 406,332 m distance it will feel nothing. But if you are oriented with your feet toward the star, your feet, which are at 406,331 m away from the star, are pulled by a gravity force that is 202 gees more than your middle, while your head, at 406,333 m distance, is being pulled by a force that is 202 gees less than your middle. If you body is oriented in a direction tangent to the neutron star, your head and feet will feel a 101-gee compression instead of a 202-gee pull. A human cannot survive at a distance of 400 km from a neutron star without some kind of protection from these tidal forces.

To protect the humans in Dragon Slayer from these residual gravity tidal forces, six tidal compensator masses were placed in a 200-meter radius ring about the science capsule and arranged so that the plane of the six masses was always at right angles to the direction to the neutron star. The compensator masses were made from asteroids about 250 km in diameter that were condensed to 100 m in diameter.

In the center of that ring of ultra-dense spheres, the masses are attempting to pull anything at the center out toward them. At the exact center of the ring all the forces cancel. However, if your head or feet are in the plane of the ring, since they are about one meter away from the exact center of the ring, they will be pulled with a force of 101 gees. If you try to orient your body to point along the axis of the ring, your head and feet will be compressed with a force of 202 gees. If made dense enough and placed at the right distances, the six compensator masses will cancel the neutron star tidal forces over a seven-meter diameter spherical region. (See Figure 9 which shows the residual tidal forces around Dragon Slayer).

In operation, the six compensators rotate about Dragon Slayer as it orbits the star at 5.018 rps. The individual orbits of the compensator masses are almost in a natural gravitational orbit, but require that the masses change speed slightly each half orbit to maintain the circular formation. This is accomplished by magnetic interactions between the magnetically charged compensators, assisted by trimming maneuvers carried out by robotic herder probes using monopole-catalyzed fusion rockets.

From DRAGON'S EGG by Robert Forward (1980)
COMPENSATOR MASSES 2

      Many of the experiments presently carried out on Space Shuttle flights, especially those where the Spacelab is flown as cargo, are called "zero-gravity" materials processing experiments. Some involve forming "perfect" spheres of metal or latex by squeezing out drops of liquid into free-fall. The surface tension forces form the drops into spheres and then the drops solidify into balls. Others involve mixing two metals with greatly differing density, such as lithium and lead (to make a bearing alloy). If you attempted to cast such an alloy on Earth, the bottom of the crucible would contain mostly lead and the top would contain mostly lithium. Another space manufacturing process, called electrophoresis, uses the flow of strong electrical currents through a liquid to collect dilute quantities of precious biological chemicals from blood samples or a watery mass of bacteria and their excretions. The purity of the end product depends strongly on the dominance of the electrochemical currents over the convention currents in the liquid caused by the heated water "rising" in any residual gravity forces.

     At the present time, these "zero-gravity" space manufacturing experiments are done using only the "Ug" form of antigravity. The Space Shuttle "jumps" into space and goes into a free-fall orbit around the Earth. This effectively cancels most of the gravity field of the Earth, but not all of it. The only part of the Space Shuttle that is under absolutely zero net gravity force is the center of mass of the spacecraft. The rest of the Space Shuttle, especially the nose, tail, and wingtips, is experiencing gravity forces due to the tides of the Earth. These residual gravity forces are not large, a few microgravities, and do not cause any large effects in the present crude space manufacturing experiments. But as the manufacturing apparatus goes from the experimental stage on the Space Shuttle to the "making money" manufacturing phase on the Space Station, the apparatus will become larger, the residual gravity tidal forces will become larger, and the tidal forces will begin to affect the quality of the manufactured product.

     I have invented a way to reduce these gravity effects by another factor of a million, so that the residual forces are less than a picogravity (a trillionth of Earth gravity). I do this by using various arrangements of massive dense spheres, disks, and rings to nullify the residual gravity effects inside the processing apparatus. (Those interested in the details can read my technical paper in "Recommended Reading" at the end of the chapter.) (Robert L. Forward, "Flattening Spacetime Near the Earth," Physical Review, Vol. D26, pp. 735-744 (15 August 1982).)

     Suppose you were floating around in the bay of the Space Shuttle. The Shuttle has all of its control thrusters off and is floating in free-fall, its nose pointing to the ground below. If you were floating at the point in the middle of the bay that is the center of mass of the Shuttle, you would stay at that point, since both you and the Shuttle are in exactly the same orbit. If, however, you were up in the nose of the Shuttle, fifteen meters away from the center of mass, you would find that after two minutes of time that you would have drifted some thirty centimeters away from the center of mass of the Shuttle, closer to the nose. Your motion was caused by a residual tidal force of 4.5 microgravities. In two minutes under this intense gravity force you will have reached the tremendous velocity of five millimeters per second and are about to be smashed against the forward bulkhead, where you will be crushed by the intense 4.5 microgravity acceleration. Although you are perfectly capable of surviving this experience, a space manufacturing facility located in the nose of the Space Shuttle would be significantly affected by these residual gravity tidal forces. The "perfect" ball bearings would be elliptical, the "uniform" alloy would have density gradations, and the "pure" biological extract would be contaminated with impurities.

     There are two ways to look at how these residual tidal forces occur. One picture uses the concept of orbital motion and the other uses the concept of gravity gradients. The two ways are equivalent as long as the region we are interested in (the inside of a Space Shuttle or a manufacturing facility on the Space Station) is much smaller than the distance to the center of the Earth.

     In the orbital picture, the center of mass of the Space Shuttle is in orbit around the Earth, moving at a certain speed appropriate for that orbit. You are in the nose of the Space Shuttle, fifteen meters closer to the Earth. However, at the start of the experiment you have arranged your velocity so that you are not moving with respect to the walls of the Shuttle. You are now moving with the velocity of the Space Shuttle, but you are in a lower orbit which requires a higher velocity than the Space Shuttle velocity if it is to be a circular orbit. Since your velocity is too low for your altitude, you are not in a circular orbit, but at the peak of an elliptical orbit. As you and the Space Shuttle continue in orbit, the Space Shuttle remains at the same distance above the Earth, while you drop away in your elliptical orbit and soon smash against the front bulkhead. The same picture applies if you start out near the tail of the Space Shuttle, only now in your higher orbit you are going too fast for your altitude and rise up away from the Shuttle orbit.

     Now suppose the Space Shuttle were in a perfect equatorial orbit, always following the equator of the Earth, with its wings pointing north and south. If you started your space-float at the end of the north wingtip, you would be at the same altitude as the Space Shuttle, moving at the same speed as the Space Shuttle, but your orbit started out a wingtip's length north of the equator. Your orbit has to cross the equator after a quarter of an orbit, go south until it reaches a wingtip's length after a half orbit, cross back over the equator again and then return to the north after a full revolution. Since your orbit has to cross over the equatorial orbit of the Space Shuttle, you will find that you will float from the wingtip "toward" the center of mass of the Space Shuttle.

     A similar effect occurs if the wings of the Space Shuttle are oriented along the equator. Now, however, the line from the wingtips through the center of mass is a straight line, while the Shuttle orbit is curved. If you start out on a wingtip, you are in a higher orbit than the Space Shuttle and going too fast. As you rise in your elliptical orbit, you slow down and the Space Shuttle overtakes you, bringing you closer to its center of mass.

     Thus, from the orbital picture, objects inside the Space Shuttle that are not right at the center of mass of the Shuttle move in their own orbits. From the viewpoint of those in the Shuttle, those objects that are above or below the Space Shuttle center of mass move outward, while those objects in a plane tangent to the Earth move inward.

     There is an alternate way of looking at the same effect that uses the concept of gravity gradients, or the change of the gravity field of the Earth with distance. Imagine that the Space Shuttle is not in orbit. Instead it is just dropping nose first toward the Earth. If you were floating in the nose of the Space Shuttle, dropping along with it, you would be closer to the center of the Earth than the center of mass of the Shuttle. Since the Newton Theory of Gravity says that the gravity field of the Earth gets weaker with distance, then the gravity field on you is stronger than the gravity field on the Space Shuttle and you fall faster than the center of mass of the Space Shuttle, pulling you toward the nose. If you were at the back of the Shuttle bay, you would be in a weaker gravity field, while the Shuttle is in a stronger field and is pulled away from you. Thus, because the gravity field of the Earth changes with vertical distance above the Earth, objects at different altitudes fall at different rates. The farther apart the objects are from each other, the greater the difference in their rates of fall.

     This gravity gradient or differential acceleration effect is better known to you as the tidal force. The tides in the oceans of the Earth are caused mostly by the gravity gradient forces of the Moon. The Moon pulls on the oceans of the Earth that are underneath it, and pulls them up away from the center of mass of the Earth, causing the below-Moon tidal bulge. At the same time, the Moon is pulling the Earth away from the ocean water on the far side, causing the opposite-Moon tidal bulge. That is why the tides come about every twelve hours instead of every twenty-four hours.

     There is also a horizontal gravity gradient. The reason for the horizontal accelerations is a little harder to understand, but the horizontal gradients are always just as important as the vertical gradient. For a spherical attracting mass like the Earth, the horizontal gradients are half the strength of the vertical gradients, but there are two of them. Going back (briefly) to our still-falling Space Shuttle, suppose you were out near one wingtip, falling along with the Shuttle. Both you and the Space Shuttle are falling directly toward the center of the Earth. But since the two trajectories ultimately meet at the center of the Earth, as you fall along your trajectory, your trajectory gets closer to the Space Shuttle trajectory and you observe an inward motion.

     If we move our point of view to the center of the mass of the Space Shuttle, we see that the gravity tide pattern from the Earth consists of a tension in the vertical direction that is twice as strong as the uniform compression in the horizontal direction. [See Figure 8a.]

 

     To eliminate these residual gravity fields we can use my gravity gradient compensator consisting of six dense masses in a ring around the region to be protected. (A solid ring or any number of masses greater than three can be used instead, but six seems to be optimum.) The plane of the ring of masses is arranged to always be tangent to the surface of the Earth below. The tidal gravity pattern from the six compensator spheres in a ring is almost exactly the same as the tidal gravity pattern from the Earth, except the accelerations are reversed in direction.

     This pattern of forces is easily understood if you imagine a small test object in the middle of the ring. If the test object is exactly in the center, the combined gravitational attraction of the six spheres cancels out. If the test object moves above or below the plane, the combined attractions of the spheres will pull it back. If the test object moves toward one of the spheres, the attraction of that sphere increases while the attraction of the sphere on the opposite side of the ring decreases, and the test object is pulled even farther away from the center. By merely adjusting the radius and tilt of the ring of compensator spheres we can "fine tune" the gravity tidal pattern of the compensator to match the tidal pattern of the Earth at any altitude. Since we are not trying to compensate the whole gravity field of the Earth, but only the much weaker tidal forces, we will not need ultradense matter for the compensator spheres, but only normal density materials like lead or tungsten.


 

     If we assume that the six spheres in the compensator are each a 100 kilogram ball of tungsten, then the spheres will be twenty-two centimeters (nine inches) in diameter. The match of the compensating fields to the Earth fields is only perfect at the exact center of the ring. The match is fairly good, however, in a significant region about the central point. Calculations show that if the compensator ring were properly adjusted, the residual gravity forces inside a disk-shaped region about the size of a box of bath powder at the center of the compensator ring would be reduced by a factor of one hundred. At geostationary orbit altitude, the tidal fields to be compensated become smaller and the size of the compensated region becomes larger. The compensator ring can now lower the residual accelerations to less than a picogravity (a trillionth of an Earth gravity) over a disk-shaped volume the size of a large hatbox.

     These large volumes of force-free space will certainly be valuable for scientific experiments that require a region free from Earth tides. They also will be useful, up to a point, for space manufacturing. The lower acceleration limit for space processing is set by the self-gravity of the molten metals or liquids being processed. A ball of water and bacteria one meter across will have a self-gravity field at its surface of thirty nanogravities, while a molten ball of steel ten centimeters across has a self-gravity field of twenty nanogravities (greater than the accelerations due to the Earth tides). These self-gravity forces will cause convection currents to flow in the liquid, disturbing the desired equilibrium conditions.

     It turns out, however, that with a little bit of Newtonian antigravity magic, we can not only cancel any Earth tides that might affect those materials processing experiments, but we can also cancel the self-gravity field everywhere inside the sample! The shape for a space materials processing experiment sample that gives the most volume with the lowest residual gravity is a thick disk. For a specific example, let us assume a disk of material with the density of water that is thirty centimeters in diameter and ten centimeters thick (about the size of a large double-layer cake). The self-gravity field pattern of this thick disk is quite complicated. It is zero at the center and becomes stronger as you go toward the surface, reaching about three nanogravities at the top and bottom and around the rim.

     We first can smooth out the variations in the acceleration due to the "edge effects" by surrounding the sample volume with a "guard ring" consisting of a container in the shape of a ring filled with material that has the same density as the material in the sample chamber. The material in the sample volume and the guard ring need to be kept separated by a thin wall. The material in the guard ring will not be free from accelerations, and convection currents will be set up in it. The thin wall will keep the protected material in the sample volume from being disturbed by these currents.

     We then add "guard caps" to the top and bottom of the sample volume plus guard ring. With the guard ring and guard caps in place, we find that the original complicated self-gravity force pattern inside the sample has become very regular and increases linearly with distance from the center. How can we cancel these self-gravity accelerations? Let us take them one at a time.

     To compensate for the inward vertical component of the self-gravity of the disk we will use the outward vertical acceleration of the Earth tides. If the Earth tide at the altitude of our manufacturing facility is too strong for the self-gravity of the disk, we cancel a portion of it with our six-sphere tidal compensator. If the Earth tide at that altitude is too weak, we augment the Earth tidal forces using my two-sphere tidal augmentor.

     A tidal augmentor consists of two 100 kilogram spheres placed above and below the sample disk. The gravity tidal pattern the augmentor produces at the point between the two spheres is identical to the tidal pattern of the Earth. [See Figure 9.] Thus, by judicious use of either the compensator or augmentor, depending upon the orbital altitude and the density of the sample of material undergoing processing, we can adjust the Earth tides so they will compensate for the vertical component of the self-gravity of a properly guarded sample disk.

     The horizontal component of acceleration is another matter. The horizontal self-gravity accelerations of the disk are inward directed, as are the accelerations induced by the Earth tides. After we have used the Earth tides to null out the vertical self-gravity, we will find that the horizontal accelerations have been doubled. The combined self-gravity and Earth tide accelerations can now be canceled by a last bit of Newtonian magic. Instead of using the Newton Theory of Gravity, however, we will use the Newton Theory of Mechanics. We can cancel the horizontal accelerations by a slow rotation of the sample disk about its vertical axis.

     The rotation of a disk causes an outward centrifugal acceleration that has no component along the vertical spin axis, just a horizontal acceleration that everywhere increases linearly with distance from the axis. A carefully chosen rotation of about one revolution every few hours will now cancel both the inward acceleration of the self-gravity of the sample and the inward acceleration of the Earth tides.

     Thus, by a combination of guard rings and guard caps to make the self-gravity more uniform, the use of the Earth tides augmented or compensated by 100-kilogram masses, and a slight rotation of the sample volume, it is possible to cancel all the gravity inside a sample volume of material some thirty centimeters in diameter and ten centimeters thick (the size of a birthday cake). The technique can be used at any orbital altitude, but the best results can be obtained in a space manufacturing facility in geostationary orbit. In one example that I calculated, our birthday-cake sized sample disk of water had the gravity fields inside decreased by a factor of a thousand, so that the maximum gravity acceleration anywhere inside the disk was less than a picogravity or a trillionth of an Earth gravity. At this level of acceleration it would take an atom eight seconds to fall its own diameter!

     One of these days there will be large space laboratories in orbit, with special isolated rooms where ultra-low gravity experiments can be carried out. There will be no humans near those rooms, for the gravity of even the most petite experimenter would be enough to disturb the delicate experiments floating inside. From some of the laboratories will come exotic alloys, from others ultra-light, ultra-strong foamed metals. From still other laboratories the valuables extracted will not be tangible products like pharmaceuticals and new materials, but that intangible yet infinitely more valuable product of scientific research—knowledge. Perhaps new knowledge about the innermost secrets of gravity.

From INDISTINGUISHABLE FROM MAGIC by Robert Forward (1995)
NEUTRON STAR TIDE

      The ship lay on the sand beyond the roof. It was a No. 2 General Products hull: a cylinder three hundred feet long and twenty feet through, pointed at both ends and with a, slight wasp-waist constriction near the tail. For some reason it was lying on its side, with the landing shocks still folded in at the tail.
     Ever notice how all ships have begun to look the same? A good ninety-five percent of today’s spacecraft are built around one of the four General Products hulls. It’s easier and safer to build that way, but somehow all ships end as they began: mass-produced look-alikes.
     The hulls are delivered fully transparent, and you use paint where you feel like it. Most of this particular hull had been left transparent. Only the nose had been painted, around the lifesystem. There was no major reaction drive. A series of retractable attitude jets had been mounted in the sides, and the hull was pierced with smaller holes, square and round, for observational instruments. I could see them gleaming through the hull.
     The puppeteer was moving toward the nose, but something made me turn toward the stern for a closer look at the landing shocks. They were bent. Behind the curved transparent hull panels some tremendous pressure had forced the metal to flow like warm wax, back and into the pointed stern.
     “What did this?” I asked.
     “We do not know. We wish strenuously to find out.”
     “What do you mean?”
     “Have you heard of the neutron star BVS-l?”
     I had to think a moment. “First neutron star ever found, and so far the only. Someone located it two years ago, by stellar displacement.”
     “BVS-l was found by the Institute of Knowledge on Jinx. We learned through a go-between that the Institute wished to explore the star. They needed a ship to do it.
     They had not yet sufficient money. We offered to supply them with a ship’s hull, with the usual guarantees, if they would turn over to us all data they acquired through using our ship.”
     “Sounds fair enough.” I didn’t ask why they hadn’t done their own exploring. Like most sentient vegetarians, puppeteers find discretion to be the only part of valor.
     “Two humans named Peter Laskin and Sonya Laskin wished to use the ship. They intended to come within one mile of the surface in a hyperbolic orbit. At some point during their trip an unknown force apparently reached through the hull to do this to the landing shocks. The unknown force also seems to have killed the pilots.”
     “But that’s impossible. Isn’t it?”
     “You see the point. Come with me.” The puppeteer trotted toward the bow.

     I saw the point, all right. Nothing, but nothing, can get through a General Products hull. No kind of electromagnetic energy except visible light. No kind of matter, from the smallest subatomic particle to the fastest meteor. That’s what the company’s advertisements claim, and the guarantee backs them up. I’ve never doubted it, and I’ve never heard of a General Products hull being damaged by a weapon or by anything else.
     We rode an escalladder into the nose.
     The lifesystem was in two compartments. Here the Laskins had used heat-reflective paint. In the conical control cabin the hull had been divided into windows. The relaxation room behind it was a windowless reflective silver. From the back wall of the relaxation room an access tube ran aft, opening on various instruments and the hyperdrive motors.
     There were two acceleration couches in the control cabin. Both had been torn loose from their mountings and wadded into the nose like so much tissue paper, crushing the instrument paneL The backs of the crumpled couches were splashed with rust brown. Flecks of the same color were all over everything, the walls, the windows, the viewscreens. It was as if something had hit the couches from behind: something like a dozen paint-filled toy balloons striking with tremendous force.
     “That’s blood,” I said.
     “That is correct. Human circulatory fluid.”

(ed note: the protagonist has been forced by the president of General Products to fly the exact same mission that killed the Laskins in an attempt to figure out what can get through a General Products hull)

     Two hours’ to go—and I was sure they were turning blue. Was my speed that high? Then the stars behind should be red. Machinery blocked the view behind me, so I used the gyros. The ship turned with peculiar sluggishness. And the stars behind were blue, not red. All around me were blue-white stars.
     Imagine light falling into a savagely steep gravitational well. It won’t accelerate. Light can’t move faster than light. But it can gain in energy, in frequency. The light was falling on me, harder and harder as I dropped.
     I told the dictaphone about it. That dictaphone was probably the best-protected item on the ship. I had already decided to earn my money by using it, just as if I expected to collect. Privately I wondered just how intense the light would get.
     Skydiver had drifted back to vertical, with its axis through the neutron star, but now it faced outward. I’d thought I had the ship stopped horizontally. More clumsiness. I used the gyros. Again the ship moved mushily, until it was halfway through the swing. Then it seemed to fall automatically into place. It was as if the Skydiver preferred to have its axis through the neutron star.

     I didn’t like that.

