The second fantastic proposal is even more interesting from the theoretical point of view. I am referring now to the prohibition that the special theory of relativity places on attempts to reach and surpass the speed of light. A way around this prohibition may be to move beyond the special theory. The basic intuition behind this idea is as follows: The speed barrier applies within the special theory of relativity, which requires the formula for addition of velocities we have seen above, and which presupposes non-accelerated frames. But does it have to hold within the accelerated frames of the general theory of relativity, or within a theory of quantum gravity?
Indeed the suggestions that have aroused the greatest interest in the last twenty years or so concerning travel faster than light both make use of the General Theory. I will discuss briefly two of them, the most interesting two. Please keep in mind, however, that at this stage the goal of the discussion is not to determine which of these suggestions is more likely to take us to the stars in faster-than-light starships, but whether physical theory permits traveling faster than light.
The first suggestion is Kip S. Thorne’s idea to use a Wheeler quantum wormhole to travel in a very short time to places that in normal spacetime could be thousands or even millions of light years away. Imagine that space time is folded (for example in a fifth dimension in addition to the three of space and the one of time). That fold may bring close together, in that fifth dimension (or in so called “hyperspace”), regions of space that are extremely far from one another in the normal three space dimensions. It is as if we took a long cloth and brought close together the two ends. If the cloth were laid flat the two ends might be separated by a distance of one meter, but now that we have folded the cloth, the two ends might be only, say, a millimeter apart. If we could only make a little tube that connected them across that millimeter, the trip from end to end would be far shorter. John Archibald Wheeler’s proposed that, in extremely small regions (around a Planck length, 1x10-33 cm), strong gravitational quantum fluctuations create a sort of “quantum foam,” in which we might find such a little tube, a “wormhole.” The trick is to find one wormhole in the foam, to enlarge it so a ship can go through it, and then to keep it open so it will not crush the ship.
Let us consider all three aspects of Thorne’s idea, which he developed upon a request from his friend Carl Sagan. The first problem is to find the wormhole. No one has ever detected one, and we do not even know if they exist. If none exist, or we cannot find them, an alternative would be to create one, as long as wormholes could exist. But can they? Wheeler’s results came from his attempts to construct a theory of quantum gravity. Unfortunately, half a century later we do not yet have an adequate theory on the subject. It is difficult to say then, even if we take Wheeler’s imaginative idea seriously, that physical theory does not forbid faster-than-light travel. The special theory of relativity certainly seems to forbid it. Does Wheeler’s joining of the General Theory and quantum theory somehow bring to light enough evidence to show some limitations to the special theory? It might if it were true, but that is precisely what we do not know.
Since we do not have an acceptable theory of quantum gravity, we are simply in a state of ignorance. From that ignorant perspective, travel faster than light may or may not be permitted by the laws of the universe (which we do not really know). The situation would be similar to asking in, say, 1855, whether it is possible in principle for a ship to travel at 300.000 Km/s. Nothing would seem to forbid such a feat, but only because Einstein’s formula for the relativistic addition of velocities was still 50 years away from appearing in print. Some may believe that the situation is actually worse, since we have no trustworthy theory to give us even seemingly reliable guidance – in 1855 we had Newton’s.
Some reason for optimism comes from the Casimir effect, which demonstrates that the vacuum is indeed teeming with virtual particles coming in and out of existence, as we would expect in Wheeler’s account. Cassimir suggested in 1948 that if two metal plates were placed micrometers away from each other in a vacuum, and in the absence of an electromagnetic field, some virtual photons would not appear between them because of their long wavelengths. In that case, there would be a greater density of virtual photons outside the plates than between them. This difference in density would result in pressure being applied to the plates from the outside, and thus they would move towards each other. The confirmation of the Casimir effect in 1958 is strong evidence for the hypothesis that virtual particles are prevalent in the vacuum, and many now see it as confirmation also that there is some sort of spacetime foam a la Wheeler. Notice, however, that the Casimir effect seems accounted for within quantum theory and is, at the very least, neutral about possible interactions between gravity and quantum effects.
Suppose, however, that we do find or create a Wheeler wormhole. Unlike the wormholes that might exist as a result of black hole singularities (in which the matter that disappears into the singularity “tunnels out” to another universe or another part of the universe, and in which the tunnel would close too quickly and the extraordinary gravity would crush any would-be traveler), Wheeler wormholes would be extremely small, of Planck dimensions. It would be necessary to make them longer, so as to connect one of the entrances with some desirable destination, and wider and stable, so we could send our astronauts through them. How could this be accomplished? The favorite answer: exotic matter. Now exotic matter is truly exotic. Presumably it would have negative mass, or at least exert negative energy (it would push the walls of the wormhole outward). And of course we have no idea whether it could exist. But Thorne and his coworkers think that something like the Casimir effect might produce negative energy inside the wormhole to keep it open.
Think back, however, to the description of the Casimir effect given above. If we think of the vacuum as having zero energy, then we could think of the volume between the metal plates as having negative energy. It is a relative assignment of sign given the description we choose. But it does not seem sensible to say, for example, that the virtual particles within that volume have negative mass, or anything of the sort. Those photons have no peculiar properties compared to the virtual photons outside of the plates. So it is not as if we could go looking for some exotic matter to spoon into the wormholes. But perhaps what Thorne is after is what he calls “exotic fluctuations,” which would create negative energies, and which Hawking presumably showed existed at the event horizon of a black hole. Such exotic fluctuations would account for Hawking’s radiation. Nevertheless, a less exotic description is that the black hole pulls a member of a virtual particle pair inside the horizon while letting the other member escape into the universe, thus creating a glow of energy around the event horizon. We may then say that this positive energy is compensated by negative energy being sucked into the black hole (again a relative assignment of sign).
In any event, to expand a wormhole’s diameter along these lines, it would seem that a great deal of energy would have to be concentrated into the small region of the mouth of the wormhole so as to create a pronounced spacetime curvature in that region. Whether this would really lead to the desired opportunity for faster-than-light travel would have to be determined by a good theory of the interaction of gravity and quantum phenomena. If we only had one.
Of course, some of these theoretical ideas may turn out to be correct. Perhaps new experimental work that concentrates large energies into small regions could confirm the existence of spacetime foam, wormholes, and exotic matter (or at least some way of bringing about something akin to the Casimir effect inside a wormhole). But until such a time we will not really be in a position to say that travel faster than light is possible.
Imagine, nevertheless, that we do find or create a Wheeler wormhole, expand it and ensure its stability. We are still faced with a major conceptual difficulty: an outcome of travel through the wormhole is that an astronaut would also travel back in time. You may return before you take off! This gives rise to all sorts of puzzles about landing on your infant grandfather and killing him, which would make it then impossible for you to be born and thus to go on the trip in the first place. This absurd consequence would be a possibility in an established wormhole, if we do find one, that is, since it is a possibility in general for travel faster than light, as has been known for a long time. An example I recall from my student days was that if you had a gun that shot tachyon bullets, one such bullet could ricochet off the wall and kill you before you pulled the trigger (tachyons are particles that always travel faster than light, and thus do not violate special relativity since they never accelerate to the velocity of light).
Thorne offers an interesting illustration of time travel in a manufactured wormhole. He imagines making a short wormhole with one mouth in his living room and the other in a starship sitting just outside on his lawn. His wife takes off in the starship traveling at close to the speed of light. Obviously, the two mouths of the wormhole have different times, once her trip begins, as measured in a framework outside of the wormhole, although inside the wormhole the times remain the same. Thorne’s wife returns some hours later (her ship time), although years have gone by on Earth. She has two choices. She can meet Thorne on the lawn upon the landing of the ship and notice how much he has aged. Or she can crawl back using the wormhole to a time before she left on her space journey. Of course, she would then meet her own old self getting ready to go on her space journey. And of course, accidents could happen that would prevent her old self from starting that journey.
These paradoxes make travel back in time conceptually absurd, which makes this type of faster-than-light travel also conceptually absurd. But could the paradoxes be resolved? One suggestion is that unknown laws of quantum physics (or quantum gravity, or who knows what) prevent anyone, or anything, to travel to the past and create impossibilities (it is impossible to go back and kill your grandfather if you were never born because you killed him when he was an infant). This possibility is not only ad hoc but mere wishful thinking.