     I tried the maneuver again, and again the Skydiver’ fought back. But this time there was something else. Something was pulling at me.
     So I unfastened my safety net—and fell headfirst into the nose.
     The pull was light, about a tenth of a gee. It felt more like sinking through honey than falling. I climbed back into my chair, tied myself in with Lhe net, now hanging face down, and turned on the dictaphone. I told my story in such nitpicking detail that my hypothetical listeners could not but doubt my hypothetical sanity. “I think this is what happened to the Laskins,” I finished. “If the pull increases, I’ll call back.”
     Think? I never doubted it. This strange, gentle pull was inexplicable. Something inexplicable had killed Peter and Sonya Laskin. Q.E.D.
     Around the point where the neutron star must be, the stars were like smeared dots of oil paint, smeared radially. They glared with an angry, painful light. I hung face down in the net and tried to think.

     It was an hour before I was sure. The pull was increasing. And I still had an hour to fall.
     Something was pulling on me, but not on the ship.
     No, that was nonsense. What could reach out to me through a General Products hull? It must be the other way around. Something was pushing on the ship, pushing it off course.
     If it got worse, I could use the drive to compensate. Meanwhile, the ship was being pushed away from BVS-l, which was fine by me.
     But if I was wrong, if the ship was not somehow being pushed away from BVS-l, the rocket motor would send the Skydiver crashing into eleven miles of neutronium.
     And why wasn’t the rocket already firing? If the ship was being pushed off course, the autopilot should be fighting back. The accelerometer was in good order. It had looked fine when I made my inspection tour down the access tube.
     Could something be pushing on the ship and on the accelerometer, but not on me? It came down to the same impossibility: something that could reach through a General Products hull.

     To hell with theory, said I to myself, said I. I’m getting out of here. To the dictaphone I said, “The pull has increased dangerously. I’m going to try to alter my orbit.”
     Of course, once I turned the ship outward and used the rocket, I’d be adding my own acceleration to the X-force. It would be a strain, but I could stand it for a while. If I came within a mile of BVS-l, I’d end like Sonya Laskin. She must have waited face down in a net like mine, waited without a drive unit, waited while the pressure rose and the net cut into her’ flesh, waited until the net snapped and dropped her into the nose, to lie crushed and broken until the X-force tore the very chairs loose and dropped them on her.
     I hit the gyros.
     The gyros weren’t strong enough to turn me. I tried it three times. Each time the ship rotated about fifty degrees and hung there, motionless, while the whine of the gyros went up and up. Released, the ship immediately swung back to position. I was nose down to the neutron star, and I was going to stay that way.

     Half an hour to fall, and the X-force was over a gee. My sinuses were in agony. My eyes were ripe and ready to fall out. I don’t know if I could have stood a cigarette, but I didn’t get the chance. My pack of Fortunados had fallen out of my pocket when I dropped into the nose. There it was, four feet beyond my fingers, proof that the X-force acted on other objects besides me. Fascinating.
     I couldn’t take any more. If it dropped me shrieking into the neutron star, I had to use the drive. And I did. I ran the thrust up until I was approximately in free fall. The blood which had pooled in my extremities went back where it belonged. The gee dial registered one point two gee. I cursed it for a lying robot.
     The soft-pack was bobbing around in the nose, and it occurred to me that a little extra nudge on the throttle would bring it to me. I tried it. The pack drifted toward me, and I reached, and like a sentient thing it speeded up to avoid my clutching hand. I snatched at it again as it went past my ear, and again it was moving too fast. That pack was going at a hell of a clip, considering that here I was practically in free fall. It dropped through the door to the relaxation room, still picking up speed, blurred and vanished as it entered the access tube. Seconds later I heard a solid thump.
     But that was crazy. Already the X-force was pulling blood into my face. I pulled my lighter out, held it at arm’s length and let go. It fell gently into the nose. But the pack of Fortunados had hit like I’d dropped it from a building.

     Well.

     I nudged the throttle again. The mutter of fusing hydrogen reminded me that if I tried to keep this up all the way, I might well put the General Products hull to its toughest test yet: smashing it into a neutron star at half light speed. I could see it now: a transparent hull containing only a few cubic inches of dwarf-star matter wedged into the tip of the nose.
     At one point four gee, according to that lying gee dial, the lighter came loose and drifted toward me. I let it go. It was clearly falling when it reached the doorway. I pulled the throttle back. The loss of power jerked me violently forward, but I kept my face turned. The lighter slowed and hesitated at the entrance to the access tube. Decided to go through. I cocked my ears for the sound, then jumped as the whole ship rang like a gong.
     And the accelerometer was right at the ship’s center of mass. Otherwise the ship’s mass would have thrown the needle off. The puppeteers were fiends for ten-decimal-point accuracy.

     I favored the dictaphone with a few fast comments, then got to work reprogramming the autopilot. Luckily what I wanted was simple. The X-force was but an X-force to me, but now I knew how it behaved. I might actually live through this.
     The stars were fiercely blue, warped to streaked lines near that special point. I thought I could see it now, very small and dim and red, but it might have been imagination. In twenty minutes I’d be rounding the neutron star. The drive grumbled behind me. In effective free fall, I unfastened the safety net and pushed myself out of the chair.
     A gentle push aft—and ghostly hands grasped my legs. Ten pounds of weight hung by my fingers from the back of the chair. The pressure should drop fast. I’d programmed the autopilot to reduce the thrust from two gees to zero during the next two minutes. All I had to do was be at the center of mass, in the access tube, when the thrust went to zero.
     I knew what the X-force was trying to do. It was trying to pull the ship apart.

     There was no pull on my fingers. I pushed aft and landed on the back wall, on bent legs. I knelt over the door, looking aft/down. When free fall came, I pulled myself through and was in the relaxation room looking down, forward into the nose.
     Gravity was changing faster than I liked. The X-force was growing as zero hour approached, while the compensating rocket thrust dropped. The X-force tended to pull the ship apart; it was two gee forward at the nose, two gee backward at the tail, and diminished to zero at the center of mass. Or so I hoped. The pack and lighter had behaved as if the force pulling them had increased for every inch they moved sternward.
     The back wall was fifteen feet away. I had to jump it with gravity changing in midair. I hit on my hands, bounced away. I’d jumped too late. The region of free fall was moving through the ship like a wave as the thrust dropped. It had left me behind. Now the back wall was “up” to me, and so was the access tube.
     Under something less than half a gee, I jumped for the access tube. For one long moment I stared into the three-foot tunnel, stopped in midair and already beginning to fall back, as I realized that there was nothing to hang on to. Then I stuck my hands in the tube and spread them against the sides. It was all I needed. I levered myself up and started to crawl.
     The dictaphone was fifty feet below, utterly unreachable. If I had anything more to say to General Products, I’d have to say it in person. Maybe I’d get the chance. Because I knew what force was trying to tear the ship apart.
     It was the tide.

     The motor was off, and I was at the ship’s midpoint. My spread-eagled position was getting uncomfortable. It was four minutes to perihelion.
     Something creaked in the cabin below me. I couldn’t see what it was, but I could clearly see a red point glaring among blue radial lines, like a lantern at the bottom of a well. To the sides, between the fusion tube and the tanks and other equipment, the blue stars glared at me with a light that was almost violet. I was afraid to look too long. I actually thought they might blind me.
     There must have been hundreds of gravities in the cabin. I could even feel the pressure change. The air was thin at this height, one hundred and fifty feet above the control room.
     And now, almost suddenly, the red dot was more than a dot. My time was up. A red disk leapt up at me; the ship swung around me; I gasped and shut my eyes tight.
     Giants’ hands gripped my arms and legs and head, gently but with great firmness, and tried to pull me in two. In that moment it came to me that Peter Laskin had died like this. He’d made the same guesses I had, and he’d tried to hide in the access tube. But he’d slipped… as I was slipping… From the control room came a multiple shriek of tearing metal. I tried to dig my feet into the hard tube walls. Somehow they held.
     When I got my eyes open the red dot was shrinking into nothing.

(ed note: later, back home, in the hospital)

     I was floating between a pair of sleeping plates, hideously uncomfortable, when the nurse came to announce a visitor. I knew who it was from her peculiar expression.
     “What can get through a General Products hull?” I asked it.
     “I hoped you would tell me.” The president (of General Products Inc.) rested on its single back leg, holding a stick that gave off green incense smelling smoke.
     “And so I will. Gravity.”
     “Do not play with me, Beowuif Shaeffer. This matter is vital.”
     “I’m not playing. Does your world have a moon?”
     “That information is classified.” The puppeteers are cowards. Nobody knows where they come from, and nobody is likely to find out.
     “Do you know what happens when a moon gets too close to its primary?
     “It falls apart.
     “Why?”
     “I do not know.”
     “Tides.”
     “What is a tide?”
     Oho, said I to myself, said I. “I’m going to try to tell you. The Earth’s moon is almost two thousand miles in diameter and does not rotate with respect to Earth. I want you to pick two rocks on the moon, one at the point nearest the Earth, one at the point farthest away.
     “Very well.”
     “Now, isn’t it obvious that if those rocks were left to themselves, they’d fall away from each other? They’re in two different orbits, mind you, concentric orbits, one almost two thousand miles outside the other. Yet those rocks are forced to move at the same orbital speed.”
     “The one outside is moving faster.”
     “Good point. So there is a force trying to pull the moon apart. Gravity holds it together. Bring the moon close enough to Earth, and those two rocks would simply ‘float away.”
     “I see. Then this ‘tide’ tried to pull your ship apart. It was powerful enough in the lifesystem of the Institute ship to pull the acceleration chairs out of their mounts.”
     “And to crush a human being. Picture it. The ship’s nose was just seven miles from the center of BVS-l. The tail was three hundred feet farther out. Left to themselves, they’d have gone in completely different orbits. My head and feet tried to do the same thing when I got close enough.

From NEUTRON STAR by Larry Niven (1966)

Halo Drive

This is from The Halo Drive: Fuel-Free Relativistic Propulsion of Large Masses via Recycled Boomerang Photons. It is a very clever way of constructing a Dyson slingshot without requiring the spacecraft to approach the binary so closely that it risks spaghettification. It performs the gravitational slingshot remotely.

Of course it does require a sizable black hole moving at high velocity. Which should not be a surprise, since this is the page about unobtainium.

As with the Dyson slingshot, the energy used to accelerate the spacecraft is coming from the motion of the hypergravity object. It is just that you could use the blasted thing daily for ten-thousand years before the slowdown of the black hole became detectable.

The spacecraft starts at a reasonble distance from a moving black hole. It fires a beam of photons (laser beam) at the edge of the black hole. The beam skims the black hole's photon sphere, being bent by gravity into a path around the far side of the black hole. The beam breaks free of the opposite edge, and travels back to the spacecraft. What's more, the black hole's relative motion has given the beam a blue-shift. Translation: the beam's energy has been increased and the black hole's relative motion has been slowed by an undetectable microscopic amount. The black hole acts like a gravitational mirror.

The spacecraft loses energy when it emits the photon beam, and normally it gains back exactly the same energy when it reabsorbs the reflected beam. Except that the beam has been blue-shifted, so the spacecraft gains the blue shift energy. This is used to accelerate the spacecraft. The old energy is used to send another bit of photon beam to go harvest some more blueshift. Keep this up until the spacecraft is too far away from the black hole for the beam to reach.

The end result is the spacecraft has been accelerated to 133% (4/3rd) the black hole's velocity, using none of its own energy. As previously mentioned, all the energy is coming from the black hole, but it has energy to spare. The spacecraft does not get close enough to the black hole to be damaged by dangerous gravitational tides nor deadly radiation. The only thing that gets dangerously close is the beam of photons, and photons are much more durable than a spacecraft.

Once the spacecraft has accelerated to 100% of the black hole's velocity, the halo drive will not get any more blue-shift energy. But by that point, it will have gathered enough blue shift energy to eventually accelerate to 133% of the black hole's velocity.

When using a black hole binary to make a halo drive, the spacecraft will be accelerated best if it is moving in a direction along the plane of the binary orbit. To move out of the plane of the orbit the spacecraft will have to use onboard propellant and use up some of the blue-shift energy. Kipping said he has not run the numbers but thinks that a spacecraft could move up to 20° out of the binary orbit plane and still have a final acceleration of 100% of the black holes orbital velocity.

Also interesting is the fact this drive is not limited to low-mass spacecraft, such as solar sail. The spacecraft can be arbitrarily large. "Arbitraily" being defined as "much less mass than the black hole". In other words it could accelerate a spacecraft with the mass of Jupiter.

If you are lucky enough to find a black hole moving near relativistic velocity, then you can kick your ship to relativistic velocities as well. Then you'd really better have a relativistic black hole at the destination or you'll never slow down.


To be practical, you had better set up another black hole halo drive at the destination in order to decelerate to a halt. If your ship can brake to a stand-still using its internal propulsion, it can probably perform the initial acceleration unaided as well, In which case you don't need the blasted black holes in the first place.

It is not required, but the scheme works better with a pair of black holes orbiting each other in compact binary configuration. Especially at relativistic speeds. For details see the paper.

Predictably for this to work the photon beam has to be aimed incredibly precisely. The radius of a black hole is called the Schwarzschild radius (rs). For the photon beam to boomerang, it has to approach the black hole's center closer than 2rs (yes, I know theoretically the distance to a black hole's center is infinity, just roll with it, OK?). But if it approaches too close, 1.5rs, the beam will become trapped in orbit around the hole (the "photon sphere").

Bottom line, the typical boomarange distance is one skillinth of a whillimeter above 1.5rs


The paper points out that this effect can be used for other things besides accelerating spacecraft. Instead of using the energy for propulsion, store it and use it for some other useful purpose. It could also be used to manipulate a binary black hole into a desired configuration, using the halo drive like titanic optical tweezers.

Broadcast Power

This was a totally silly sci-fi idea when I was a young man. The idea was since a pocket transistor radio could pick up music broadcasts from radio stations with no wires invovled (wirelessly), perhaps it would be possible for an engine to pick up electricity broadcast from a power station with no wires involved. The technical term is Inductive Charging or Wireless power transfer.

Nikola Tesla found out the hard way the drawback to this little scheme. The lions share of the power radiates into the wild blue yonder and is wasted, since Tesla's attempt to channel the energy into standing waves around the entire globe was an utter failure. This means the inverse square law is your enemy.

True, there was lots of work done in the 1960s on transmitting power with beams of microwaves aimed at rectennas. However, while this was wireless, it was not a "broadcast." It was a narrowcast beam, if the rectenna wandered outside the beam the power would be cut off.

Broadcast power was officially confirmed to be a handwavium idea.

Until everything changed in 2006 when some geniuses at M.I.T. figured out how to use resonant coupling to transfer large amounts of power over a distance of a few times the resonator size. You sometimes see this used to charge smartphones, by laying the phone on a "charging mat".

For now, broadcast power seems to have made the jump from pure handwavium into fringe unobtanium.

The main practical problem is how does the power company determine who tapped some power, so the company knows where to send the bill?

THE FORLORN HOPE

(ed note: instead of conventional electrical power lines, the planet uses broadcast power technology. A row of broadcast power pylons is built, with each pylon being in line-of-sight of its neighbors. Any truck or other electrical power using equipment with an installed power receptor which is in line-of-sight of a pylon can tap the pylon for power. So roads tend to follow a broadcast pylon row. Of course the pylon row has to be attached to some kind of power generator in order to be energized, just like electrical power lines.)

      The lower curve of the freighter’s hull rested a meter and a half deep in the ground. Normally the Karyn Forest would have docked at a proper spaceport like the one at Praha. Copper would he carried from the smelter to the port on ground-effect trucks which hissed down the line of broadcast power pylons. Increased pressure on the Front thirty kilometers to the east had brought a modification. A starship would be landed directly at the mine and refinery complex (Smiricky #4) to eliminate the slow process of transferring the cargo and to free scarce transport to carry materials to the Front.
     From what the crew had seen when the Katyn Forest popped out of hyperspace on her landing run, the Federal side of the Front needed more help than it was likely to get.

(ed note: Katyn Forest's main fusion reactor is destroyed by a carefully placed enemy missile. All it has now is the one-lung Auxiliary Power Unit {APU}. The ship does not have enough power to lift and run away)


     "I apologize," Ortschugin (captain of the Katyn Forest) said. "I know you must be busy, but—" he took a leather-covered flask out of his breast pocket and uncapped it—"we know now what we must have, and it is crucial that we leam as soon as possible who we must see to get it." He handed the flask to Waldstejn, shifting his cud of tobacco to his right cheek in preparation for the liquor’s return. "We must have a truck power receptor so that we can fly to Praha on broadcast power."
     Waldstejn choked on his sip of what seemed to be industrial-strength ethanol. “What?” he said through his coughing. It was not that the request was wholly impossible, but it certainly had not been anything the local man had expected.
     The Spacer drank deeply from his own flask and belched. He stared gloomily upward before he resumed speaking. Several of the brighter stars were tremblingly visible through the plastic sheets. "Our powerplant is gone, kaput," the bearded man said at last. Replacement and patching the hull, those are dockyard jobs. We can fly, using the APU to drive the landing thrusters—but minutes, you see, ten, twenty at most before the little bottle ruptures also under load and we make fireworks as pretty as those this morning, yes?” (when a lucky shot from the artillery piece blew up the ship that was bombing them) He swigged again, then remembered and offered the flask to Waldstejn—who waved it away. "So we are still sitting when your Republicans take over, yes?" Ortschugin concluded with a wave of his hand.

(ed note: The Republican army over-runs the mine/refinery complex Smiricky #4, and the Federalists soldiers surrender. The starship Katyn Forest has installed a broadcast power receptor, but it is also captured by the Republican army. Captain Ortschugin is hauled in to face the army unit leader, Chaplain Bittman.)

     “You mean that your whole huge starship can run on broadcast power in good truth?" the Chaplain (Bittman) demanded.
     "We, ah, thought perhaps so," the Swobodan (Captain Ortschugin) agreed. "We didn't test it before the Complex, ah—”
     " Yes, was liberated," Chaplain Bittman finished for Ortschugin. He added, in a voice which had no more expression or mercy than the clack of a trap closing, "I advise you not to ‘test’ the system now, either, Captain. The idolators are attempting to make a stand along the line between here and Praha— they know how important it will be. Elements of the three armored regiments are pushing them back. Major elements.” Bittman permitted himself a smile at something he probably thought was funny. "What do you suppose the concentrated fire of, say, four Terra-built tanks would do to the hull even of your starship, Captain?"
     " We're at your service, E-Chaplain Bittman," the spacer said through dry lips, " but the pylons do lead only west from here.”
     "For the moment! " the Chaplain retorted with a zeal that shone across his slim, swarthy face. "Do you know why this line is crucial to the Lord's work, Captain?" he demanded rhetorically. "Because the fusion plant here, for the mining and smelting operations, was more than big enough to energize a broadcast system as well. That means that when we complete a temporary link from our own system east of Bradova, we have a channel for the heaviest, bulkiest supplies straight to the idolators' capital! Our armor is the head of the spear plunging into the heart of schism and idolatryl "
     For the moment, Ortschugin‘s mind made of him an engineer again and not merely a victim. He understood the situation perfectly. Pylons were easy enough to raise and align. They were, after all, little more than lattices with two pairs of antennas. The lower alignments beamed power to whatever vehicle was equipped to receive it, while the upper alignments charged the system itself. Cutting a pylon would prevent vehicles from proceeding until the gap was repaired, but the other parts of the system would continue to function.

     If it were energized from both sides of the gap.

     Republicans and Federalists both had crisscrossed their sides of the Front with branch lines to supply their troops. The power and load capacity of the branches was limited, however. The working, full-scale fusion plant of Smiricky #4 could very well tip the scales. The next Republican thrust would not outrun its supplies and so be contained, the way previous victories had been.

(ed note: The protagonist mercenary unit sneaks back into the captured refinery and makes common cause with Captain Ortschugin. The Katyn Forest lifts under broadcast power and heads for friendly territory down the line of broadcast power pylons. It can only manage an altitude of a few tens of meters but that is enough. The reason it did not do this earlier is because it was surrounded by Republican troops who would shoot the starship down. The reason it can do this now is because it is full of mercenary soldiers along with their artillery piece, who proceed to shoot the living snot out of the Republican troops and the base.

The surviving Republican troops are not amused, especially Chaplain Bittman. He angrily sends an order to Colonel Kadar, located further down the pylon row.)

     Kadar did not need a repetition. The orders were as simple as their accomplishment should be.
     A ripple of interest was running through the troops who a moment before had been waiting in bored lethargy. They knew a signal had been received, but only Colonel Kadar knew what the message was. Exulting in the power of secret knowledge, Kadar himself swung the turret of his tank. His gunner peered up at him, as much at a loss as were the infantrymen outside.
     The laser had been in ready position, zero deflection (yaw), zero elevation (pitch). Instead of aiming, Kadar kept his foot down on the traversing pedal as he squeezed the hand switch. The weapon drew a pale line across the daylight. The beam merely hissed until the turret rotated it through the nearest broadcast pylon. Steel latticework vaporized with a roar and a coruscant white glare. Larger, fluid gobbets spit from the supports and sparkled as they rained into the dust and stunted vegetation below.
     The Republican soldiers were on their feet now. Heads twisted even from the commo van to watch the fireworks. The power-broadcasting antennas waved madly as their support toppled, taking them out of the circuit. Kadar continued to traverse his blade of pure energy. A pylon of the east-bound roadway collapsed as the beam slashed it also. There was now a one-kilometer gap in the Praha-Smiricky truck route. Both halves of the lines were still energized, but the receptor antenna of a vehicle could not align across the gap and leap it.