Another is that the astronauts traveling through a wormhole would not create any inconsistent “time loops” because they would actually end up in an Everett alternative universe (according to Everett, each of two possible alternative quantum states is real, although each is real in a different historical line (or world, or parallel universe). So you would not really land on your grandfather, you would land on your grandfather’s equivalent in a different historical line. It is difficult to distinguish this physics from science fiction, but even a less cynical appraisal of this possibility should let us see that we are no longer talking about going to the past but rather to a different dimension or universe that is almost like your past and landing (and killing) someone who is exactly like your infant grandfather. It is also obvious that you never arrive at your destination, but at a planet around a star that is exactly like the one you were trying to reach, except for being located in another dimension or universe. And it seems that one should expect similar dislocation on the return trip; that is, you can never come home. Wormholes appear to be problematic enough without combining them with Everett’s interpretation of quantum mechanics.
A third suggestion is that there are indeed many worlds, more or less a la Everett, but that some are destroyed by inconsistent “time loops.” Our world exists because no one has killed his grandfather, etc., in any travel to the past. Time-travel consistency would function as a selection factor for possible worlds. The problem is, however, that when time travel alters the past it destroys a history that could be tens, hundreds, thousands, millions, or billions of years long. We do not know from when the fatal time traveler is going to come. Moreover, he may arrive tomorrow at noon, or a million years ago. And we would no longer be. In fact, in the second scenario, we would no longer have been. This suggestion does not seem to work well as a solution to the paradox.
Thorne proposes an apparently more sensible approach. He discovered that some round-trip trajectories through a wormhole may be perfectly consistent: a billiard ball may return and hit itself a glancing blow that will still permit its earlier version to go on the trip. Presumably, since this loop is causally consistent, we no longer face a paradox. Paul Davies seems to agree and provides an interesting variant: A rich man travels back in time, meets his (young) grandmother and unwittingly gives her information about stock prices in her future. She invests her money using that information, which leads to immense wealth for her and for her grandson. Davies claims that “[N]o paradox ensues here.” Surprisingly he finds paradox in a case essentially alike. A professor travels to the future, finds a mathematical formula in a book, returns to his time and gives the formula to a student, who then publishes it. That is the publication that the professor reads many years later. But neither the professor nor the student created the formula. Thus information has come from nowhere, or rather just from the time travel. In the earlier case the grandmother could not have created her fortune (or the student written the paper) without the foreknowledge made possible by the relevant time traveler (grandson, professor). Because the association between information and entropy, Davies thinks that this “free” information is “equivalent to heat flowing backward from cold to hot.”
It seems to me that the situation is even more dire than that. In Thorne’s example a sequence of events, a history, leads to a future event that in turn causes a destruction of that very history and its replacement by another. Something had happened, and now it has not. But if it has not, how could the inconsistent causal loop arise in the first place? Those who have no trouble accepting something like Everett’s many-worlds view, or the even fancier notions of string theory, perhaps are not bothered by this new paradox all that much. But it must be pointed out, as it is generally accepted, that the empirical evidence for the first is scant and for the second non-existent. In Davies’ examples, there is not even an original history to create the conditions for the consistent causal loop: the man is already rich (without his grandmother having made the right investments), the professor already finds the mathematical formula (that no one has really invented). The loop just is. Causality is violated. Jorge Luis Borges would be pleased. But on the basis of such physics we do not have enough to say that faster-than-light travel is possible.
One point of logic needs to be considered. Even if causally consistent time loops did not fall prey to these objections, it is difficult to see how such loops fix the conceptual absurdity of going to the past. The paradox is not that every time we go to the past we kill our infant grandfather, etc. The paradox is that we could, accidentally or otherwise. Thorne’s proposed solution is that there may be consistent loops. But, the danger still exists that, for example, the rich man’s son, years after his father’s time trip, indeed, years after his father’s death, finds the time machine, pushes the wrong button and ends up landing on his infant great grandmother, crushing her to death. That would make his family’s history, including the presumed consistent causal loop, become non-existent! The paradox has not been resolved.