     MERCENARY IDOLATORS IN CAPTURED STARSHIP PROCEEDING WEST ON ROADWAY FROM SMIRICKY the message had read. WEAPONS CAPABLE OF DEFEATING LIGHT ARMOR. IMMOBILIZE AND DESTROY VESSEL BETWEEN SEVERED PYLONS.
     TAKE NO PRISONERS.

(ed note: The Katyn Forest travels the gap by straining its APU. Kadar and his unit rips into the Katyn Forest with their laser tanks, only to discover that the ship is using its high pressure hoses to spray a protecting cloud of mercury, from the ship's ore cargo. The cloud severely attenuates the weapon laser beams. At least enough so the ship is not sliced like a giant salami. Meanwhile the mercenaries on the ship use their artillery gun as a direct-fire weapon and manage to mission-kill all the hostile laser tanks. The lighter hostile vehicles are converted into metal confetti.)

From THE FORLORN HOPE by David Drake (1984)
GALLAGHER'S GLACIER

      The landing system was from what Gallagher called their solar tap. They were tapping the electrical potential that exists between a planet and its orbiting proton and electron belts—the belts of ionized particles caught in the planet's magnetic field.
     The landing system was part of a power system that produced, from this one site, enough electricity to power the entire continent on a broadcast basis.
     Broadcast power. It had been known on Earth since the days of Nicola Tesla—the system for putting power on the airwaves the way radio and TV are broadcast. Electric power that you could tune into, the way you tune in a radio.
     With broadcast power, you didn't have to have wires strung around the continent to plug in motors and appliances and furnaces and the like. You didn't have to carry your own fuel in! your ground car. You tuned in your motor to the power frequency, the way you tune in a radio to the frequency of the station you want to hear.
     Earth hadn't had broadcast power, though she'd known how to broadcast it, because the production of power was geared to installations that didn't have sufficient potential that you could waste it on the airwaves. But the power potential in the solar tap was so great you could throw it away on an inverse-square: basis and still be able to tune in at the coast lines, two thousand miles distant, and run anything you wanted to run, from a manufacturing complex to a skimmer.
     The power that exists between the ground potential on any planet and the orbiting proton and electron belts trapped in the magnetic field of any planet, is fed by the solar wind of the sun around which the planet orbits, and it is a practically limitless potential. Electrons from the solar wind make their way in through the magnetic poles of the planet, distribute themselves at its crust, and seep through the insulating atmosphere towards the strong positive potential of the inner proton belt.
     If you make a "short circuit" through the atmosphere by creating an ionized pathway with a laser beam that reaches to the ionosphere, the top of the insulating atmospheric layers, the electrons will jump across the short circuit, changing the groundside potential. When the groundside potential lowers, it makes it possible for more electrons to pour in from the solar wind to equalize the potential. The planet is effectively recharged, and you can short-circuit again.
     It's done in milliseconds, and it's done on a pulse-basis. You turn the laser-beam short circuit off and on in an alternating-current effect, and it's most efficient at a low sonic frequency, although it has radio-frequency overtones.
     There was a group of huge pyramidal structures that were the bases for the solar tap and landing system. A huge, central pyramid was the tap itself; built of granite with a marble overlay, and of sufficient size to insulate the tremendous bursts of power flow from the ground. The laser installation was on a small platform at the peak of the pyramid, and the control systems were centered well inside where the X rays and other radiation from the flow would not harm the technicians.
     From this, central pyramid, the pulsed power was broadcast across the continent, and even from inside the canteen and at this distance you could hear the deep-throated roar of that power, pulsing through at a frequency within the audible range. Chee-ops, chee-ops, chee-ops, it seemed to say as it shorted in, was cut off, and pulsed in again.

From GALLAGHER'S GLACIER by Walt and Leigh Richmond (1970)
SEETEE SHOCK

(ed note: Seetee is antimatter (from the work Contraterrene or C.T.) In the story it can be found in antimatter meteor drifts in the asteroid belt. The Brand Transmitter is a species of power broadcast. Naturally the powers that be are angry at this threat to their monopoly on fission power because no empire has ever survived an energy-related phase shift with its full power intact.)

      A dull, hopeless anger took hold of Jenkins. He hated the stubborn stupidity of old Bruce O’Banion, and raged against the anonymous leaders of the, Free Space Party. He detested the complacent aristocracy of the Interplanet directors, despised the sordid greed of the Mandate bureaucrats, and bitterly scorned the cynical schemes of his uncle.
     All humanity, it seemed to him, impelled by its confusion of ignorant fears and blind desires, was somehow involved in a monstrous conspiracy against the bright dream of the Fifth Freedom. The engineering problems of the Brand transmitter were solved long ago, but the human difficulties loomed gigantic, complex beyond solution. The great barrier to human progress stood revealed as the nature of man himself.
     Urgently, he tugged at O’Banion’s arm.
     “Listen!” he whispered. “Your revolt has failed—but the Brand transmitter hasn’t. It can still bring peace and freedom to the people of the rocks—and all the planets.”

     “Physical power is the basis of political power,” he went on grimly. “The Mandate is able to oppress you because the governments of its member planets bave joined to establish a monopoly of the fissionable elements and fission energy. Your rebellion has failed to break that monopoly of power. But there is another way to do it, with a new power-source—the seetee drift!”
     They still listened, their lean, battle-soiled faces bleakly mistrustful.
     “Free power!” he whispered huskily. “Just look at the actual meaning of that. The Brand transmitter, that we’re trying to build on Freedonia, can supply free seetee energy to all men everywhere. That will mean economic freedom, and economic freedom will create political freedom. Our Freedonia plant can set you free of the Mandate and also from the rule of your own Party leaders.”

(ed note: The protagonist is dying from Seetee Shock: radiation sickness caused by being too close to a matter-antimatter explosion)
     But he towed them into place. He aligned them, with painful care. Groggily, swaying at the task, he tightened the connections and brazed them with condulloy metal. He inspected the assembly, tested all the circuits, and straightened triumphantly in the chafing confinement of his armor.
     The Brand transmitter was finished!


     Awkward now in the powered suit, he missed the high control platform. He plunged on past it, fumbling feebly at the control studs, toward the untouchable metal of the upper hemisphere and the red signs that warned: SEETEE—KEEP OFF!
     The steel rails of the terrene barrier caught him. His trembling fingers found the studs again, and he alighted at last on the platform. Abruptly ill, he vomited again. Darkness came down upon him, and he thought he was blind.
     He lay a long time, merely clinging to the platform rail, until he found that he could see again. Nearly too weak to move the stiff armor, he drew himself erect. He waited for his head to clear, and make meaning come back to the gauges and controls before him. He pressed buttons and pulled switches.
     The generator ran.
     A green indicator light told him that the Levin-Dahlberg field was functioning. The fuel-milling machines ran silently in that airless space, grinding terrene and seetee rock to dust. Separator coils refined the fuel, and paragravity injectors metered it into the reaction field.
     Matter was annihilated there, but Jenkins saw no frightful fire. He heard no ultimate crash. He was not destroyed. For the reaction field contained that raving energy, and converted it into a silent tide of power flowing in the condulloy coils.
     Meter needles crept over, as that river of tamed energy flooded higher. They steadied, as full output of the generator built up the power field extending beyond the far sun to the limits of the solar system. They dropped back suddenly, as the full potential was established and automatic relays shut off the flow of fuel.
     Swaying over the board, Jenkins pressed one final button. Fever was burning his body. Unquenchable thirst consumed him. He felt the drip of unstaunchable blood from his nose. Illness crushed him down, until only the cruel stiffness of the armor supported him. Yet he clung to consciousness, and tried to listen.
     “People of all the planets—”
     Those triumphant words came faintly from the speaker in his helmet, spoken in the deep voice of old Jim Drake. A red photophone light was flickering on the board, and his mind could see the powerful automatic photophone and ultra-wave beam transmitters above, sweeping every rock and planet in the ecliptic with that recorded announcement, as Freedonia turned.
     “The Fifth Freedom has arrived!” Drake’s canned voice proclaimed—for he had planned and toiled against this crucial hour. “Free power is flowing out from our contraterrene plant, and all you who hear can tap the power field with simple tri-polar receptors.
     “Receptor voltage is set by the dimensions of the elements, current output limited only by circuit resistance. Specifications are—”
     Jenkins vomited again, into the rubber bag beneath his chin. Sweat was clammy on his body, and the vast, untouchable machines beyond the barriers blurred and dimmed. But he tried to listen, and he heard Drake’s recorded voice again.
     “… benefit all men. But there are men too blind to see the good. There are a few selfish men and women, anxious to preserve their cruel old monopoly of power, who will attempt to stop the Brand transmitter. We beg all common men, everywhere, not to let that happen.”
     A pause, and then the tape repeated:
     “People of all the planets—

     “Open this.” Smiling mysteriously, she gave him a little package. “Ann wanted me to bring flowers, but Rick said you’d like this better. Even if it’s just a toy.”
     Eagerly, he opened the box. He found a small light bulb and another tiny gadget made of insulating plastic, sheet copper, and a few turns of wire. Peering at it, he caught his breath.
     “A Brand receptor !” he whispered. “Does it work?”
     “Try it.”
     Anxiously, he twisted the bulb into the gadget. It lit—and its tiny glow was enough to show him the illimitable might of the Brand power field, pervading all the planets of man. It was a searchlight, probing feebly into the misty splendor of a new human era.

From SEETEE SHOCK by Jack Williamson (1949)
THE PRODIGAL SUN

(ed note: Director Rickman and his wife Gelda have to escape out of the city since the government has put out an order for them to be assasinated. They use their flying car, powered by broadcast power.)

      He said brusquely, "Come, we've got to get out of here."
     "Of course." She rose, pale and unsteady but obviously clear-headed. "We'd better take my flyer. It's out at the front."
     "Yes." He nodded quickly. "I'll pre-set my own flyer to take off in an hour. No one will worry about Trudy and Valance for some time. They like to enjoy their fun." He hurried from the house and was back in less than a minute. "Let's go." He gripped her hand and almost pulled her from the house.
     The parked vehicle which belonged to his wife was a luxury craft but fortunately discreet in appearance. He was glad he had insisted on a four-contact receptor. If they wanted to bring him down by cutting the beam they would have to bring down about a third of the normal air traffic as well.

(ed note: I guess that means there are 12 power channels total.)

From THE PRODIGAL SUN by Philip E. High (1964)
INVADER ON MY BACK

"Forgive me for being obtuse but where is the outline?"

"You're not being obtuse, my friend, merely looking in the same damn direction I was looking. Now look at it this way: suppose this alleged telepathic broadcast affects different kinds of minds in different ways. To give a rather broad example, take a power broadcast. A ground car will pick up that power and translate it into energy for propulsion, a radiant unit will convert that same power into heat, and so on. Suppose this telepathic broadcast reacts on different types of brains in different ways. Let us assume, therefore, that it doesn't touch the Norms but plays hell with what we call a Delink-type brain. In short, again drawing a parallel with a power broadcast, the Delink-type brain converts that broadcast into lawlessness… ."

From INVADER ON MY BACK by Philip E. High (1968)
LIMITING FACTOR

"There is an old story in our folklore," he continued, "about a boy who bought himself an animal somewhat like your terrestrial calf. He thought that if he lifted it above his head ten times a day while it was little, he would build up his strength gradually until he would still be able to lift it over his head when it was a full-grown animal. He soon discovered the existence of a natural limiting factor. Do you see what I mean? When those people down there reached their natural limits, there was no place for them to go but backward. We had the machine, though, and the machine can always be made smaller and better, so we had no stopping point."

He reached inside his vest and pulled out a small shining object about the size of a cigarette case. "This is hooked by a tight beam to the great generators on Altair. Of course I wouldn't, but I could move planets with it if I wanted to. It's simply a matter of applying a long enough lever, and the lever, if you'll remember, is a simple machine."

From LIMITING FACTOR by Theodore R. Cogswell (1954)
WALDO

      While his friend complied, Grimes shucked himself out of the outlandish anachronistic greatcoat he was wearing and threw it more or less in the direction of the robing alcove. It hit the floor heavily, much more heavily than its appearance justified, despite its unwieldy bulk. It clunked.
     Stooping, he peeled off thick overtrousers as massive as the coat.
     He was dressed underneath in conventional business tights in blue and sable. It was not a style that suited him. To an eye unsophisticated in matters of civilized dress, let us say the mythical Man-from-Antares — he might have seemed uncouth, even unsightly. He looked a good bit like an elderly fat beetle.
     James Stevens’s eye made no note of the tights, but he looked with disapproval on the garments which had just been discarded.
     ‘Still wearing that fool armour,’ he commented.
     ‘Certainly.’
     ‘Damn it, Doc — you’ll make yourself sick, carrying that junk around. It’s unhealthy.’
     ‘Danged sight sicker if I don’t.’
     ‘Rats! I don’t get sick, and I don’t wear armour — outside the lab.’
     ‘You should.’ Grimes walked over to where Stevens had reseated himself. ‘Cross your knees.’ Stevens complied; Grimes struck him smartly below the kneecap with the edge of his palm. The reflex jerk was barely perceptible. ‘Lousy,’ he remarked, then peeled back his friend’s right eyelid.
     ‘You’re in poor shape,’ he added after a moment. Stevens drew away impatiently. ‘I’m all right. It’s you we’re talking about.’
     ‘What about me?’
     ‘Well—Damnation, Doc, you’re throwing away your reputation. They talk about you.’
     Grimes nodded. ‘I know. “Poor old Gus Grimes — a slight touch of cerebral termites.” Don’t worry about my reputation; I’ve always been out of step. What’s your fatigue index?’
     ‘I don’t know. It’s all right.’
     ‘It is, eh? I’ll wrestle you, two falls out of three.’ Stevens rubbed his eyes. ‘Don’t needle me, Doc. I’m rundown. I know that, but it isn’t anything but overwork.’
     ‘Humph! James, you are a fair-to-middlin’ radiation physicist —
     ‘Engineer.’
     ‘—engineer. But you’re no medical man. You can’t expect to pour every sort of radiant energy through the human system year after year and not pay for it. It wasn’t designed to stand it.’
     ‘But I wear armour in the lab. You know that.’
     ‘Surely. And how about outside the lab?’
     ‘But—Look, Doc — I hate to say it, but your whole thesis is ridiculous. Sure there is radiant energy in the air these days, but nothing harmful. All the colloidal chemists agree—‘
     ‘Colloidal, fiddlesticks!’
     ‘But you’ve got to admit that biological economy is a matter of colloidal chemistry.’
     ‘I’ve got to admit nothing. I’m not contending that colloids are not the fabric of living tissue—They are. But I’ve maintained for forty years that it was dangerous to expose living tissue to assorted radiation without being sure of the effect. From an evolutionary standpoint the human animal is habituated to and adapted to only the natural radiation of the sun, and he can’t stand that any too well, even under a thick blanket of ionization. Without that blanket—Did you ever see a solar-X type cancer?’
     ‘Of course not.’
     ‘No, you’re too young. I have. Assisted at the autopsy of one, when I was an intern. Chap was on the Second Venus Expedition. Four hundred and thirty-eight cancers we counted in him, then gave up.’
     ‘Solar-X is whipped.’
     ‘Sure it is. But it ought to be a warning. You bright young squirts can cook up things in your labs that we medicos can’t begin to cope with. We’re behind — bound to be. We usually don’t know what’s happened until the damage is done. This time you’ve torn it.’

     Even though the thesis be too broad and much oversimplified, it is nonetheless true that much which characterized the long peace which followed the constitutional establishrnent of the United Nations grew out of the technologies which were hot-house-forced by the needs of the belligerents in the war of the forties. Up to that time broadcast and beamcast were used only for commercial radio, with rare exceptions.
     Even telephony was done almost entirely by actual metallic connexion from one instrument to another. If a man in Monterey wished to speak to his wife or partner in Boston, a physical, copper neuron stretched bodily across the continent from one to the other.
     Radiant power was then a hop dream, found in Sunday supplements and comic books.
     A concatenation, no, a meshwork of new developments was necessary before the web of copper covering the continent could be dispensed with.
     Power could not be broadcast economically; it was necessary to wait for the co-axial beam, a direct result of the imperative military shortages of the Great War. Radio telephony could not replace wired telephony until ultra micro-wave techniques made room in the ether, so to speak, for the traffic load. Even then it was necessary to invent a tuning device which could be used by a nontechnical person, a ten-year-old child, let us say, as easily as the dial selector which was characteristic of the commercial wired telephone of the era then terminating.
     Bell Laboratories cracked that problem; the solution led directly to the radiant power receptor, domestic type, keyed, sealed, and metered.
     The way was open for commercial radio power transmission, except in one respect: efficiency. Aviation waited on the development of the Otto-cycle engine; the Industrial Revolution waited on the steam engine; radiant power waited on a really cheap, plentiful power source. Since radiation of power is inherently wasteful, it was necessary to have power cheap and plentiful enough to waste.
     The same war brought atomic energy. The physicists working for the United States Army, the United States of North America had its own army then, produced a superexplosive; the notebooks recording their tests contained, when properly correlated, everything necessary to produce almost any other sort of nuclear reaction, even the so-called Solar Phoenix, the hydrogen-helium cycle, which is the source of the sun’s power.
     The reaction whereby copper is broken down into phosphorus, silicon-29, and helium-8, plus degenerating chain reactions, was one of the several cheap and convenient means developed for producing unlimited and practically free power.
     Radiant power became economically feasible, and inevitable.
     Of course Stevens included none of this in his explanation to Grimes.
     Grimes was absent-mindedly aware of the whole dynamic process; he had seen radiant power grow up, just as his grandfather had seen the development of aviation. He had seen the great transmission lines removed from the sky — ‘mined’ for their copper; he had seen the heavy cables being torn from the dug-up streets of Manhattan.

     ‘I don’t think you appreciate the importance of this problem, Doc. Have you any idea of the amount of horsepower involved in transportation? Counting both private and commercial vehicles and common carriers, North American Power-Air supplies more than half the energy used in this continent. We have to be right.
     You can add to that our city-power affiliate. No trouble there, yet. But we don’t dare think what a city-power breakdown would mean.’
     ‘I’ll give you a solution.’
     ‘Yeah? Well, give.’
     ‘Junk it. Go back to oil-powered and steam-powered vehicles. Get rid of these damned radiant-powered deathtraps.’
     ‘Utterly impossible. You don’t know what you’re saying. It took more than fifteen years to make the change-over. Now we’re geared to it. Gus, if NAPA closed up shop, half the population of the northwest seaboard would starve, to say nothing of the lake states and the Philly-Boston axis.’
     ‘Hrrmph—Well, all I’ve got to say is that that might be better than the slow poisoning that is going on now.’
     Stevens brushed it away impatiently. ‘Look, Doc, nurse a bee in your bonnet if you like, but don’t ask me to figure it into my calculations. Nobody else sees any danger in radiant power.’
     Grimes answered mildly. ‘Point is, son, they aren’t looking in the right place. Do you know what the high-jump record was last year?’
     ‘I never listen to the sports news.’
     ‘Might try it sometime. The record levelled off at seven foot two, ‘bout twenty years back. Been dropping ever since. You might try graphing athletic records against radiation in the air — artificial radiation. Might find some results that would surprise you.’
     ‘Shucks, everybody knows there has been a swing away from heavy sports. The sweat-and-muscles fad died out, that’s all. We’ve simply advanced into a more intellectual culture.’
     ‘Intellectual, hogwash! People quit playing tennis and such because they are tired all the time. Look at you. You’re a mess.’
     ‘Don’t needle me, Doc.’
     ‘Sorry. But there has been a clear deterioration in the performance of the human animal. If we had decent records on such things I could prove it, but any physician who’s worth his salt can see it, if he’s got eyes in him and isn’t wedded to a lot of fancy instruments. I can’t prove what causes it, not yet, but I’ve a damned good hunch that it’s caused by the stuff you peddle.’
     ‘Impossible. There isn’t a radiation put on the air that hasn’t been tested very carefully in the bio labs. We’re neither fools nor knaves.
     ‘Maybe you don’t test ‘em long enough. I’m not talking about a few hours, or a few weeks; I’m talking about the cumulative effects of years of radiant frequencies pouring through the tissues. What does that do?’
     ‘Why, nothing—I believe.’
     ‘You believe, but you don’t know. Nobody has ever tried to find out. F’rinstance — what effect does sunlight have on silicate glass? Ordinarily you would say “none”, but you’ve seen desert glass?’
     ‘That bluish-lavender stuff? Of course.’
     ‘Yes. A bottle turns coloured in a few months in the Mojave Desert. But have you ever seen the windowpanes in the old houses on Beacon Hill?’
     ‘I’ve never been on Beacon Hill.’
     ‘OK, then I’ll tell you. Same phenomena, only it takes a century more, in Boston. Now tell me, you savvy physics — could you measure the change taking place in those Beacon Hill windows?’
     ‘Mm-rn-in — probably not.’
     ‘But it’s going on just the same. Has anyone ever tried to measure the changes produced in human tissue by thirty years of exposure to ultra short-wave radiation?’
     ‘No, but—‘
     ‘No “buts”. I see an effect. I’ve made a wild guess at a cause. Maybe I’m wrong. But I’ve felt a lot more spry since I’ve taken to invariably wearing my lead overcoat whenever I go out.’