One might think that if it is possible for someone from further in the future to annihilate that consistent loop, then that consistent loop was part of a longer but inconsistent loop; but in that case the longer loop itself would have been eliminated, and thus we have nothing to fear from time travel. Therefore we have no paradox. This response might make some sense if we hold to a metaphor of a frozen four-dimensional spacetime (like a vine made up of time slices of the other three dimensions). In that metaphor time is already all laid out and some Cosmic Pruner has cut out all the inconsistent loops from the cosmic vine. This would be as ad hoc as it is convenient. But the universe we experience unfolds in time, and we need a rather long causal sequence of events to create the conditions under which someone can go back to his past to wipe it out. That sequence of events, however, would have no particular marks to distinguish it from the one humans find themselves in already. Since the building of an actual time machine is presumably way in the future, if ever, we would not know whether we are in a real world (because either we will not invent time machines, or if we do the time loops they bring about will all be consistent) or in a world that one unexpected day will no longer have existed.
No wonder, then, that to save physics from absurdity, Hawking conjectured that the unknown laws of quantum gravity provide chronology protection, that is, that the universe does not allow time machines. This protection, he said, will “keep the world safe for historians.”
To say that faster-than-light travel is possible, then, we need to show that we have accepted some relevant theories that permit it, or else we need to point to empirical evidence that, even in the absence of theory, suggest that possibility (e.g. people knew that flight was possible because they saw birds and insects fly, long before they had any theories that explained the flight of birds and insects). One problem with the theories of quantum gravity I have mentioned is that they have not been accepted because the empirical support is not there. I suspect the reason their proponents openly pursue such wild imaginings is that relativity and quantum theory presumably granted physicists the license to make unintuitive claims. Hypotheses about Wheeler wormholes, branes, the multiverse, and the like, it seems, do not sound any stranger today than, say, the wave-particle duality of light and matter did almost a hundred years ago. But I think there is a difference. When Einstein accounted for the photoelectric effect by suggesting quanta of light, his explanation was generally rejected, even by those who used his calculations. Bohr, for example, pointed out that Einstein’s account was contradicted by many experiments that showed clearly the wave nature of light. Eventually Compton’s X-ray scattering experiments made Bohr accept the dual nature of light and this led to his famous principle of complementarity. The moral of the story is that physicists were forced by the phenomena to propose and accept otherwise extremely unintuitive views. Their experiments were their warrant. Perhaps other, more sensible views would have done the job, but no one proposed a persuasive one. Moreover, as I have argued elsewhere, the unintuitive character of their views, at least in the case of the principle of complementarity, was due to the general acceptance of a mistaken epistemology. Einstein’s theory of relativity, although not similarly prompted by experimental results, was nevertheless soon an important tool in contrasting our ideas with the world. None of this is the case with the highly speculative ideas so much in vogue today, and as we have seen, those ideas do not permit us to say whether we will ever be able to go faster than light.
To rule on that possibility, we need, in addition to the requirements of theory or empirical evidence mentioned above, a way of travel that does not imply going back to the past. A way out of this difficulty is to realize that the speed of light operates as a limit only within the special theory of relativity. But within the general theory we may find ways to travel faster than light without going back in time.
Miguel Alcoubierre argued in a paper published in The Journal of Classical and Quantum Gravity in 1994 that, if we built an engine that contracts spacetime in front of the starship, and expands it behind it, we could accelerate the starship to a velocity arbitrarily higher than that of light. Since the local spacetime for the ship would be flat, the astronauts would not violate the relativistic speed limit at any one point in their journey, although, from the perspective of the Earth-bound observers, the ship might be traveling much faster than light. By thus warping spacetime, the ship may make a return trip to Vega, which is 25 light years away, in, say, three or four Earth years, from the point of view of Earth-bound observers, instead of more than fifty, as would be the case under special-relativity considerations. Alcoubierre’s arrangement also has the ship move only into the future, as airplanes and slugs do, and so we do not have to worry about time paradoxes.