From WALDO by Robert Heinlein (1942)
THE MIGHTIEST MACHINE

      "Hello, boss!" said a deep voice immediately above and behind his left ear. "Won't you come in?"
     Spencer rose six inches from his chair in a spasmodic jump and turned on Aarn with a sour face. "You misplaced decimal point, if it weren't for my memories and loyalty to dear old Mass Tech, I'd amputate you from the pay roll."
     "Would you?" asked Aarn, with a pensive air. When pensive, Aarn's broad face and huge body succeeded in looking like a cow of subnormal intelligence, ruminating on the possible source of its next meal. He did now. "I'd hate that, Russ. But I think you'd hate it worst. I got my super-permeable space condition. That's about the poorest name imaginable, so I've decided to invent a name. Be it herein after referred to by the party of the first part as the 'transpon' condition. Anyway, come on in."

     Aarn's workship was large and divided into two parts, the apparatus room, inhabited by four technical assistants who made up the apparatus Aarn called for, and Munro's own sanctum.
     In Aarn's inner lab were a series of benches and cabinets and tables. These were all loaded with junked apparatus, unused parts, spare voltmeters, and coils of wire. The floor was reserved for the heavier junk that would have crushed the tables.
     Spencer was quite surprised to see that one of the largest benches had actually been entirely cleared, and two sets of apparatus set up on it. Aarn smiled his blank grin again. Spencer knew from sad experience that that smile meant something completely revolutionary that would upset all his calculations and probably cost him, temporarily at least, several million dollars.
     "Look," said Aarn.
     He waved his hands toward the new apparatus he had set up on the bench. The apparatus consisted of two main groups. At one end of the bench was a squat control panel, backed by a complex assortment of tubes and a device that closely resembled the magnetic atmosphere apparatus connected with a curious wire cone. There was a standard a foot tall surmounted by a cone of copper bars running lengthwise to form the sides and around, binding the longitudinal bars in position.
     The tip of the cone was a block of copper, the size of a golf ball. The mouth of the device was some four inches across and the length over all about ten inches. But the copper bars that formed the sides of the cone were care fully insulated from the block that was at the tip. From this block, a single straight bar of copper projected along the axis of the cone.
     Aarn smiled and turned on the apparatus. A low, musical hum rose from the tubes and coils, and slowly a faint blue glow centered about the copper block at the tip of the cone and the pencil of metal that extended up the axis. For five seconds this held steady while a similar blue glow began to build up about the outer system of copper conductors. Presently, as this reached a maximum, the inner glow began to fade, then swiftly a pulsing rhythm was set up, first the inner, then the outer conductor system glowing more intensely. The light settled down to a steady flickering that the eye could barely perceive, and Aarn smiled at it thoughtfully.
     "The apparatus takes a few minutes to warm up. That's the first half. That was the hardest part, too, curiously, though this projector here is a far more important discovery."
     Aarn pushed a second standard into view, which was surmounted by a metal bowl that closely resembled a deep soup dish. The inner surface was evidently a parabolic one, made up of a maze of tiny coils, each oriented carefully toward some definite aim, while the entire rim of the "soup dish" was a single larger coil.
     Carefully Aarn adjusted it so that it pointed toward the flickering cage of copper wires, and beyond it to the apparatus at the other end of the bench. This apparatus seemed fairly simple, merely a number of standards with various arrangements of wires. Two parallel copper bars, a double spiral made of two insulated wires, two metal disks.
     "Those," said Aarn softly, "are simply connected with the normal power supply. It is alternating current of sixty cycles at two hundred and twenty volts. The device I have is a pickup. It will collect the power from those wires. The projector here is the real secret—it makes space itself become a perfect conductor of electric-space-strain. Not electricity. Electric-space-strain. But the result is the same. It makes the space along its axis capable of carrying power along the axis—and along the axis only. When I start this, the space between here and that interrupter coil back there will be come a perfect conductor. The interrupter coil is necessary to prevent the thing reaching on, out indefinitely.
     "The pick-up there, will be in that path of conduction, and so will the first of those lead-offs there. That pair of straight wires. The wires will not be mutually short circuited because this will conduct current only along the axis. But the pick-up there keeps sending out flashes of a somewhat similar energy at an angle so that it covers the entire column, and so can pick up the power in it.
     "I can't make that pick-up work continuously, because the energies would then interfere and simply short-circuit things. But I can make it work at any frequency from one cycle a second to about fifty megacycles. Now I'm going to adjust it to sixty cycles, and it will get in step with the power on the two leads—and run that series of lights and that motor."
     Aarn pushed a switch. Instantly three tumblers snapped over automatically, a powerful surge of power seemed to draw at the men themselves momentarily, and then the little flickering pick-up was sending out searchlight beams of brilliant ionization. They started out along the shape of the cone, spread rapidly, till they filled the tight, round column of power coming from the transpon condition projector, then the ionization stretched along like a luminous liquid flower in a pipe.
     "The thing isn't in phase—wasting a lot of power," said Aarn.
     He began adjusting a dial, and the slight visible flickering vanished as the frequency rose. Suddenly the ionization all but vanished, leaving only a slight glow about the pick up itself. Then an instant later it was back, but vanished again. Each time the ionization stopped, the lights glowed, and the motor Aarn had pointed out hummed into speed.

     Presently he had it exactly adjusted, and the lights burned steadily, the five horse-power motor continuing smoothly.
     "The efficiency is about seventy-five per cent, which is not very good, I'll admit—but good enough for what I have in mind."
     Spencer was looking at the device intently. At last he asked: "But why doesn't the pick-up short-circuit the thing when it has thrown out its pick-up force? It throws a conducting band or disk completely across the tube of the transpon beam, as you said you called it. That will carry current at right angles to the axis, so it lies completely across the two terminals of the wires."
     Aarn smiled grimly. "That, Russ, Is why I took nearly nine months to do this. I had to prevent that. The answer is that the lock and the grid don't project the same force. The grid projects a force which will accept only a negative electric force, while the block will accept only positive. Therefore it can't short-circuit."
     "Then it rectifies, too? Some little device! It's a thing we've sought for a century, Aarn —power broadcast along a beam."
     "No," said Aarn sharply. "That's the point—it isn't broadcast along a beam. A beam reaches out and picks it up. The difference is as great and as vital as the difference between being hit and stopping something going by. If a man's fist connects with the button, your jaw absorbs kinetic energy. He has broadcast it along the beam of his arm.
     "But if you reach out and grab hold of a man running by you, you have reached out for and taken hold of a source of kinetic energy and momentum. Right?"
     "Hm—hum! Distinct difference. But why does it count here? What difference does it maker'
     "Nuts—a system of difference. No beam any man ever made could hold an absolute beam—a fixed diameter from here to infinity. Any power beam you make has to carry so much power per square-inch cross section at the point where the power is picked up. Suppose I'm sending power to a ship going to the Moon. On Earth the beam is ten feet across. Fine, the ship has an absorber or pick-up twenty feet in diameter, let's say. When the ship is fifty miles up, the beam and the pick-up are the same size. At one hundred miles the beam is wasting seventy-five per cent of its power because it has to maintain a certain power at the ship, and only twenty-five per cent of the beam is impinging on the target.
     "Now—take it the other way. If the ship projects the beam, the earth power station is simply pouring power into a funnel. The energy can go only one way, and no matter how widespread it is at Earth, it has to get out on the pick up in the beam. It's bound to be infinitely more efficient after you get more than ten miles away."
     "Slightly," agreed Spencer with a smile. "So hereafter, ships won't carry accumulators, eh? Just send back a beam and pick up power from Earth. But say—how are they going to be —made to pay for it? They could tap any power source or any line on Earth?"
     Aarn smiled and replied: "In the first place, they won't get their power from Earth, and in the second place, just suppose you sent back one of the beams to tap any sixty cycle line on Earth. What would happen? First, you'd have to get in phase with some one of the big power-line net works. Then, bingo, you have everything from one hundred and ten to one hundred and ten thousand and above volts coming smashing along. It would blow you to kingdom come and wreck the apparatus. Might do some damage back on Earth, but I doubt it."
     "Not get the power from Earth? Where then? Not from one of the other planets surely, because they have power troubles of their own."
     "From the mightiest machine!"
     "Good Heaven! The Sun! Do you mean that thing could tap the awful power of the Sun?"
     Spencer's face was suddenly pale. He could visualize that beam as though a visible thing reaching from some tiny dust mote out across space to impinge on the Sun, and drink of the power in that million-mile electric furnace, where matter was smashed beyond atoms, ground to radiation.
     "The Sun," Aarn nodded. "It's hard to think of all at once. Tapping the mightiest machine—the most inconceivably huge engine in the universe really—for any star would do. Making a star supply your power. A furnace that consumes nearly four million tons of matter a second.
     "It's simple really. You need a power stack, of course— a huge supply of power storage to operate your machine when you were not in position to tap the Sun. It would require only a modification of this device—one I have worked out completely—and we could draw a billion billion horse power in direct current at any voltage you wished, up to a maximum of about five hundred million, which would make insulation impossible in any circumstances."
     "Then—unlimited power—and I thought it was just a new power-transmission device. Atomic energy! Man could never build—of course he couldn't make one as big—a sun—two million million million tons of engine—three hundred thousand worlds like this—"
     He laughed suddenly. "Car, you wanted to know why physics didn't give you the atomic energy they promised. Here's physics' answer! Atomic energy would be too expensive—require too elaborate a control—so physics taps a sun!"

From THE MIGHTIEST MACHINE by John W. Campbell Jr. (1947)

Gravity train

This is an ancient idea that is hard-core unobtanium. The idea is if you pick a spot on Terra, somehow dig from that spot to the core of the planet and continue until you emerge at the antipode, in some manner (left as an excercise for the reader) prevent the tunnel from imploding, you will have a gravitationally powered subway. Unobtanium, we can calculate exactly how it would operate, but there is no way we could make one.

The technical term is Gravity Train.

You can get a more precise view of a given tunnel's antipodes locations by using the online Antipodes Map. Though a cursor glance at the map above shows that most tunnels have both ends located in the ocean (white areas), and of the ones that involve dry land most have an oceanic end (gold and blue areas). Very frew location have both ends on dry land (orange areas).

Actually, the tunnel does not require the ends to be at the antipodes, it does not have to pass through the center of the planet. All straight-line tunnels (using only gravity as the propulsive force) take the same amount of time to transit, regardless of where the end points are. Transit time is faster if the tunnel is a hypocycloid curve between the points. Sadly if the two points are antipodes, the hypocycloid curve becomes a straight line. For the equations to calculate the transit time, go here.

GRAVITY TRAIN

A gravity train is a theoretical means of transportation intended to go between two points on the surface of a sphere, following a straight tunnel that goes directly from one point to the other through the interior of the sphere.

In a large body such as a planet, this train could be left to accelerate using just the force of gravity, since during the first half of the trip (from the point of departure until the middle), the downward pull towards the center of gravity would pull it towards the destination. During the second half of the trip, the acceleration would be in the opposite direction relative to the trajectory, but (ignoring the effects of friction) the speed acquired before would be enough to cancel this deceleration exactly (so that the train would reach its destination with speed equal to zero).

Objections

In reality, there are two reasons gravity trains do not exist. First, a lengthy transit distance would pierce the Earth's mantle and traverse a region where rock is more fluid than solid. No materials are known that would withstand the tremendous heat and pressure in the inner core. Temperature is estimated as 5,700 K (5,430 °C; 9,800 °F), and pressure as high as about 330 to 360 gigapascals (3,300,000 to 3,600,000 atm). Secondly, frictional losses would be significant. Rolling friction losses could be reduced by using a magnetically levitated train. However, unless all air is evacuated from the tunnel, frictional losses due to air resistance would render the gravity train unusable. Evacuating the atmosphere to make it a vactrain would eliminate this drag but would require additional power. Such objections would not apply for solid planets and moons that do not have an atmosphere.

Origin of the concept

In the 17th century, British scientist Robert Hooke presented the idea of an object accelerating inside a planet in a letter to Isaac Newton. A gravity train project was seriously presented to the Paris Academy of Sciences in the 19th century. The same idea was proposed, without calculation, by Lewis Carroll in 1893 in Sylvie and Bruno Concluded. The idea was rediscovered in the 1960s when physicist Paul Cooper published a paper in the American Journal of Physics suggesting that gravity trains be considered for a future transportation project.

Mathematical considerations

Under the assumption of a spherical planet with uniform density, and ignoring relativistic effects as well as friction, a gravity train has the following properties:

  • The duration of a trip depends only on the density of the planet and the gravitational constant, but not on the diameter of the planet.
  • The maximum speed is reached at the middle point of the trajectory.

For gravity trains between points which are not the antipodes of each other, the following hold:

  • The shortest time tunnel through a homogeneous earth is a hypocycloid; in the special case of two antipodal points, the hypocycloid degenerates to a straight line.
  • All straight-line gravity trains on a given planet take exactly the same amount of time to complete a journey (that is, no matter where on the surface the two endpoints of its trajectory are located).

On the planet Earth specifically, a gravity train has the following parameters:

  • The travel time equals 2530.30 seconds (nearly 42.2 minutes), assuming Earth were a perfect sphere of uniform density.
  • By taking into account the realistic density distribution inside the Earth, as known from the Preliminary Reference Earth Model, the expected fall-through time is reduced from 42 to 38 minutes.
  • For a train that goes directly through the center of the Earth, the maximum speed is about 7,900 meters per second (28440 km/h) (Mach 23.2).

To put some numbers in perspective, the deepest current bore hole is the Kola Superdeep Borehole with a true depth of 12,262 meters. While to cover a distance between London and Paris (350 km) via a hypocycloidical path would need the creation of a 55,704-metre-deep hole. This depth isn't only 4.5 times as deep; it will also already need a tunnel that passes inside the Earth's mantle.

In fiction

The 1914 book Tik-Tok of Oz has a tube, that passed from Oz, through the center of the earth, emerging in the country of the Great Jinjin, Tittiti-Hoochoo.

In the 2012 movie Total Recall, a gravity train called "The Fall" goes through the center of the Earth to commute between Western Europe and Australia.

In the video game Super Mario Galaxy, there are various planets with holes that Mario can jump through to illustrate the gravity train effect.

From the Wikipedia entry for GRAVITY TRAIN
TRAVEL ON AIRLESS WORLDS PART II

This is a continuation of Travel on Airless Worlds where I looked at suborbital hops.

The surface of airless worlds will be exposed to radiation so it's likely the inhabitants would live underground.

Moreover, it is not as hard to burrow. The deepest gold mine on earth goes down about 4 kilometers. The heat and immense pressure make it hard to dig deeper. In contrast, the entire volume of a small body can be reached.

Courtney Seligman shows how to compute the pressure of a body with uniform density. The bodies we look at don't have uniform density but we'll use his method as a first order approximation.

Central pressure of a spherical body with uniform density is 3 g2/(8 π G)

Where G is universal gravitation constant, g is body's surface gravity and R is body's radius.

At distance r from center, pressure is (1 - (r/R)^2) * central pressure.

What is the pressure 4 kilometers below earth's surface?
Earths's radius R is 6378000 meters. r is that number minus 4000 meters. g is about 9.8 meters/sec^2.
Plugging those numbers into
(1 - (r/R)^2) * 3 g2/(8 π G)
gives 2120 atmospheres.

Besides pressure, heat also discourages us from burrowing deeper. So it might be possible to dig deeper on cooler worlds but for now we'll use 2120 atmospheres as the limit beyond which we can't dig.

3/(8 π G) * g * R2 gives different central pressures for various worlds:

Ceres center is 1430 atmospheres, well below our 2120 atmosphere limit. And Ceres is a cooler world than earth. We would be able to tunnel clear through the largest asteroid in the main belt. Since smaller asteroids would have smaller central pressure, we would be able to tunnel through the centers of every asteroid in the main belt.

Imagine a mohole going from a body's north pole to south pole:


The diagram above breaks the acceleration vector into vertical and horizontal components. The mohole payload has the same vertical acceleration components as an object in a circular orbit with orbital radius R, R being body radius.

Somone jumping into this mohole could travel to the opposite pole for zero energy. Trip time would be the orbital period: 2 π sqrt(R3/μ).

Other chords besides a diameter could be burrowed. I like to imagine 12 subway stations corresponding to the vertices of an icosahedron:



The red subway lines to nearest neighbors would correspond to the 30 edges of an icosahedron .

Green subway lines to the next nearest neighbors would correspond to the 30 edges of a small stellated dodecahedron.

And there could be 6 diameter subway lines linking a station to stations to their antipodes.

The energy free travel time of all these lines would be the same as the diameter trip time: 2 π sqrt(R3/μ).

It would be possible have a faster trip time than 2 π sqrt(R3/μ). A train could be accelerated during the first half of the trip and decelerated the second half. During the second half, energy could be recovered using regenerative braking.

(ed note: Mr. David also mentioned to me that if you omitted the regenerative braking and had the destination end of the tunnel open to the sky, you could use this to launch spacecraft)

Most of small bodies in our solar system have internal pressures that don't prohibit access. But in some cases central pressure exceeds 2120 atmospheres. We'd be able to burrow only so deep. Here's my guesstimate of the maximum depth for various bodies:

Luna 40 kilometers
Mars 15 kilometers
Ganymede 77 kilometers
Callisto 97 kilometers
Europa 55 kilometers
Titania 318 kilometers
Oberon 61 kilometers
Pluto 200 kilometers
Haumea 82 kilometers
Eris 108 kilometers

Here is the spreadsheet I used to look at internal pressures.

The top four kilometers of earth's surface is only a tiny fraction of the accessible mass in our solar system.

Standup Maths did a nice look at moholes going through a body.

From TRAVEL ON AIRLESS WORLDS PART II by Hollister David (2014)
THE REEFS OF SPACE

      The car raced through broad boulevards to a huge marble structure on the other side of the city.
     Over its wide entrance were the carved letters:

THE PLAN OF MAN

SUBTRAIN STATION


     They made their way through a wide concourse, noisy and crowded; but everyone gave them plenty of room. Ryeland grinned sourly to himself. No side trips! Of course not — and for the same reason. It wasn't healthy for a man who wore the collar to step out of line. And it wasn't healthy for anyone else to be in his immediate neighborhood if he did (Ryeland is a prisoner being transported, as a security measure he is wearing a remotely detonated exploding collar).
     "Track Six, was it?"
     "Train 667, Compartment 93.
     "There's Track Six." Ryeland led the way. Track Six was a freight platform. They went down a flight of motionless moving stairs and emerged beside the cradle track of the subtrains.
     Since the subtrains spanned the world, there was no clue as to where they were going. From Iceland they could be going to Canada, to Brazil, even to South Africa; the monstrous atomic drills of the Plan had burrowed perfectly straight shafts from everywhere to everywhere. The subtrains rocketed through air-exhausted tunnels, swung between hoops of electrostatic force. Without friction, their speed compared with the velocity of interplanetary travel.
     "Where is it?" Oporto grumbled, looking around. A harsh light flooded the grimy platforms, glittering on the huge aluminum llalloons that lay in their cradles outside the vacuum locks. Men with trucks and cranes were loading a long row of freightspheres in the platform next to theirs; a little cluster of passengers began to appear down the moving stairs of a platform a hundred yards away.
     Red signals flickered from the enormous gates of the vacuum lock on Track Six. Air valves gasped. The gates swung slowly open and a tractor emerged towing a cradle with the special car they were waiting for.
     The car stopped. Equalizer valves snorted again, and then its tall door flopped out from the top, forming a ramp to the platform. Escalators began to crawl along it.
     Ryeland shook his head. "No, you're not lightheaded. We're moving." The hand at the controls of the subtrain knew whose private car he was driving down the electrostatic tubes. The giant sphere was being given a featherbed ride. They had felt no jar at all on starting, but now they began to feel curiously light.
     That was intrinsic to the way of travel. The subtrain was arrowing along a chord from point to point; on long hauls the tunnels dipped nearly a thousand miles below the earth's surface at the halfway mark. Once the initial acceleration was over, the first half of a trip by subtrain was like dropping in a superspeed express elevator.
     Absently Ryeland reached out an arm to brace Oporto as the little man weaved and shuddered. He frowned. The helical fields which walled the tunnels of the subtrains owed part of their stability to himself. On that Friday night, three years before, when the Plan Police burst in upon him, he had just finished dictating the specifications for a new helical unit that halved hysteresis losses, had a service life at least double the old ones.