Of course, from this theoretical possibility to building a starship with a “warp” engine there is a long gap. What kind of technology could possibly contract spacetime? Some have suggested strange matter, but we have discussed that enough in this work not to pin our hope on it. We actually do not know what would work. But we do know that spacetime can expand, for that is precisely what dark energy accomplishes. We do not know how dark energy does it, just as we do not know what dark energy is. A hypothesis, however, is that the expansion of spacetime results from some kind of scalar field. To understand how a scalar field works, let us think about a spring that is pulled open until suddenly returns to its original state, or how a rubber ball pressed on all sides suddenly expands. If one takes seriously the suggestion by string theorists that there exist “space atoms,” then one can also imagine that only a limited amount of energy can be held in one of those atoms. Once it reaches the maximum, the energy “bounces” like the rubber of the compressed ball, carrying spacetime with it as it expands. But these are all metaphors. What matters is that it happens, that spacetime does seem to expand, even if we cannot explain why. Birds did fly at a time when people could not explain how they could fly. Besides, such expansions, and contractions, of spacetime could be seen as variants of the lambda term that Einstein added to his equations to keep the universe from expanding.
Perhaps to construct the right kind of machine we may still need an acceptable theory of quantum gravity. For example, to produce the required local expansions and contractions we may use some form of interaction between electromagnetic and gravitational forces in very small volumes. But further speculations along these lines go beyond the intent of this work. What matters is that the desired processes are possible, given Einstein’s theory of general relativity and the existence of dark energy. Theory and experience thus permit travel faster than light, as long as such travel does not include the possibility of traveling to the past. Alcubierre’s proposal accords with the conceptual requirements, although of course there are no guarantees that such a spaceship will ever travel through interstellar space, just as there are no guarantees that we will ever achieve relativistic velocities either.
Whether these technologies will ever come to fruition I do not know. But what seems rather clear to me is that the physical expansion of humankind into the cosmos will vastly enhance our ability to preserve the dynamic character of science, while at the same time making it far more likely that a sun, some sun, will rise on the world of our descendants in a future so distant that most species on the surface of the Earth will have long disappeared. It is the process toward that long expansion that will make it possible to determine whether the relativistic velocities are technologically possible. I can only hope that we will set in motion the events that will ultimately allow our descendants to make that determination if they so choose.
This possibility of continuous expansion offers, then, a double bounty for our species. It increases our chances of survival, as we have seen. And it also preserves for a long time the opportunity to challenge our views of the universe. As Robert Goddard wrote in a letter to H.G. Wells, in 1932, "there can be no thought of finishing, for `aiming at the stars,' both literally and figuratively is a problem to occupy generations, so that no matter how much progress one makes, there is always t
 K.S. Thorne, Black holes and time warps: Einstein’s outrageous legacy. W.W. Norton and Company. 1994.
 J.A. Wheeler. (1962): Geometrodynamics. Academic Press.
 Another approach is to nip all these speculations in the bud, by pointing out, as Jeffrey Barrett does, that “One might argue that there can be no threat of temporal paradoxes in GTR (General Theory of Relativity) since a particular mass-energy distribution and spacetime either is or isnot a solution to the field equations--if it is, then the solution provides a model for all spacetime events” (personal communication).
 Thorne, K. (1994): pp. 508-516.
 Davies, P. (2003): How to build a time machine. Penguin Books, p. 96.
 Ibid., pp. 102-105.
 For some strange reason many physicists, including Thorne and Davies, thought at one time that the paradoxes of time travel arose out of the exercise of free will. Obviously that is not so.
 As quoted in Thorne (2003), p. 521. Vacuum fluctuations would destroy the wormhole before it can become a time machine.
 For a fascinating account see Brush, S.G.
 See, for example, “Bohr and evolutionary relativism,” Ch. 3 of my Evolution and the Naked Truth, Ashgate (1998).
 Few ideas in the history of science have been corroborated as much as, say, Einstein’s formula for relativistic mass (discussed above). Practically every time we use a particle accelerator we confirm it with millions, perhaps billions of instances.
 Another possibility – and this is admittedly speculation – would be a machine capable of producing the gravito-magnito effect described in Ch. 5. Ning Li predicted that a rapidly rotating disk (this experiment uses superconductors) would produce the kind of distortion of spacetime that the Gravity B Probe may measure for the planet Earth. Objects placed in front of such objects would show a decrease in mass! Experiments carried out by Podkletnov in 1992 apparently confirmed Li’s astonishing prediction. Unfortunately no one has been able to reproduce Podkletnov’s results.