From THE REEFS OF SPACE by Jack Williamson and Frederik Pohl (1963)

High-Tech Materials

Dating back to the Orichalcum that was all the rage in Atlantis, to modern-day Wolverine's indestructable Adamantium bones, fiction is full of marvelous materials that would be oh so useful if we could only lay our hands on some.

Neutronium

Material composed of nothing but closely packed neutrons. Found in the core of neutron stars. The best figure I can find for the density of neutronium is 4×1017 kilograms per cubic meter, and dwarf star matter 1×109 kilograms per cubic meter.

No, you can't us it as the ultimate armor because if you somehow take a chunk out of the neutron star's core, the accurséd chunk explodes.

Outside of the core the neutrons undergo beta-decay with a half-life of 10 minutes and 11 seconds (611 seconds) with each cubic centimeter emitting energy at a rate of 19 megawatts average over the first half life.

Translation: sitting next to a cube of neutronium will be like having four and a half sticks of TNT blow up in your lap every second for 611 seconds.

As with all half-life decays, the second half-life will only have half the energy (two and a quarter sticks TNT per second) but by that point there won't be much left of your miserable carcass anyway.


Physicist Luke Campbell points out to me that my understanding is imperfect. Beta-decay is the least of your worries. He told me "An additional thing I didn't see mentioned in the section on neutronium is that all the neutrons are unbound. That means, there is nothing sticking them together. Once removed from the crushing gravity of a neutron star, all the individual neutrons fly off on their own independent happy trajectories. In an instant, you no longer have any kind of -ium any more, but rather a flash of highly penetrating energetic ionizing radiation."

In atomic nuclei, neutrons and protons stick together due to the strong nuclear force. Since the neutrons in a neutron star are not in a nucleus, there ain't no strong nuclear force gluing them. They are unbound.

The only thing keeping them together is the neutron star's outrageous gravity field. Once you take a chunk of neutronium away from the neutron star's gravity, the unbound neutrons composing the chunk instantly go flying in all direction at relativistic speeds. In other words it becomes a blast of neutron radiation with a flux strong enough to shred you into subatomic particles.

NEUTRONIUM

Neutronium (sometimes shortened to neutrium) is a proposed name for a substance composed purely of neutrons. The word was coined by scientist Andreas von Antropoff in 1926 (before the discovery of the neutron) for the conjectured "element of atomic number zero" that he placed at the head of the periodic table. However, the meaning of the term has changed over time, and from the last half of the 20th century onward it has been also used legitimately to refer to extremely dense substances resembling the neutron-degenerate matter theorized to exist in the cores of neutron stars; hereinafter "degenerate neutronium" will refer to this. Science fiction and popular literature frequently use the term "neutronium" to refer to a highly dense phase of matter composed primarily of neutrons.

Neutronium and neutron stars

Neutronium is used in popular literature to refer to the material present in the cores of neutron stars (stars which are too massive to be supported by electron degeneracy pressure and which collapse into a denser phase of matter). This term is very rarely used in scientific literature, for three reasons: there are multiple definitions for the term "neutronium"; there is considerable uncertainty over the composition of the material in the cores of neutron stars (it could be neutron-degenerate matter, strange matter, quark matter, or a variant or combination of the above); the properties of neutron star material should depend on depth due to changing pressure (see below), and no sharp boundary between the crust (consisting primarily of atomic nuclei) and almost protonless inner layer is expected to exist.

When neutron star core material is presumed to consist mostly of free neutrons, it is typically referred to as neutron-degenerate matter in scientific literature.

Properties

Due to beta (β) decay of mononeutron and extreme instability of aforementioned heavier "isotopes", degenerate neutronium is not expected to be stable under ordinary pressures. Free neutrons decay with a half-life of 10 minutes, 11 seconds. A teaspoon of degenerate neutronium gas would have a mass of two billion tonnes, and if moved to standard temperature and pressure, would emit 57 billion joules of β decay energy in the first half-life (average of 95 MW of power). This energy may be absorbed as the neutronium gas expands. Though, in the presence of atomic matter compressed to the state of electron degeneracy, the β decay may be inhibited due to Pauli exclusion principle, thus making free neutrons stable. Also, elevated pressures should make neutrons degenerate themselves. Compared to ordinary elements, neutronium should be more compressible due to the absence of electrically charged protons and electrons. This makes neutronium more energetically favorable than (positive-Z) atomic nuclei and leads to their conversion to (degenerate) neutronium through electron capture, a process which is believed to occur in stellar cores in the final seconds of the lifetime of massive stars, where it is facilitated by cooling via νe emission. As a result, degenerate neutronium can have a density of 4×1017 kg/m3, roughly 13 magnitudes denser than the densest known ordinary substances. It was theorized that extreme pressures of order 100 MeV/Fermi3 may deform the neutrons into a cubic symmetry, allowing tighter packing of neutrons, or cause a strange matter formation.

In fiction

The term "neutronium" has been popular in science fiction since at least the middle of the 20th century. It typically refers to an extremely dense, incredibly strong form of matter. While presumably inspired by the concept of neutron-degenerate matter in the cores of neutron stars, the material used in fiction bears at most only a superficial resemblance, usually depicted as an extremely strong solid under Earth-like conditions, or possessing exotic properties such as the ability to manipulate time and space. In contrast, all proposed forms of neutron star core material are fluids and are extremely unstable at pressures lower than that found in stellar cores. According to one analysis, a neutron star with a mass below about 0.2 solar masses will explode.

From the Wikipedia entry for NEUTRONIUM

Higgsinium and Monopolium

Higgsinium may or may not be handwavium. It depends upon a subatomic particle called the negative Higgsino predicted by supersymmetry theory. So far there is no evidence for supersymmetry from any physics experiment, and obviously no proof the negative Higgsino exists.

Monopolium may or may not be handwavium. It depends upon a subatomic particle called a magnetic monopole. There have been a couple of experiments which produced candidate events that were initially interpreted as monopoles, but are now regarded as inconclusive. On the other hand, pretty much all of the various theories of subatomic physics predict the existence of monopoles.

HIGGSINIUM AND MONOPOLIUM

Higgsinium

The theoretical physicists make some tentative promises. Supersymmetry is a class of theories that predicts "spin-reflected" analogs of all of the known (and some merely predicted) particles. The theories are not well enough along to assign exact masses to these new particles, but, constrained by already performed experiments, do set bounds. Accelerators being completed now may produce some of these before 1990. One possibility is that the peculiarly named negative Higgsino particle is stable, and has a mass about 75 times that of a proton (or 150,000 electrons).

Suppose we start with a mass of Hydrogen, the simplest atom. In it one electron orbits one proton. Since Higgsinos are heavier than protons, substituting one for the electron will turn the atom inside out: the massive Higgsino will become the nucleus, and the proton will do most of the orbiting, and will set the size of the atom, about 2000 times smaller in diameter than a normal one. The force between adjacent atoms would be 20002 or four million times as great — only astronomical temperatures would break those bonds — the material would remain a solid under any earthly conditions, and there would be 20003 or eight billion times as many atoms per cubic centimeter. Because Higgsinos are heavy, each atom will weigh 75 times as much, so the density would be about 1012 times that of normal matter. But there's a surprise. Each Higgsino added will itself generate about 20,000 electron volts of energy as it captures a proton — enough to radiate gamma rays. That's minor. But then the exposed orbiting protons of adjacent resulting "Higgsino Hydrogen" atoms will be in an optimum position to combine with one another in fours to form Helium nuclei in a fusion reaction. Each fusion liberates a whopping 10 million electron volts, and frees the Higgsinos to catalyse more fusions. This will continue until the resulting nuclear explosion blows the material apart. The Higgsinos may cause fusion of heavier elements as well, and perhaps fission of very heavy nuclei. Great opportunities here, but not quite what we had in mind!

Iron nuclei are prone neither to fusion nor fission — it takes energy to both break them down or to build them up — and so can (perhaps) be combined safely with Higgsinos. Each iron nucleus contains 26 protons, and must be neutralized by 26 negative Higgsinos. But it's unlikely that the Higgsinos can overcome their mutual repulsion to neatly form the right sized nuclei. A different, more condensed, arrangement is probable. Suppose we mix small amounts of hydrogen and Higgsinos very slowly and carefully, taking away waste energy (perhaps to help power the Higgsino manufacturing accelerator). The resulting mass will settle down to some lowest energy configuration, probably a crystal of Higgsinos and protons, electrically neutralizing each other, and some neutrons, bound by both electromagnetism and the strong nuclear force. If there are too many neutrons, some will decay radioactively until a stable mix is reached. The protons and neutrons, being the lighter and fuzzier of the particles, will determine the spacing: about that found in neutron stars. The millionfold speedups possible there will apply here also.

The final material (let's call it Higgsinium) would be 1018 times as dense as water; a thimbleful has the weight of a mountain. It'll be a while before that much of it is manufactured. A cubical speck a micron on a side weighs a gram, and should be enough to make thousands of very complex integrated circuits — analogous to a cubic centimeter of silicon. Their speed would be a millionfold greater, as would their power consumption and operating temperature. It may be possible to build the circuits with high energy versions of the optical and particle beam methods used to construct today's ICs, though the engineering challenges are huge! And in the long run tiny machines of Higgsinium might be dropped onto neutron stars to seed the construction of immense Neutronium minds.


Magnetic Monopoles

Higgsinos, and the rest of the supersymmetric stable, were "invented" only recently. An equally plausible, and even more interesting, kind of particle was theorized in 1930, by Paul Dirac. In a calculation that combined Quantum Mechanics with Special Relativity, Dirac deduced the existence of the positrons, mirror images of the electrons. This was the first indication of antimatter, and positrons were actually observed in 1932. The same calculation predicted the existence of a magnetic monopole, a stable particle carrying a charge like an isolated north or south pole of a magnet. Dirac's calculation did not give the monopole's mass, but it did specify the magnitude of its "charge". Recent "gauge" theories, in which the forces of nature are treated as distortions in higher dimensional spaces, also predict monopoles (as knots in spacetime), and even assign masses. Unfortunately there are competing versions with different mass predictions ranging from 1000 to 1016 times that of a proton. These masses are beyond the energy of existing and planned particle accelerators. Some cosmic rays are energetic enough.

For over forty years searches for monopoles all came up empty handed, and there was great skepticism about their existence. But they may have been fleetingly observed three times in the last decade, though none has yet been caught for extended observation. In 1973 a Berkeley cosmic ray expirement was lofted above most of the scattering atmosphere in a high altitude balloon. In 1975, after two years of study, a very heavy track bearing the stigmata of a monopole was noted in the lexan sheets that served as three dimensional detecting film. Calculations suggested it had twice Dirac's predicted charge, and a mass over 600 times that of a proton. Since monopoles had never been observed before, there was much skepticism. Other, more elaborate but more conventional possibilities were devised, and the incident was shelved.

On Valentine's day in 1982, a modest experiment in Blas Cabrera's Stanford physics lab registered a clean, persistent, steplike jump in the current in a superconducting loop. The size of the step was just what a monopole with Dirac's quantum of magnetic charge would have caused had it passed through the loop. The only alternative explanation was mechanical failure in the experimental apparatus. Subsequent prodding and banging produced no effect — everything seemed shipshape. The result was so exciting many groups around the world, including Cabrera's, built larger detectors, hoping to confirm the observation. For four years there was silence. By then the cumulative experience of the new detectors (collecting area multiplied by time) was over a thousand times that of Cabrera's original experiment. Once again the possibility of monopoles faded. Then, on May 22, 1986, a detector at Imperial College, London, whose experience was over four hundred times as large as Cabrera's original, registered another event. Until a monopole is caught and held, its existence will be in question. Yet, each additional detection greatly increases the odds that the others were not mistakes.

Magnetism and electricity are right angle versions of the same thing. A monopole waved up and down will cause a nearby electric charge to move side to side (and vice versa). A current of monopoles flowing in one wire will induce an electric current at right angles to itself. An electric current in a loop of conductor will flow in lockstep with a current of monopoles in a monopole-conducting loop chain linked with it. Two coils of wire wrapped around a monopole loop make a DC transformer — a current started in one coil will induce a monopole current in the loop, which will produce an electric current in the other coil's circuit. If good DC transformers had existed in the late nineteenth century, Thomas Edison and George Westinghouse would have had less to fight about, and all our electrical outlets would produce direct current. With monopoles we might refrain from making electrical connections at the plug at all, and draw power simply by passing the two ends of our power cords through a partially exposed monopole loop.

But let's get serious. If there are monopoles, they're not very common, and few will be simply picked out of the air. If they're very heavy, they will be hard to stop. Perhaps a few can be found already trapped here and there, and can be coaxed out (such a search was conducted worldwide by Kenneth Ford of Brandeis University, armed with a portable electromagnetic solenoid, in the early 1960s). Many things are possible given a few monopoles. Physicists routinely build superconducting solenoids with powerful magnetic fields several hundred thousand times as strong as Earth's. A monopole accelerates along magnetic field lines (for instance, a "North" monopole is strongly attracted to the south pole of a magnet). A monopole riding the field lines down the center of a powerful solenoid will gain an energy equivalent to the mass of several protons for every centimeter of travel. Ten meters of solenoid will impart an energy matching that of the most powerful existing accelerators. A few kilometers of solenoids will produce energies equal to millions of proton masses. The fireball resulting from a head on collision of two monopoles moving thusly is intense enough to produce some number of additional monopoles, in North/South matching pairs. These can be sorted out magnetically, and so monopoles can be harnessed to breed more monopoles.

Detectors of the Cabrera type do not measure the mass of passing monopoles, and the theories are little help. Monopoles can't be too light or they would have been created in existing accelerators. As mentioned above, the theoretical range of uncertainty is enormous. Things are especially interesting if there are at least two kinds of non mutually annihilating stable monopole, analogous to the proton and electron in normal matter (the North/South pairs mentioned above don't count — the two are antiparticles of each other, and annihilate when brought in contact). Here's a real leap of ignorance: let's suppose there are two kinds and that they are near the low end of the possible mass range. Let's suppose the lighter variety weighs 1000 protons, and the the heavier 1,000,000 protons. If two kinds don't exist, or if monopoles turn out to be much heavier many of the following proposals will become more extreme, or impossible. Others may open in their place.

An atom of Monopolium has a light monopole of one polarity (let's say North) bound to a heavy monopole of the opposite pole. Its size is set by the fuzzier light monopole. We assumed this has a mass of 1000 protons (or two million electrons), making the monopole atom about two million times smaller than a normal one. The particle spacing in Monopolium is thus comparable to that in Neutronium or Higgsinium. Its density, however, will be a million times beyond those because of the great mass of the central heavy monopole. This makes it 1025 times as heavy as normal matter. A thimbleful weighs as much as the Moon. Dirac's calculation found the magnetic quantum of charge to be 68.5 times as intense as the electric quantum. Two monopoles a certain distance apart would attract or repel each other 68.52 or 4,692 times as strongly as two equally separated electric particles. Combining this with the (inverse square) effects of much closer spacing and the increased density, makes Monopolium ten thousand times as strong for its weight as normal matter, though this number changes radically with changes in the assumed masses of the two kinds of monopole. The limiting switching speeds may be a thousand times higher than those we found for Higgsinium.

Other Applications

If Higgsinium or Monopolium can be made they may have applications beyond circuitry. Both materials are very tightly held together, and have no mechanism for absorbing small amounts of energy such as those found in photons, even soft gamma rays. This should make the materials very transparent. Yet the internal electromagnetic fields are huge, making for a tremendous index of refraction. Submicroscopic gamma ray microscopes, telescopes and lasers merely hint at the possibilities. In larger optics, gravitational effects will become important. If the materials can host loose electric or magnetic charges, they would be almost certainly be superconductors up to very high temperatures. because the tremendous binding forces would limit the number of states that the conducting particles can assume. To them the surface of the sun would is still very close to absolute zero in temperature. Superconducting versions of the materials should be nearly perfect mirrors, again up to gamma ray energies.

(ed note: amusingly enough, in his story THE BLACK STAR PASSES and in INVADERS FROM THE INFINITE the legendary John W. Campbell jr. postulates an absurdly strong transparent metal called "Lux" (density 103,500 kg/m3) which is a perfect insulator, and an absurdly strong mirror metal called "Relux" which is a conductor. Though in Campbell's stories these materials were composed out of solidified photons, i.e., Bose–Einstein condensates. )

Macroscopic extents of these substances are possible in very thin fibers or sheets. An (utterly invisible) Higgsinium strand one conventional atom (= 106 particles) in diameter masses 100 grams per centimeter of length. It may be able to support a 100 million tonnes, being about ten thousand times stronger for its weight than normal materials. Although it would slice through conventional matter as through a cloud (but sometimes the extremely thin cut would heal itself immediately), properly mounted it would make gargantuan engineering projects such as orbital elevators trivial. A single particle thick layer of Higgsinium would weigh about ten kilograms per square centimeter. Overlayed on structures of conventional matter the superconducting version especially would make powerful armor that would shield against essentially all normal matter projectiles, temperatures into the nuclear range, and all but the highest energy radiation. (But it could be penetrated by even denser Monopolium tipped bullets. Arms races are relentless!)

The same armor could be used to line the combustion chamber and expansion bell of a matter-antimatter rocket. Normal matter is instantly disintegrated by the violence of the reaction, but Higgsinium would easily bounce the pions, gamma rays and X rays produced when hydrogen meets antihydrogen. Single particle thick Monopolium, at a hundred tonnes per square centimeter, may be too heavy to use as a veneer at macroscopic scales. But it might be just the thing for constructing microscopic interstellar ships. A ship with two tiny tanks crammed with ultra compressed hydrogen and antihydrogen could rapidly propel itself at high acceleration to a few percent of the speed of light. Unaffected by either protons or antiprotons, Monopolium it would be better for building the engine and tanks than Higgsinium. The ship's front end might house a superfast mind, and tiny robot arms. It could probably land on a neutron star and start raising Neutronium crops and children.

Combining electrically conducting matter and Monopolium is interesting. Our Monopolium is about 10,000 times as strong for its weight as normal matter. Properly exploited, it can store $10,000$ as much energy in mechanical or electromagnetic form. Monopolium superconductor plated in a ring around a copper rod should make a lovely storage battery. To charge it, pass a current through the rod, thus setting up a monopole supercurrent in the ring. The magnetic current remains when you break the electrical connection, and causes the ends of the rod keep the voltage you had applied. When you connect a load to the rod ends, a current flows, and the voltage gradually drops towards zero as the monopole current slowly converts to electrical power. A kilogram of Monopolium should be able to store a fantastic one million watt hours. Caution: Do Not Overcharge! If the monopole current becomes too large, the electric field it generates will burst the ring, and all of the stored energy will be released at once in an explosion equal to a ton of TNT. There are other possibilities, especially involving intimate mixtures of monopoles and electrically charged matter (intertwined, like links of a chain), but we're out far enough on this limb for now.

From HARVARD DOESN'T PUBLISH SCIENCE FICTION by Hans P. Moravec (1988)
DRAGON'S EGG MONOPOLIUM

The largest of the probes was really an automated factory, but its single output was very unusual—monopoles. It had some monopoles on board already, both positive and negative types. These were not for output, but the seed material needed to run the monopole factory. The factory probe headed for the first of the large nickel-iron planetoids that the strong magnetic fields of the neutron star had slowed and captured during its travels. It started preparing the site while the other probes proceeded with the job of building the power supply necessary to operate the monopole factory, for the power that would be needed was so great that there was no way the factory probe could have carried the fuel. In fact, the power levels needed would exceed the total power-plant capability of the human race on Earth, Colonies, Luna, Mars, asteroids, and scientific outposts combined.

Although the electrical power required was beyond the capability of those in the Solar System, this was only because they didn't have the right energy source. The Sun had been—and still was—very generous with its outpouring of energy; but so far the best available ways to convert that radiant energy into electricity, either with solar cells or by burning some fossilized sun energy and using it to rotate a magnetic field past some wires in a generator, were still limited.

Here at Dragon's Egg (neutron star), there was no need for solar cells or heat engines, for the rapidly spinning, highly magnetized neutron star was at one time the energy source and the rotor of a dynamo. All that was needed were some wires to convert the energy of that rotating magnetic field into electrical current.

The job of the smaller probes was to lay cable. They started at the factory and laid a long thin cable in a big loop that passed completely around the star, but out at a safe distance, where it would be stable for the few months that the power would be needed. Since a billion kilometers of cable was needed to reach from the positions of the asteroidal material down around the star and back out again, it had to be very unusual cable—and it was. The cables being laid were bundles of superconducting polymer threads. Although it was hot near the neutron star, there was no need of refrigeration to maintain the superconductivity, for the polymers stayed superconducting almost to their melting point—900 degrees.

The cables became longer and longer and started to react to the magnetic field lines of the star, which were whipping by them ten times a second—five sweeps of a positive magnetic field emanating from the east pole of the neutron star, interspersed with five sweeps of the negative magnetic field from the west pole. Each time the field went by, the current would surge through the cable and build up as excess charge on the probes. Before they were through, the probes were pulsating with displays of blue and pink corona discharge—positive, then negative. The last connection of the cable to complete the circuit was tricky, since it had to be made at a time when the current pulsating back and forth through the wire was passing through zero. But for semi-intelligent probes with fractional-relativistic fusion-rocket drives, one-hundredth of a second is plenty of time.

With the power source hooked up to the factory, production started. Strong alternating magnetic fields whipped the seed monopoles back and forth at high energies through a chunk of dense matter. The collisions of the monopoles with the dense nuclei took place at such high energies that elementary particle pairs were formed in profusion, including magnetic monopole pairs. These were skimmed out of the debris emanating from the target and piped outside the factory by tailored electric and magnetic fields, where they were injected into the nearby asteroid. The monopoles entered the asteroid and in their passage through the atoms interacted with the nuclei, displacing the outer electrons. A monopole didn't orbit the nucleus like an electron. Instead, it whirled in a ring, making an electric field that held the charged nucleus, while the nucleus whirled in a linked ring to make a magnetic field that held onto the magnetically charged monopole.

With the loss of the outer electrons that determined their size, the atoms became smaller, and the rock they made up became denser. As more and more monopoles were poured in the center of the asteroid, the material there changed from normal matter, which is bloated with light electrons, into dense monopolium. The original atomic nuclei were still there; but, now with monopoles in linked orbits around them, the density increased to nearly that of a neutron star. As the total amount of converted matter in the asteroid increased, the gravitational field from the condensed matter became higher and soon began to assist in the process, crushing the electron orbits about the atoms into nuclear dimensions after they had only been partially converted into monopolium. After the month-long process was complete, the 250-kilometer-diameter asteroid had been converted into a 100-meter-diameter sphere with a core of monopolium, a mantle of degenerate matter of white dwarf density, and a glowing crust of partially collapsed normal matter.

From DRAGON'S EGG by Robert L. Forward (1980)

Nanotechnology

Nanotechnology (and it's extension nanorobotics) is the concept of molecule sized machine. The idea is attributed to Richard Feynman and it was popularized by K. Eric Drexler. It didn't take long before military researchers and science fiction writers started to speculate about weaponizing the stuff. A good science fiction novel on the subject is Wil McCarthy's Bloom.

There are many ways nanotechnology could do awful things to a military target. One of the first hypothetical applications of nanotechnology was in the manufacturing field. Molecular robots would break down chunks of various raw materials and assemble something (like, say, an aircraft), atom by atom. Naturally this could be dangerous if the nanobots landed on something besides raw materials (like, say, an enemy aircraft). However, since they are doing this atom by atom, it would take thousands of years for some nanobots to construct something (and the same thousands of years to deconstruct the source of raw materials).

But using nanobots for manufacturing suddenly becomes scary indeed if you make the little monsters into self-replicating machines (AKA a "Von Neumann universal constructor") in an attempt to reduce the thousands of years to something more reasonable. Suddenly you are facing the horror of wildfire plague spreading with the power of exponential growth. This could happen by accident, with a mutation in the nanobots causing them to devour everything in sight. Drexler called this the dreaded "gray goo" scenario. Or it could happen on purpose, weaponizing the nanobots.

Drexler is now of the opinion that nanobots for manufacturing can be done without risking gray goo. And Robert A. Freitas Jr. did some analysis that suggest that even if some nanotech started creating gray goo, it would be detectable early enough for countermeasures to deal with the problem.

What about nanobot gray goo weapons? Anthony Jackson thinks that free nanotech that operates on a time frame that's tactically relevant is in the realm of cinema, not science. And in any event, nanobots will likely be shattered by impacting the target at relative velocities higher than 3 km/s, which makes delivery very difficult. Rick Robinson is of the opinion that once you take into account the slow rate of gray goo production and the fragility of the nanobots, it would be more cost effective to just smash the target with an inert projectile. Jason Patten agrees that nanobots will be slow, due to the fact that they will not be very heat tolerant (a robot made out of only a few molecules will be shaken into bits by mild amounts of heat), and dissipating the heat energy of tearing down and rebuilding on the atomic level will be quite difficult if the heat is generated too fast.

Other weaponized applications of nanotechnology will probably be antipersonnel, not antispacecraft. They will probably take the form of incredibly deadly chemical weapons, or artificial diseases.

Some terminology: according to Chris Phoenix, "paste" is non-replicating nano-assemblers while "goo" is replicating nano-assemblers. Paste is safe, but is slow acting and limited to the number of nano-assemblers present. Goo is dangerous, but is fast acting and potentially unlimited in numbers.

"Gray or Grey goo" is accidentally created destructive nano-assemblers. "Red goo" is deliberately created destructive nano-assemblers. "Khaki goo" is military weaponized red goo. "Blue goo" is composed of "police" nanobots, it combats destructive type goos. "Green goo" is a type of red goo which controls human population growth, generally by sterilizing people. "LOR goo" (Lake Ocean River) nano-assemblers designed to remove pollution and harvest valuable elements from water, it could mutate into golden goo. "Golden goo" are out-of-control nanobots which were designed to extract gold from seawater but won't stop (the "Sorcerer's Apprentice" scenario). "Pink goo" is a humorous reference to human beings.

ACE Paste (Atmospheric Carbon Extractor) designed to absorb excess greenhouse gasses and covert them into diamonds or something useful. Garden Paste is a "utility fog" of various nanobots which helps your garden grow (manages soil density and composition for each plant type, controls insects, creates shade, store sunlight for overcast days, etc.) LOR paste: paste version of LOR goo. Medic Paste is a paste of nanobots that heals wounds, assists in diagnosis, and does medical telemetry to monitor the patient's health.

RAYMUND EICH 1

As a longtime sf fan, one of the toughest realizations I ever came to is that Space settlements will never happen for economic reasons.

In part, the costs of getting to space are too high. Charles Stross has discussed the costs at great length here. To get one person to the Moon, bringing along the life support he needs for the trip, using advanced versions of the rocket technology we have today, would cost about US$400,000 as an optimistic estimate.

So nevermind settling the solar system; the idea of normal people going into space is so expensive, it’s a non-starter.

About now, a reader might protest, “But what about nanotechnology? Advanced materials and cheap energy production will lower all those costs dramatically.”

I read Stan Schmidt’s mid-’80s Analog editorials on nanotechnology, and K. Eric Drexler’s Engines of Creation. Although I think Drexler is intoxicated with his ideas, I completely agree that some of the fruits of nanotechnology–the super-strong, super-light materials and cheap energy referred to above–are entirely possible, and are in fact likely to appear somewhere on Earth in the coming decades. Yes, those advances will make space elevators and fusion-powered torchships possible. Yes, nanotechnology would greatly lower the costs of space travel and space settlements.

But. Nanotechnology would also greatly lower the benefits of space settlement, leaving the prospect as uneconomical as it is today. More on that point in my next post.

From ECONOMICS OF SPACE SETTLEMENTS, PART I by Raymund Eich (2011)
RAYMUND EICH 2

Previously, I talked about why space settlement, using current technology, would cost too much to ever happen. But what if the costs were to drop enough, through nanotechnology or some comparable magic wand?

Simple: the price of goods sold by space settlements would be too low to pay back even those new, low costs. Why? The same nanotechnology that lowers the costs of space settlement would lower the cost of finding or making those same goods on Earth.

Consider the Niven/Pournelle dream of asteroid mining. (I cut my teeth on Pournelle’s science fact essays collected in A Step Farther Out.) All it costs to bring thousands of tons of highly pure iron or nickel to Earth from the asteroid belt are the capital and operational expenses of round-trip travel and smelting. At current nickel prices, those expenses would have to be less than about $9/lb of delivered nickel to pay off. For iron, those expenses would have to be closer to $0.10/lb of delivered iron to pay off. (Remember, using current technology, the expenses would be at least $1000/lb, if not much more).

Let’s assume nanotechnology can lower those expenses 10,000-fold. It would do so by making both the machines to do the travel and smelting work, and the energy to drive that work, much cheaper than today. So nanotech-using miners could settle the asteroid belt, ship nickel or iron to Earth, and make a profit, right?

Except for one thing. Those lower expenses for smelting machinery and the energy to run it would also apply to Earth-based mining. Reduce the costs of Earth-based mining by, let’s say, just 1000-fold, and iron and nickel deposits that today are too marginal to pay for themselves would become immensely profitable. For that matter, mining landfills and salvage lots for the iron and nickel in junked appliances and cars would become immensely profitable. I haven’t run the numbers, but I suspect it would be profitable under those conditions to extract iron at its baseline abundance of 5% in Earth’s crust.

Comparable reasoning would apply to essentially any element or compound. Regardless of the state of technology, there’s nothing useful to Earth’s economy you could find or make in space you couldn’t find or make more cheaply on Earth.

From ECONOMICS OF SPACE SETTLEMENTS, PART II by Raymund Eich (2011)
MALIGNANCY

MOST SECRET (ULTRAVIOLET) / EYES ONLY UNGUENT SANCTION

NEED-TO-KNOW ABSOLUTE
HARD COPY ONLY/NO TRANSMISSION
ORIGINATOR-CONTROLLED DISSEMINATION
TRACKED-COPY DOCUMENT
NOCONTRACT
NOFORN
SPECIAL SECURITY PROCEDURE BASILISK FIDELIS

Proceed (+/-)? +

EXECUTION:

STRATEGIC ACTION MESSAGE ONLY
IMPERIAL SECURITY EXECUTIVE ONLY
FIFTH DIRECTORATE VETO
X-THREAT ONLY

SUMMARY:

[SSP image elided from file]

The Existential Threats Primary Working Group has maintained in secure storage a number of sub-black level threats, and has access to two black-level threats, of type BURNING ZEPHYR – i.e., unlimited autonomous nanoscale replicators (“gray goo”).

Case UNGUENT SANCTION represents an extremal response case to physically manifested excessionary-level existential threats. It is hoped that, in such cases, the deployment of an existing sub-black level or black-level existential counterthreat may ideally destroy or subsume the excessionary-level threat, replacing it with one already considered manageable, or in lesser cases, at least delay the excessionary-level threat while more sophisticated countermeasures can be developed.

Note that as an extremal response case, deployment of CASE UNGUENT SANCTION requires consensus approval of the Imperial Security Executive, subject to override veto by vote of the Fifth Directorate overwatch.

WARNING:

Communicating ANY PART of this NTK-A document to ANY SOPHONT other than those with preexisting originator-issued clearance, INCLUDING ITS EXISTENCE, is considered an alpha-level security breach and will be met with the most severe sanctions available, up to and including permanent erasure.

Proceed (+/-)?

From MALIGNANCY by Alistair Young (2015)
GRIST-BASED WEAPONS

Nanotechnology
The manipulation of materials and processes on a nanometer level using tiny robotic machines (that is, machines controlled by programming) which are themselves made of only a few molecules. Nanotech was the big technological revolution following the biotech revolution.
Grist
Nanotechnological construct that incorporates the Josephson-Feynman graviton detector invented by Raphael Merced. This nano, disseminated throughout the Met, enables instantaneous information transfer over any distance that the nano is dispersed. Grist is also a word used to describe nanotechnological constructs in a general way, whether or not instantaneous information transfer is involved.
Grist-mil
Grist used for a military purpose. Many safeguards built into normal grist are removed in these constructs.
Merced Effect
The instantaneous transfer of information between locations set at any distance apart by the use of quantum-entangled gravitons.
Aspect
The biological, bodily portion of a normal person.
Convert
The algorithmic "extra" computing and memory storage portion of a normal person.
Pellicle
The nanotechnological grist that permeates a normal person. The pellicle mediates between aspect and convert portions of a person.
DIED
The Department of Immunity Enforcement Division is the collective name for the Met armed forces and the internal police force

From
Grist-based Weapons
Federal Army Field Manual
Compiled by Forward Development Lab, Triton
Gerardo Funk, Commandant

Section I: Introduction

1. Purpose and Scope
This manual is a guide for the military use of grist (grist-mil)—its use as weaponry, for the destruction of obstacles, and for covert and time-delayed attacks. Both conventional and guerrilla tactics will be considered.
2. Grist-based weapons
AKA grist-mil weapons. Grist-based weapons incorporate Josephson-Feynman nano-technology as either a means or an end to the destruction of areas, structures, materials, or people in order to achieve a military objective. They have both offensive and defensive uses. A grist-mil weapon normally consists of a nanotechnological mechanism and an algorithm, either sentient or dumb, that is in control of the deployment of the grist on a molecular level.
3.
The type of attack desired and the method of stealth employed for concealment are two complementary elements in design of these weapons and their use in the field.
4. Comments
Field users of this manual are encouraged to submit feedback for its improvement. Comments should reference section and subsection, and should be forwarded to Commandant, Forward Development Lab. Knit address: 33 Echo Replication Charlie Toro.

Section II: Tactical Considerations

Military grist is effective for both attack and defense, and for demolitions.

Direct Assault

For many applications, grist-mil can be used as-is. These weapons generally perform one or all of the following tasks:

  1. Dissolve physical integrity of defender, leading to destruction.
  2. Disable algorithm of defender's grist, leading to destruction.
  3. Sunder defender from command and control, leading to confusion and ineffectiveness on the battlefield.
  4. Subvert defender's grist to attacker's use for one of the above functions.

The general purpose is the immediate destruction of the enemy.

Delayed Assault

Often a delayed or timed assault is called for. Multiple function weapons can wait until conditions are ripe for activation. They may also carry out a series of assaults over the course of their use. When primed with a controlling algorithm of sufficient intelligence, such weapons can adapt themselves to changing battlefield conditions and prove many times more effective than "dumb" weapons.

Fortification and Defense

Defense applications include:

1. Fortification
A grist perimeter serves as both a warning device and a frontline defense against enemy assault. Such deployment is made at a company, command, or theater level.
2. Mines and minefields
See below.
3. Anti-Information Zones
Grist-mil can be deployed to cut or confuse all communication, whether grist-based or otherwise, in a given area or system (such as, for example, the human nervous system).

Direct Demolition

Grist-mil is highly effective at destroying physical facilities and cutting lines of communication. Uses include:

1. Reserved demolitions
These are preset charges of grist useful for destruction of facilities in the event of strategic withdrawal or retreat. These generally incorporate, and are under the control of, fully sentient free converts who keep them in "safe" condition until needed.
Reserved use also includes land and space minefields armed with sentient or semisentient individual devices
2. Deliberate demolitions
These are used when enemy interference is unlikely and there is sufficient time for placement. Deliberate demolitions are economical in their use of energy and computing resources, and can thus produce a much larger effect for the effort involved.
3. Hasty demolitions
These are used when time is limited and speed is more important than economy. Common sense should be exercised as much as is possible to prevent waste. In these demolitions, special care should be given to the placement of each grist-mil charge, and each charge should be primed with its controlling algorithm immediately. Even though this will take longer than normal deployment, this will make more likely a partial success of the demolition objective should the enemy interfere.

Delayed Demolition

Delayed grist-mil demolition charges are useful for the same reasons as other delayed grist-mil weaponry. Timed and delayed charges can catch an enemy off guard. Such charges can be deployed behind enemy lines for devastating effect. In this regard, they are particularly effective when combined with a stealth feature.

This use also includes land and space minefields. In addition to their use in defense and fortification, such devices can also be used as a passive means of attack if seeded behind enemy lines.


Section III: Stealth Types

Concealment

Physically concealing a weapon or demolition charge is sometimes the only option, and can be very effective when the enemy is not actively using grist-mil detection means. Weaponry grist concealed within other weapons can provide a devastating secondary attack.

Camouflage

Grist conceals itself extremely well. Sentient and semisentient grist can be made translucent to electromagnetic radiation. Isotropic effects can be used to prevent detection by other means. Generally speaking, only specialized detection grist can locate a camouflaged grist-mil weapon or demolition device.

Mimicry

Mimicking a structure, area, or person for a length of time is extremely effective and often devastating to the enemy. Sufficiently complex military-grade grist can incorporate itself into a structure or system—become a load-bearing wall, say, or white blood cells in an enemy soldier's body—and lie in wait in such circumstances. It will then activate itself for military use when conditions are ripe.


Section IV: Delivery Systems

Grist-mil delivers itself. The methods used are a sub-microscopic version of transportation systems in the visible world.

1. Mechanical transport
Grist-mil travels on wheels, legs, pseudopods. It slinks, crawls, travels by grist-made railway and highway systems that destroy themselves behind the main grist.
2. Subversion of existing transportation
Conventional transports can deliver grist-mil. In addition, grist can take control of other transportation systems—an enemy streamer bead or even an enemy's nervous system, for instance—and use that means to transport itself.
3. Physical viral transport
Grist-mil can infect like a virus. It often infiltrates enemy positions through random or partially random physical transmission.
4. Superluminal viral transport
This is perhaps the most insidious and powerful means to use grist as a weapon. An algorithm traveling instantaneously through the virtuality can overcome and subvert controlling programs at a given destination, then manufacture its own grist substrate. If security measures can be overcome, grist weapons can be delivered anywhere within the solar system instantly. This is often easier said than done, however, as security countermeasures are usually in place.

Section V: Types of Weapons and Devices

Grist-based weapons and demolition devices are rapidly changing. To cover in detail all such weapons is beyond the scope of this manual. Forward Development releases all new weaponry with tutorial and dedicated teaching converts that can conduct classes or, in extreme situations, can provide step-by-step instruction in real time as the device or weapon is being deployed. Always keep in mind that, except in the case of very complex weaponry, individual teachers are merely semisentient programs and are not free converts. Common sense should prevail when acting on their recommendations.

ASSAULT

Grist Grenades and Rockets

Grenades come in a variety of forms and are either thrown by individual soldiers or rifle-launched. Rockets are self-propelled, usually by means of a small Casimir drive engine. They can have a range of several meters to many thousands of kilometers. In ways other than propulsion, rockets are similar to grenades.

Grenades consist of a hardened containment envelope and an inside swarming with grist-mil. Often they are combined with other explosives for maximum dissemination and a multiply devastating effect.

1. Antipersonnel grenades
These contain grist-mil that attempts to attack an enemy's grist pellicle, gain access to the enemy's aspect, and then destroy the enemy by a variety of chemical, biological, or physical means. The most common type of algorithm is a simple vibration loop for the grist within the enemy. This generates enormous heat extremely quickly, vaporizing the enemy in a flash. Most grenades contain a chemical and biological backup in case the first method of attack fails to kill.
2. Antimatériel grenades
These are designed to breach minor fortifications and physical defenses for egress by attacking forces. They contain demolition algorithms that physically disassemble a given target molecule by molecule. They can also be used effectively on humans.
3. Bangalore torpedoes
These are self-propelling devices used to breach larger fortifications and grist defenses. The algorithms they employ are "smarter" than those of simple antimatériel grenades. They are used for cutting through command-or theater-level defensive grist. They are also useful for cutting through complex swaths of molecular-diameter razor wire.

DEFENSE

Zip Wire

This is molecular-diameter razor wire that can be deployed either as a single strand or in barbed-wire-like emplacements. It will cleanly slice through any material held together by normal chemical bonds. This includes flesh, bones, metal, and diamond. Septembrinni Coil is a special form of zip wire that is encoded with an algorithm that attempts to prevent reassembling of the sliced bodily portions by the enemy's pellicle. Extreme care must be taken in setting up Septembrinni Coil, as mishandling could result in irreparable decapitation or worse.

Mines

Mines vary in size and intelligence. They deploy antipersonnel grist-mil when activated, often coupled with a physical explosion for greatest effect. They have a variety of sensors for activation—usually including constantly deployed grist "outrider" scouts that collect information in a given area. Most mines have an activation range about six feet in diameter.

"Sticky mines" are devices designed not to kill instantly, but to creep into the enemy's pellicle and be carried along with the enemy to create mayhem later. See "infiltration weapons" below.

Minefields can consist of individual mines, individually triggered. More often, they are controlled by an overall "smart" algorithm. Larger minefields are controlled by a full free convert and a complementary key convert, a sentient program without a copy, residing in, and voluntarily confined to, the grist of command headquarters. Use of this key allows passage through the minefield.

Complementary minefield keys always have the rank of captain or above.

ANTI-INFORMATION WEAPONS

One of the most effective uses of grist weapons is to set up anti-information zones, often called AIZs. These can range from simple areas of message disruption—say, of brain synapses or electromagnetic transmission—to complex, self-evolving containment algorithms that do not kill, but confuse and sometimes subvert enemy forces. Enemies trapped within a complex AIZ may wander for what seems years to them. They may be subjected to hallucinations and delusions, and their mental and physical makeup may be transformed by infiltrating grist-mil. Portions of their subconscious minds may be dissociated from their personas and used against them. In fact, their interior mental landscape can be transformed into what they perceive as a wilderness or jungle—a seemingly physical place full of deadly threats.

The hallmark of this weapon is its complexity and rapid adaptation to defenses against it. Large amounts of grist-mil must go into the construction of AIZs, and the concomitant energy and matériel expenditure is considerable. The use of the weapons is therefore limited, but AIZs are extremely effective when deployed.

INFILTRATION WEAPONS

Another use of complex grist, usually under the control of a near-sentient algorithm, is for attacks behind enemy lines. This is accomplished by infiltrating grist, which takes up position either camouflaged or mimicking something else. The grist can go through various transformations itself as it is transported toward its ultimate destination. The ability to transform and remain concealed calls for long-range planning on the part of engineers and, often, high complexity within the grist itself. At times, however, even a relatively minor transformation can serve the purpose—a load-bearing wall, the severed finger or toe of an enemy, quickly regrown before the enemy is aware of the replacement. Grist-mil successfully placed in such a tactical position can contain code that activates it as a weapon when the appropriate conditions are met. Often, all the grist-mil must do is dissolve and disappear in order to wreak havoc.


Section VI: Weapons-Grade Grist

The intelligent soldier will consider the physics of the object or enemy he or she wishes to destroy. Is the target held together by ordinary means or does it use a macro version of the strong nuclear force, as does the Met cable structure and most DIED ships? Grist-mil weapons that come from Forward Development have a simple S,M,L coding on them standing for the words "small", "medium", and "large", in Basis. S class is used against individual enemy soldiers and small fortifications. It is usually a single-method weapon. M class means a weapon that is more complex—one that employs multiple attack methods in a more intelligent fashion than the S class. L class is usually under the control of a secondary copy of a free-convert soldier who is incorporated within the weapon and expects to be destroyed with its use.


Section VII: Conclusion

Military grist is deadly material and should be handled with extreme care. Its effectiveness in modern warfare is proved. Individual soldiers should become familiar with each new grist-mil weapon as it becomes available. Forward Development is intensely involved in creating more powerful military grist. All Federal Army grist-mil is fully tested, but not all has been used under battlefield conditions. Field commanders should remain alert to areas of use not covered in the supplied tutorials and teaching modules. Remember, a half-sentient teaching program is no substitute for the common sense and good judgment of the fighting soldier.

From SUPERLUMINAL by Tony Daniel (2004)

Programmable Matter

What is a Programmable Matter™ smart material?
A Programmable Matter™ smart material is any bulk substance whose physical properties can be adjusted in real time through the application of light, voltage, electric or magnetic fields, etc. Primitive forms may allow only limited adjustment of one or two traits (e.g., the "photodarkening" or "photochromic" materials found in light-sensitive sunglasses), but there are theoretical forms which, using known principles of electronics, should be capable of emulating a broad range of naturally occurring materials, or of exhibiting unnatural properties which cannot be produced by other means.
What is Wellstone™ smart material?
Wellstone™ was a hypothetical form of smart material first proposed by Wil McCarthy in his novella "Once Upon a Matter Crushed" (Science Fiction Age, May 1999), consisting of nanoscopic semiconductor threads covered with quantum dots. These threads can be woven together to form a bulk solid with real-time adjustable properties. The terms "Wellstone™" and "Programmable Matter™" are occasionally incorrectly used interchangeably, although many other forms of smart materials exist.
Is this science fiction?
No. Various forms of smart material have appeared in fiction, but are in many cases based on technologies which exist today, or on reasonable extrapolations from them.
Where is smart material research being conducted?
Various aspects of smart materials (including quantum dots, electrochromic materials, magnetoreheologic materials, and various kinds of fiber-based circuitry) are under investigation in labs all over the world. Major players include (but are by no means limited to) IBM, Nippon Telehone and Telegraph, Fujitsu, Delft University, MIT, Harvard, Stanford, Princeton, Cornell, CalTech, and The University of California at Santa Barbara. Wellstone™, Wafflestone™, and Gridwell™, using quantum dots incorporated into fibers, ribbons, and plates are under explicit investigation at the Programmable Matter™ Corporation.
Are smart materials the same thing as nanotechnology?
Yes and no. The word "nanotechnology" simply means "technology on the scale of nanometers," or billionths of a meter, i.e. technology on the molecular scale. Most forms of Programmable Matter™ smart materials rely on nano-circuitry, designer molecules, or both, so in this literal sense they are nanotechnology. However, as originally coined by K. Eric Drexler in the 1980s and as commonly used by lay persons today, the word nanotechnology implies nanoscale machinery, more properly known as molecular nanotechnology or MNT. While bulk materials incorporating MNT may have programmable properties, they also have moving parts. Our smart materials do not rule out such materials, but more typically refers to substances whose properties can be adjusted in the solid state, with no moving parts other than photons and electrons.
Are Programmable Matter™ smart materials the same thing as MEMS?
No. Micro Electromechanical Systems, or MEMS, are microscopic machines crafted using standard methods for the manufacture of microchips. MEMS have many useful applications in the real world, but are far too large to exhibit the quantum effects necessary to affect the bulk properties of matter. However, the "Utility Fog" substance proposed by J. Storrs Hall in the early 1990s, consisting of millions or billions of MEMS micromachines — each with with 12 retractable, linkable arms -- has numerous adjustable bulk properties and can thus be considered a crude, mechanical form of smart materials. Also, The Programmable Matter™ Corporation is exploring the possible uses of Wellstone™ smart materials to enhance the properties of MEMS.
Is a cellular automaton computer simulation a smart material?
Yes, although technically speaking, a cellular automaton can only contain virtual smart material, whereas physical examples which meet the definition are available in the real world.
Does an LCD screen qualify as a smart material ? Does a transistor?
An LCD screen's optical properties can be dramatically altered by the application of electrical signals. Thus, it is clearly a form of smart material, albeit a simple one. A transistor can switch between an electrically conductive state and an electrically insulative one, but is properly a "device" rather than a substance or material. However, a bulk material fashioned from transistors (transistronium?) would be electrically switchable between these two states, and possibly numerous intermediate states. This meets (trivially) the definition for smart material stated above. In general, the more capable forms of Programmable Matter™ smart materials rely on the doping effects of "artificial atoms" or "quantum dots" inside a bulk material.
What is doping?
Doping is the addition of impurities (dopants) to a bulk material (the substrate) in order to adjust its electrical, thermal, optical, or magnetic properties. The addition of one dopant atom per million atoms of substrate is often sufficient to cause major changes in the material's behavior, and impurities in the parts-per-billion can disrupt the expected behavior of a pure crystal.
What is quantum confinement?
Quantum confinement is the trapping of electrons or electron "holes" (charge carriers) in a space small enough that their quantum (wavelike) behavior dominates over their classical (particle-like) behavior. In quantum mechanical terms, for quantum confinement to occur the dimension of the confining device or particle must be comparable to, or smaller than, the de Broglie wavelength of the carriers, and also the carrier inelastic mean free path IMFP and electron-hole Bohr radius of the material it's made from. Under cryogenic conditions, this typically occurs with dimensions of 1000 nm (0.001 mm) or less. At room temperature, depending on the materials, confinement dimensions of 20 nm or smaller are typically required.
What are quantum dots and artificial atoms? Are they the same thing?
A quantum dot is any device capable of the quantum confinement of electrons (for holes, it becomes an "antidot"). Once the electrons are confined, they repel one another and also obey the Pauli Exclusion Principle, which forbids any two electrons from having the same quantum state. Thus, the electrons in a quantum dot will form shells and orbitals highly reminiscent of (though larger than) the ones in an atom, and will in fact exhibit many of the optical, electrical, thermal, and (to some extent) chemical properties of an atom. This electron cloud is therefore referred to as an artificial atom. In their various forms, quantum dots may be referred to as single-electron transistors, controlled potential barriers, Coulomb islands, zero dimensional electron gases, colloidal nanoparticles or semiconductor nanocrystals.
What is a quantum well?
A quantum well is a device for confining electrons in one dimension, such that their quantum (wavelike) behavior dominates over their classical (particle-like) behavior along the confined axis, while classical behavior dominates along the other two axes, permitting the electrons to flow two-dimensionally through the material like billiard balls on a table. A typical quantum well may be fashioned from an N-type semiconductor, doped with electron donor atoms, trapped between two layers of P-type semiconductor, doped with electron borrower atoms. Other arrangements, such as a metal layer sandwiched between two insulators, are also possible. A quantum well is the primary component of miniature laser pointers.
What are Programmable Matter™ smart materials made of?
Programmable Matter™ smart materials are composed of manmade objects too small to perceive directly with the human senses. This may include microscopic or nanoscopic machines, but more typically refers to fixed arrangements of conductors, semiconductors, and insulators designed to trap electrons in artificial atoms.
How are Programmable Matter™ smart materials made?
Current forms of quantom dot smart materials fall into three types: colloidal films, bulk crystals, and quantum dot chips which confine electrons electrostatically. Quantum dots can be grown chemically as nanoparticles of semiconductor surrounded by an insulating layer. These particles can then be deposited onto a substrate, such as a semiconductor wafer patterned with metal electrodes, or they can be crystalized into bulk solids by a variety of methods. Either substance can be stimulated with electricity or light (e.g., lasers) in order to change its properties.

Electrostatic quantum dots are patterns of conductor (usually a metal such as gold) laid down on top of a quantum well, such that varying the electrical voltage on the conductors can drive electrons into and out of a confinement region in the well — the quantum dot. This method offers numerous advantages over nanoparticle ("colloidal") films, including a greater control over the artificial atom's size, composition, and shape. Numerous quantum dots can be placed on the same chip, forming a semiconductor material with a programmable dopant layer near its surface. A number of fabrication technologies exist whose resolution is sufficient to produce room-temperature quantum dot devices. Rolling such quantum dot chips into cylindrical fibers produces Wellstone™ smart material, a hypothetical woven solid whose bulk properties are broadly programmable.
Can Programmable Matter™ smart materials mimic the substances on the periodic table?
Yes. Artificial atoms can easily be constructed which mimic the properties of any natural atom, except that they are larger and their electrons are bound more loosely. However, these artificial atoms have negligible mass, and can exist only inside the quantum-dot substrate which generates them, usually a semiconductor. Thus, the final properties of the material are a blend of the simulated element and the underlying substrate. Note that the color of an artificial element made of oversized atoms would be redshifted as compared with the equivalent natural element.
Is this alchemy? Can it convert lead into gold?
Yes and no. An artificial atom of pseudo-lead (atomic number 82), trapped permanently inside a semiconductor material, can be converted to an artificial atom of pseudo-gold (atomic number 79) by the subtraction of three electrons. Sufficient numbers of these pseudoatoms may overwhelm the natural behavior of the semiconductor to produce a metal-like material similar to lead or gold, except for its mass, ductility, and probably color. Artificial atoms designed to mimic the colors of lead or gold might have other properties (e.g., electrical or thermal conductivity) which do not match the original metal.
Can Programmable Matter™ smart materials mimic transuranic elements?
Yes. An artificial atom can contain any number of electrons, from 1 to over 1000. The form and properties of highly transuranic atoms (atomic number >> 92) are dramatically different from those of natural atoms.
Aren't these transuranic elements highly unstable? Can you create nuclear reactions with them?
Electrons in an atom are confined by their attraction to the nucleus, and the nuclei of highly transuranic elements are unstable. However, an artificial atom does not have a nucleus of its own, relying instead on geometry, insulative barriers, and/or electrostatic repulsion to confine its electrons inside a semiconductor substrate. Thus, transuranic artificial atoms are stable as long as the device containing the electrons continues operating. The only atomic nuclei present are those of the metal and/or semiconductor atoms which make up the quantum dot. Because the confined electrons cannot affect the properties of these nuclei, they cannot be used to trigger or modify nuclear reactions. An artificial atom with 92 electrons in it is not "real" uranium, and will not be radioactive.
Can Programmable Matter™ smart materials be used to create superstrong materials?
Probably not. The binding energy of artificial atoms cannot exceed the binding energy of the semiconductor substrate. However, using diamond fibers or fullerenes as a substrate should allow for some very tough smart materials. Also, changes in the magnetic behavior of a material can affect its stiffness and tensile/compressive strength in useful ways.
What does "unnatural properties" mean?
Unlike natural atoms, artificial atoms can be square, pyramidal, two-dimensional, highly transuranic, composed of charged particles other than electrons (e.g., "holes"), and can even be asymmetrical. Their size, energy, and shape are variable quantities. Thus, artificial atoms exhibit optical, electrical, thermal, magnetic, mechanical, and (to some extent) chemical behaviors which do not occur in natural materials. This variety is bounded but infinite, in sharp contrast to the 92 stable atoms of the periodic table.
What does matter made of artificial atoms feel like? Is is solid?
Artificial atoms can exist only inside a semiconductor substrate. They are charge discontinuities rather than physical objects, so they don't "feel" like anything. However, their doping effects can dramatically alter the properties of the substrate, causing it to feel different. For example, a dramatic increase in thermal and electrical conductivity would make the semiconductor feel (in terms of thermal response) like a metal.
What are Programmablse Matter™ smart materials good for?
Almost anything. They can improve the efficient collection, storage, distribution, and use of energy from environmental sources. They can be used to create novel sensors and computing devices, probably including quantum computers. They can create materials which are not available by other means, and which change their apparent composition on demand. Currently, the design of new materials is a time- and labor-intensive process; with Programmable Matter™ smart materials, it becomes a real-time issue, similar to the design and debugging of software.
Who is Wil McCarthy?
Wil McCarthy, an aerospace engineer, is a contributing editor for WIRED magazine, the science columnist for the SciFi channel web site www.scifi.com, and an author of numerous book-length works of science fact and science fiction. He has written extensively about quantum dots and smart materials, and faces a consistent set of questions, objections, and misconceptions when presenting this material. This FAQ is intended to promote intelligent discussion of smart materials and quantum dots by increasing awareness of their underlying issues and principles.
Who invented this?
Single-electron transistors, a form of quantum dot, were first proposed by A.A. Likharev in 1984 and constructed by Gerald Dolan and Theodore Fulton at Bell Laboratories in 1987. The first semiconductor SET, a type of quantum dot sometimes referred to as a designer atom, was invented by Marc Kastner and John Scott-Thomas at MIT in 1989. The term "artificial atom" was coined by Kastner in 1993. However, Wil McCarthy was the first to use the term "Programmable Matter™" in connection with quantum dots, and to propose a mechanism for the precise, 3D control of large numbers of quantum dots inside a bulk material. The most interesting forms of this device or substance -- known as "quantum dot fiber", "programmable dopant fiber", or "Wellstone™" — are under development at The Programmable Matter™ Corporation. The term "Wellstone™" was coined by McCarthy's business associate, Gary E. Snyder.
Are there unresolved issues regarding Programmable Matter™ smart materials?
Quantum dots are a new field with much basic research still remaining, so the ultimate properties of bulk quantum-dot materials cannot be known with precision at this time. However, the principles underlying quantum confinement are fairly well understood, and the experimental evidence overwhelmingly indicates that programmable quantum-dot smart materials are feasible, and will play an important role in future technology. Many issues have been considered, and many more are under investigation.
Is the technology patented?
Wil McCarthy and Gary E. Snyder hold pending U.S. patents on the concept, one entitled "Fiber Incorporating Quantum Dots as Programmable Dopants", filed 13 August 2001.
Where can I learn more?
The best online reference for lay readers is "Ultimate Alchemy," a 7,000-word article from WIRED magazine available (minus the pictures) at: http://www.wired.com/wired/archive/9.10/atoms.html.

Offline lay-references include Richard Turton's THE QUANTUM DOT: A Journey into the Future of Microelectronics (Oxford University Press, 1996, ISBN 0-195-10959-7).

and Wil McCarthy's HACKING MATTER: Levitating Chairs, Quantum Mirages, and the Infinite Weirdness of Programmable Atoms (Basic Books, 2003, ISBN 0-465-04429-8).

For serious theoreticians, Paul Harrison's Quantum Wells, Wires, and Dots (Wiley, 2000, ISBN 0-471-98495-7) provides equations and computer code for estimating the behavior of confined electrons.
From The Programmable Matter Corporation

Computronium

Computronium is a material hypothesized by Norman Margolus and Tommaso Toffoli of the Massachusetts Institute of Technology to be used as "programmable matter," a substrate for computer modeling of virtually any real object. It also refers to a theoretical arrangement of matter that is the best possible form of computing device for that amount of matter.


COMPUTRONIUM
Matter that has been transformed from its natural state into an optimized, maximally efficient computer. (A true Extropian would argue that this is matter's "natural state".)

What constitutes "computronium" varies with the level of postulated technology. A rod logic nanocomputer is probably too primitive to qualify as computronium, since large molecular aggregates (hundreds or thousands of atoms) are used as computing elements. A more archetypal computronium would be a three-dimensional cellular automaton which attached computational significance to each individual atom, perhaps with quantum-computing elements included.

More exotic forms of computronium include neutronium, Higgsium, monopolium, or — my personal invention — an interlaced structure of positive-matter and negative-matter monopolium wrapped up in a fractal Van Den Broeck warp. (The total mass is zero, so the whole doesn't undergo gravitational collapse. If paired negative and positive matter can be manufactured in unlimited quantities, the fractal Van Den Broeck warp can continue extending indefinitely and exponentially. Threading the system with wormholes keeps latency down. And the whole thing fits in your pocket.)
From CREATING FRIENDLY AI by Singularity Institute for Artificial Intelligence, Inc. (2001)

Room Temperature Superconductor

Superconductors are nifty wires that have exactly zero resistance to the flow of electricity. They are vital to the construction of ultra-powerful magnets (for coilguns, particle beam weapons, and some propulsion systems) and for hyperfast computers.

The first superconductors had to be cooled with expensive and troublesome liquid helium. They became practical when new superconductors were discovered which could work with cheap and easy liquid nitrogen.

But the holy grail is a superconductor that doesn't need to be cooled at all. These are high-temperature superconductors, colloquially called "room-temperature superconductors."

Larry Niven used superconductors a lot in his Known Space series, especially Ringworld. His electrical superconductors are also superconductors of heat, which I have so far failed to find a reference on that topic.

HIGH-TEMPERATURE SUPERCONDUCTIVITY

High-temperature superconductors (abbreviated high-Tc or HTS) are materials that behave as superconductors at unusually high temperatures. The first high-Tc superconductor was discovered in 1986 by IBM researchers Georg Bednorz and K. Alex Müller, who were awarded the 1987 Nobel Prize in Physics "for their important break-through in the discovery of superconductivity in ceramic materials".

Whereas "ordinary" or metallic superconductors usually have transition temperatures (temperatures below which they are superconductive) below 30 K (−243.2 °C), and must be cooled using liquid helium in order to achieve superconductivity, HTS have been observed with transition temperatures as high as 138 K (−135 °C), and can be cooled to superconductivity using liquid nitrogen. Until 2008, only certain compounds of copper and oxygen (so-called "cuprates") were believed to have HTS properties, and the term high-temperature superconductor was used interchangeably with cuprate superconductor for compounds such as bismuth strontium calcium copper oxide (BSCCO) and yttrium barium copper oxide (YBCO). Several iron-based compounds (the iron pnictides) are now known to be superconducting at high temperatures.

In 2015, hydrogen sulfide (H2S) under extremely high pressure (around 150 gigapascals) was found to undergo superconducting transition near 203 K (-70 °C), the highest temperature superconductor known to date.

For an explanation about Tc (the critical temperature for superconductivity), see Superconductivity § Superconducting phase transition and the second bullet item of BCS theory § Successes of the BCS theory.

History

The phenomenon of superconductivity was discovered by Kamerlingh Onnes in 1911, in metallic mercury below 4 K (−269.15 °C). Ever since, researchers have attempted to observe superconductivity at increasing temperatures with the goal of finding a room-temperature superconductor. In the late 1970s, superconductivity was observed in certain metal oxides at temperatures as high as 13 K (−260.1 °C), which were much higher than those for elemental metals. In 1986, J. Georg Bednorz and K. Alex Müller, working at the IBM research lab near Zurich, Switzerland were exploring a new class of ceramics for superconductivity. Bednorz encountered a barium-doped compound of lanthanum and copper oxide whose resistance dropped down to zero at a temperature around 35 K (−238.2 °C). Their results were soon confirmed by many groups, notably Paul Chu at the University of Houston and Shoji Tanaka at the University of Tokyo.

Shortly after, P. W. Anderson, at Princeton University came up with the first theoretical description of these materials, using the resonating valence bond theory, but a full understanding of these materials is still developing today. These superconductors are now known to possess a d-wave pair symmetry. The first proposal that high-temperature cuprate superconductivity involves d-wave pairing was made in 1987 by Bickers, Scalapino and Scalettar, followed by three subsequent theories in 1988 by Inui, Doniach, Hirschfeld and Ruckenstein, using spin-fluctuation theory, and by Gros, Poilblanc, Rice and Zhang, and by Kotliar and Liu identifying d-wave pairing as a natural consequence of the RVB theory. The confirmation of the d-wave nature of the cuprate superconductors was made by a variety of experiments, including the direct observation of the d-wave nodes in the excitation spectrum through Angle Resolved Photoemission Spectroscopy, the observation of a half-integer flux in tunneling experiments, and indirectly from the temperature dependence of the penetration depth, specific heat and thermal conductivity.

Until 2015 the superconductor with the highest transition temperature that had been confirmed by multiple independent research groups (a prerequisite to be called a discovery, verified by peer review) was mercury barium calcium copper oxide (HgBa2Ca2Cu3O8) at around 133 K.

After more than twenty years of intensive research, the origin of high-temperature superconductivity is still not clear, but it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity, one is dealing with genuine electronic mechanisms (e.g. by antiferromagnetic correlations), and instead of conventional, purely s-wave pairing, more exotic pairing symmetries are thought to be involved (d-wave in the case of the cuprates; primarily extended s-wave, but occasionally d-wave, in the case of the iron-based superconductors). In 2014, evidence showing that fractional particles can happen in quasi two-dimensional magnetic materials, was found by EPFL scientists lending support for Anderson's theory of high-temperature superconductivity.

Properties

"High-temperature" has two common definitions in the context of superconductivity:

  1. Above the temperature of 30 K that had historically been taken as the upper limit allowed by BCS theory(1957). This is also above the 1973 record of 23 K that had lasted until copper-oxide materials were discovered in 1986.
  2. Having a transition temperature that is a larger fraction of the Fermi temperature than for conventional superconductors such as elemental mercury or lead. This definition encompasses a wider variety of unconventional superconductors and is used in the context of theoretical models.

The label high-Tc may be reserved by some authors for materials with critical temperature greater than the boiling point of liquid nitrogen (77 K or −196 °C). However, a number of materials – including the original discovery and recently discovered pnictide superconductors – had critical temperatures below 77 K but are commonly referred to in publication as being in the high-Tc class.

Technological applications could benefit from both the higher critical temperature being above the boiling point of liquid nitrogen and also the higher critical magnetic field (and critical current density) at which superconductivity is destroyed. In magnet applications, the high critical magnetic field may prove more valuable than the high Tc itself. Some cuprates have an upper critical field of about 100 tesla. However, cuprate materials are brittle ceramics which are expensive to manufacture and not easily turned into wires or other useful shapes. Also, high-temperature superconductors do not form large, continuous superconducting domains, but only clusters of microdomains within which superconductivity occurs. They are therefore unsuitable for applications requiring actual superconducted currents, such as magnets for magnetic resonance spectrometers.

After two decades of intense experimental and theoretical research, with over 100,000 published papers on the subject, several common features in the properties of high-temperature superconductors have been identified. As of 2011, no widely accepted theory explains their properties. Relative to conventional superconductors, such as elemental mercury or lead that are adequately explained by the BCS theory, cuprate superconductors (and other unconventional superconductors) remain distinctive. There also has been much debate as to high-temperature superconductivity coexisting with magnetic ordering in YBCO, iron-based superconductors, several ruthenocuprates and other exotic superconductors, and the search continues for other families of materials. HTS are Type-II superconductors, which allow magnetic fields to penetrate their interior in quantized units of flux, meaning that much higher magnetic fields are required to suppress superconductivity. The layered structure also gives a directional dependence to the magnetic field response.

From the Wikipedia entry for HIGH-TEMPERATURE SUPERCONDUCTIVITY

Molecule Chain

This is an unnaturally strong thread one molecule thick. This means it has remarkably low mass per towing capacity, which makes it popular for moving asteroids and for waterskiing spacecraft and starships.

It will basically cut through anything except another molecule chain. Naturally it is also used to make edged weapons.

MONOMOLECULAR WIRE

In fiction

Monomolecular wire is often used as a weapon in fiction. It has applications in cutting objects and severing adjacent molecules. A similar or identical concept may be called a microfilament wire or, as a weapon, a microfilament whip.

Among the first references in fiction to a monofilament is in John Brunner's Stand on Zanzibar (1968), where hobby terrorists deploy this over-the-shelf General Technics product across roads to kill or injure the people passing there. According to Brunner, the monofilament will easily cut through glass, metal and flesh, but in any non-strained structure the molecules will immediately rebond. No harm is done if the cut object is not under mechanical stress.

An early example of a substance similar to monomolecular wire is 'borazon-tungsten filament' from G. Randall Garrett's "Thin Edge." (Analog, Dec 1963) The main character uses a strand from an asteroid towing-cable to cut jail bars and to booby-trap the door of his room. Frank Herbert later described shigawire in his Dune novels. First making its appearance in Dune (1965), shigawire is a metallic extrusion produced naturally from a ground vine found on the planets Salusa Secundus and III Delta Kaising. It varies in diameter from approximately 1.5 cm down to monomolecular (micronic) diameters, and is notable for its incredible tensile and mechanical strength. Shigawire is able to cut through almost any material cleanly, possessing edges that are incredibly sharp. It is a weapon of choice for assassins.

Monomolecular wire is a plot element in the short story "Johnny Mnemonic" by William Gibson. The assassin following the protagonist has a diamond spindle of monomolecular wire (or filament) implanted in his thumb, the idea being that diamond is also made of a single molecule and thus hard enough to not be cut by a monomolecular wire. The top of a prosthesis, attached to the other side of the wire, was used as a weight and the wire could be used as a whip-like weapon or a garotte.

Monomolecular wire (in the form of wide 'tapes' of a "pseudo-one-dimensional modified diamond crystal") is used as the basic building material of the space elevator in Arthur C. Clarke's novel The Fountains of Paradise.

Monomolecular wires are seen in the Star Wars expanded universe, Cyber City Oedo 808, Hyperion Cantos, Robert J. Sawyer's Illegal Alien, Battle Angel Alita, Naruto, Akame ga Kill, Hellsing, Trinity Blood, My-Hime, Vampire Knight, Simon R. Green's Deathstalker series, Alastair Reynolds's Revelation Space universe, as well as the roleplaying games Shadowrun, One Piece as Doflamingo's string-string devil fruit and Cyberpunk 2020. Monomolecular wires are also seen in Larry Niven's "Known Space" universe as human-produced "Sinclair Molecule Chain".

In the One Piece manga, the character Donquixote Doflamingo ate the Ito Ito no Mi, a devil fruit that grants the user the ability to create and manipulate strings. He is capable of creating strings so thin that they cannot be seen, and he can use this ability to ensnare people and control them like a puppet. His strings are also incredibly strong, being able to cut through stone with ease.

Various Imperial and alien technologies in the Warhammer 40,000 universe use monomolecular blades or wire offensively. Possibly the most notable example are Eldar Warp Spiders, whose Deathspinner weaponry traps targets in a mesh of such filaments or the Dark Eldar Shredder weapon which shoots meshes of it.

The game Chaos Overlords featured a weapon 'monom rod' which used this technology.

Sion Eltnam Atlasia wields a monofilament whip called the Etherlite in Melty Blood.

In the 2000 film XChange, the main character acquires an Urban survival Kit which includes a monomolecular wire.

Monomolecular swords are used by some Kzin in Larry Niven's Known Space series.

Monomolecular wire ranks 14th on IGN's list of the "25 Coolest Sci-Fi weapons".

From the Wikipedia entry for MONOMOLECULAR WIRE
THIN EDGE

      The instrument man opened the outer door and saw the surface of the gigantic rock a couple of yards in front of him. And projecting from that surface was the eye of an eyebolt that had been firmly anchored in the depths of the asteroid, a nickel-steel shaft thirty feet long and eight inches in diameter, of which only the eye at the end showed.
     The instrument man checked to make sure that his safety line was firmly anchored and then pushed himself across the intervening space to grasp the eye with a space-gloved hand.
     This was the anchor.
     Moving a nickel-iron asteroid across space to nearest processing plant is a relatively simple job. You slap a powerful electromagnet on her, pour on the juice, and off you go.
     The stony asteroids are a different matter. You have to have something to latch on to, and that’s where the anchor-setter comes in. His job is to put that anchor in there. That’s the first space job a man can get in the Belt, the only way to get space experience. Working by himself, a man learns to preserve his own life out there.
     Operating a space tug, on the other hand, is a two-man job because a man cannot both be on the surface of the asteroid and in his ship at the same time. But every space tug man has had long experience as an anchor setter before he’s allowed to be in a position where he is capable of killing someone besides himself if he makes a stupid mistake in that deadly vacuum.
     “On contact, Jack,” the instrument man said as soon as he had a firm grip on the anchor. “Release safety line.”
     “Safety line released, Harry,” Jack’s voice said in his earphones.
     Jack had pressed a switch that released the ship’s end of the safety line so that it now floated free. Harry pulled it towards himself and attached the free end to the eye of the anchor bolt, on a loop of nickel-steel that had been placed there for that purpose. “Safety line secured,” he reported. “Ready for tug line.”
     In the pilot’s compartment, Jack manipulated the controls again. The ship moved away from the asteroid and yawed around so that the “tail” was pointed toward the anchor bolt. Protruding from a special port was a heavy-duty universal joint with special attachments. Harry reached out, grasped it with one hand, and pulled it toward him, guiding it toward the eyebolt. A cable attached to its other end snaked out of the tug.
     Harry worked hard for some ten or fifteen minutes to get the universal joint firmly bolted to the eye of the anchor. When he was through, he said: “O.K., Jack. Try ’er.”
     The tug moved gently away from the asteroid, and the cable that bound the two together became taut. Harry carefully inspected his handiwork to make sure that everything had been done properly and that the mechanism would stand the stress.
     “So far so good,” he muttered, more to himself than to Jack.
     Then he carefully set two compact little strain gauges on the anchor itself, at ninety degrees from each other on the circumference of the huge anchor bolt. Two others were already in position in the universal joint itself. When everything was ready, he said: “Give ’er a try at length.”
     The tug moved away from the asteroid, paying out the cable as it went.
     Hauling around an asteroid that had a mass on the order of one hundred seventy-four million metric tons required adequate preparation.
     This particular asteroid presented problems. Not highly unusual problems, but problems nonetheless. It was massive and had a high rate of spin. In addition, its axis of spin was at an angle of eighty-one degrees to the direction in which the tug would have to tow it to get it to the processing plant. The asteroid was, in effect, a huge gyroscope, and it would take quite a bit of push to get that axis tilted in the direction that Harry Morgan and Jack Latrobe wanted it to go. In theory, they could just have latched on, pulled, and let the thing precess in any way it wanted to. The trouble is that that would not have been too good for the anchor bolt. A steady pull on the anchor bolt was one thing: a nickel-steel bolt like that could take a pull of close to twelve million pounds as long as that pull was along the axis. Flexing it—which would happen if they let the asteroid precess at will—would soon fatigue even that heavy bolt.
     The cable they didn’t have to worry about. Each strand was a fine wire of two-phase material—the harder phase being borazon, the softer being tungsten carbide. Winding these fine wires into a cable made a flexible rope that was essentially a three-phase material—with the vacuum of space acting as the third phase. With a tensile strength above a hundred million pounds per square inch, a half inch cable could easily apply more pressure to that anchor than it could take. There was a need for that strong cable: a snapping cable that is suddenly released from a tension of many millions of pounds can be dangerous in the extreme, forming a writhing whip that can lash through a spacesuit as though it did not exist. What damage it did to flesh and bone after that was of minor importance; a man who loses all his air in explosive decompression certainly has very little use for flesh and bone thereafter.

     “What…what do you want?” Fergus asked.
     “I want to give you the information you want. The information that you killed Jack for.” There was cold hatred in his voice. “I am going to tell you something that you have thought you wanted, but which you really will wish you had never heard. I’m going to tell you about that cable.”
     Neither Fergus nor Tarnhorst said a word.
     “You want a cable. You’ve heard that we use a cable that has a tensile strength of better than a hundred million pounds per square inch, and you want to know how it’s made. You tried to get the secret out of Jack because he was sent here as a commercial dealer. And he wouldn’t talk, so one of your goons blackjacked him too hard and then you had to drop him off a bridge to make it look like an accident.
     “Then you got your hands on me. You were going to wring it out of me. Well, there is no necessity of that.” His grin became wolfish. “I’ll give you everything.” He paused. “If you want it.”
     Fergus found his voice. “I want it. I’ll pay a million—”
     “You’ll pay nothing,” Morgan said flatly. “You’ll listen.”
     Fergus nodded wordlessly.
     “The composition is simple. Basically, it is a two-phase material-like fiberglass. It consists of a strong, hard material imbedded in a matrix of softer material. The difference is that, in this case, the stronger fibers are borazon—boron nitride formed under tremendous pressure—while the softer matrix is composed of tungsten carbide. If the fibers are only a thousandth or two thousandths of an inch in diameter—the thickness of a human hair or less—then the cable from which they are made has tremendous strength and flexibility.
     “Do you want the details of the process now?” His teeth were showing in his wolfish grin.
     Fergus swallowed. “Yes, of course. But…but why do you—”
     “Why do I give it to you? Because it will kill you. You have seen what the stuff will do. A strand a thousandth of an inch thick, encased in silon for lubrication purposes, got me out of that filthy hole you call a prison. You’ve heard about that?”
     Fergus blinked. “You cut yourself out of there with the cable you’re talking about?
     “Not with the cable. With a thin fiber. With one of the hairlike fibers that makes up the cable. Did you ever cut cheese with a wire? In effect, that wire is a knife—a knife that consists only of an edge.
     “Or, another experiment you may have heard of. Take a block of ice. Connect a couple of ten-pound weights together with a few feet of piano wire and loop it across the ice block to that the weights hang free on either side, with the wire over the top of the block. The wire will cut right through the ice in a short time. The trouble is that the ice block remains whole—because the ice melts under the pressure of the wire and then flows around it and freezes again on the other side. But if you lubricate the wire with ordinary glycerine, it prevents the re-freezing and the ice block will be cut in two.”
     Tarnhorst nodded. “I remember. In school. They—” He let his voice trail off.
     “Yeah. Exactly. It’s a common experiment in basic science. Borazon fiber works the same way. Because it is so fine and has such tremendous tensile strength, it is possible to apply a pressure of hundreds of millions of pounds per square inch over a very small area. Under pressures like that, steel cuts easily. With silon covering to lubricate the cut, there’s nothing to it. As you have heard from the guards in your little hell-hole.
     “Hell-hole?” Tarnhorst’s eyes narrowed and he flicked a quick glance at Fergus. Morgan realized that Tarnhorst had known nothing of the extent of Fergus’ machinations.
     “That lovely little political prison up in Fort Tryon Park that the World Welfare State, with its usual solicitousness for the common man, keeps for its favorite guests,” Morgan said. His wolfish smile returned. “I’d’ve cut the whole thing down if I’d had had the time. Not the stone—just the steel. In order to apply that kind of pressure you have to have the filament fastened to something considerably harder than the stuff you’re trying to cut, you see. Don’t try it with your fingers or you’ll lose fingers.”
     Fergus’ eyes widened again and he looked both ill and frightened. “The man we sent…uh…who was found in your room. You—” He stopped and seemed to have trouble swallowing.
     “Me? I didn’t do anything.” Morgan did a good imitation of a shark trying to look innocent. “I’ll admit that I looped a very fine filament of the stuff across the doorway a few times, so that if anyone tried to enter my room illegally I would be warned.” He didn’t bother to add that a pressure-sensitive device had released and reeled in the filament after it had done its work. “It doesn’t need to be nearly as tough and heavy to cut through soft stuff like…er…say, a beefsteak, as it does to cut through steel. It’s as fine as cobweb almost invisible. Won’t the World Welfare State have fun when that stuff gets into the hands of its happy, crime-free populace?”
     Edway Tarnhorst became suddenly alert. “What?”
     “Yes. Think of the fun they’ll have, all those lovely slobs who get their basic subsistence and their dignity and their honor as a free gift from the State. The kids, especially. They’ll love it. It’s so fine it can be hidden inside an ordinary thread—or woven into the hair—or…” He spread his hands. “A million places.”
     Fergus was gaping. Tarnhorst was concentrating on Morgan’s words.
     “And there’s no possible way to leave fingerprints on anything that fine,” Morgan continued. “You just hook it around a couple of nails or screws, across an open doorway or an alleyway—and wait.”
     “We wouldn’t let it get into the people’s hands,” Tarnhorst said.
     “You couldn’t stop it,” Morgan said flatly. “Manufacture the stuff and eventually one of the workers in the plant will figure out a way to steal some of it.”
     “Guards—” Fergus said faintly.
     “Pfui. But even you had a perfect guard system, I think I can guarantee that some of it would get into the hands of the—common people. Unless you want to cut off all imports from the Belt.”
     Tarnhorst’s voice hardened. “You mean you’d deliberately—”
     “I mean exactly what I said,” Morgan cut in sharply. “Make of it what you want.”
     “I suppose you have that kind of trouble out in the Belt?” Tarnhorst asked.
     “No. We don’t have your kind of people out in the Belt, Mr. Tarnhorst. We have men who kill, yes. But we don’t have the kind of juvenile and grown-up delinquents who will kill senselessly, just for kicks. That kind is too stupid to live long out there. We are in no danger from borazon-tungsten filaments. You are.” He paused just for a moment, then said: “I’m ready to give you the details of the process now, Mr. Fergus.”
     “I don’t think I—” Fergus began with a sickly sound in his voice. But Tarnhorst interrupted him.
     “We don’t want it, commodore. Forget it.”
     “Forget it?” Morgan’s voice was as cutting as the filament he had been discussing. “Forget that Jack Latrobe was murdered?”
     “We will pay indemnities, of course,” Tarnhorst said, feeling that it was futile.
     “Fergus will pay indemnities,” Morgan said. “In money, the indemnities will come to the precise amount he was willing to pay for the cable secret. I suggest that your Government confiscate that amount from him and send it to us. That may be necessary in view of the second indemnity.”
     “Second indemnity?”
     “Mr. Fergus’ life.”
     Tarnhorst shook his head briskly. “No. We can’t execute Fergus. Impossible.”
     “Of course not,” Morgan said soothingly. “I don’t suggest that you should. But I do suggest that Mr. Fergus be very careful about going through doorways—or any other kind of opening—from now on. I suggest that he refrain from passing between any pair of reasonably solid, well-anchored objects. I suggest that he stay away from bathtubs. I suggest that he be very careful about putting his legs under a table or desk. I suggest that he not look out of windows. I could make several suggestions. And he shouldn’t go around feeling in front of him, either. He might lose something.”
     “I understand,” said Edway Tarnhorst.
     So did Sam Fergus. Morgan could tell by his face.

From THIN EDGE by Randall Garrett (1963)
A GIFT FROM EARTH

Interstellar Ramscoop Robot #143 left Juno at the end of a linear accelerator. Coasting toward interstellar space, she looked like a huge metal insect, makeshift and hastily built. Yet, except for the contents of her cargo pod, she was identical to the last forty of her predecessors. Her nose was the ramscoop generator, a massive, heavily armored cylinder with a large orifice in the center. Along the sides were two big fusion motors, aimed ten degrees outward, mounted on oddly jointed metal structures like the folded legs of a praying mantis. The hull was small, containing only a computer and an insystem fuel tank.

Juno was invisible behind her when the fusion motors fired. Immediately the cable at her tail began to unroll. The cable was thirty miles long and was made of braided Sinclair molecule chain. Trailing at the end was a lead capsule as heavy as the ramrobot itself.

(ed note: "Sinclair molecule chain" is an unobtainium wire that is only one molecule thick and absurdly strong. The theoretical ultimate of low mass cable.)

From A GIFT FROM EARTH by Larry Niven (1968)

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This week's featured addition is Robot Asteroid Prospector

This week's featured addition is Endurance from Interstellar

This week's featured addition is Direct Fusion Drive

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