CHAPTER THREE
Shows His Hand “How little do you mortals understand time. Must you be so linear, Jean-Luc?”
Q to Picard, in "All Good Things... .
The planet Vulcan, home to Spock, actually has a venerable history in twentieth-century physics. A great puzzle in astrophysics in the early part of this century was the fact that the perihelion of Mercurythe point of its closest approach to the Sunwas precess-ing around the Sun each Mercurian year by a very small amount in a way that was not consistent with Newtonian gravity. It was suggested that a new planet existed inside Mercury's orbit which could perturb it in such a way as to fix the problem. (In fact, the same solution to an anomaly in the orbit of Uranus had earlier led to the discovery of the planet Neptune.) The name given to the hypothetical planet was Vulcan.
Alas, the mystery planet Vulcan is not there. Instead, Einstein proposed that the flat space of Newton and Minkowski had to be given up for the curved spacetime of general relativity. In this curved space, Mercury's orbit would deviate slightly from that predicted by Newton, explaining the observed discrepancy. While this removed the need for the planet Vulcan, it introduced possibilities that are much more exciting. Along with curved space come black holes, wormholes, and perhaps even warp speeds and time travel.
Indeed, long before the Star Trek writers conjured up warp fields, Einstein warped spacetime, and, like the Star Trek writers, he was armed with nothing other than his imagination. Instead of imagining twenty-second-century starship technology, however, Einstein imagined an elevator. He was undoubtedly a great physicist, but he probably never would have sold a screenplay.
Nonetheless, his arguments remain intact when translated aboard the Enterprise. Because light is the thread that weaves together space and time, the trajectories of light rays give us a map of spacetime just as surely as warp and weft threads elucidate the patterns of a tapestry. Light generally travels in straight lines. But what if a Romulan commander aboard a nearby Warbird shoots a phaser beam at Picard as he sits on the bridge of his captain's yacht Calypso, having just engaged the impulse drive (we will assume the inertial dampers are turned off for this example)? Picard would accelerate forward, narrowly missing the brunt of the phaser blast. When viewed in Picard's frame of reference, things would look like the figure at the top of the following page.
So, for Picard, the trajectory of the phaser ray would be curved. What else would Picard notice? Well, recalling the argument in the first chapter, as long as the inertial dampers are turned off, he would be thrust back in his seat. In fact, I also noted there that if Picard was being accelerated forward at the same rate as gravity causes things to accelerate downward at the Earth's surface, he would feel exactly the same force pushing him back against his seat that he would feel pushing him down if he were standing on Earth. In fact, Einstein argued that Picard (or his equivalent in a rising elevator) would never be able to perform any experiment that could tell the difference between the reaction force due to his acceleration and the pull of gravity from some nearby heavy object outside the ship. Because of this, Einstein boldly went where no physicist had gone before, and reasoned that whatever phenomena an accelerating observer experienced would be identical to the phenomena an observer in a gravitational field experienced.
Our example implies the following: Since Picard observes the phaser ray bending when he is accelerating away from it, the ray must also bend in a gravitational field. But if light rays map out spacetime, then spacetime must bend in a gravitational field. Finally, since matter produces a gravitational field, then matter must bend spacetime!
Now, you may argue that since light has energy, and mass and energy are related by Einstein's famous equation, then the fact that light bends in a gravitational field is no big surpriseand certainly doesn't seem to imply that we have to believe that spacetime itself need be curved. After all, the paths that matter follows bend too (try throwing a ball in the air). Galileo could have shown, had he known about such objects, that the trajectories of baseballs and Pathfinder missiles bend, but he never would have mentioned curved space.
Well, it turns out that you can calculate how much a light ray should bend if light behaved the same way a baseball does, and then you can go ahead and measure this bending, as Sir Arthur Stanley Eddington did in 1919 when he led an expedition to observe the apparent position of stars on the sky very near the Sun during a solar eclipse. Remarkably, you would find, as Eddington did, that light bends exactly twice as much as Galileo might have predicted if it behaved like a baseball in flat space. As you may have guessed, this factor of 2 is just what Einstein predicted if spacetime was curved in the vicinity of the Sun and light (or the planet Mercury, for that matter) was locally traveling in a straight line in this curved space! Suddenly, Einstein's was a household name.
Curved space opens up a whole universe of possibilities, if you will excuse the pun. Suddenly we, and the Enterprise, are freed from the shackles of the kind of linear thinking imposed on us in the context of special relativity, which Q, for one, seemed to so abhor. One can do many things on a curved manifold which are impossible on a flat one. For example, it is possible to keep traveling in the same direction and yet return to where you beganpeople who travel around the world do it all the time.
The central premise of Einstein's general relativity is simple to state in words: the curvature of spacetime is
directly determined by the distribution of matter and energy contained within it. Einstein's equations, in fact, provide simply the strict mathematical relation between curvature on the one hand and matter and energy on the other:
What makes the theory so devilishly difficult to work with is this simple feedback loop: The curvature of spacetime is determined by the distribution of matter and energy in the universe, but this distribution is in turn governed by the curvature of space. It is like the chicken and the egg. Which was there first? Matter acts as the source of curvature, which in turn determines how matter evolves, which in turn alters the curvature, and so on.
Indeed, this may be perhaps the most important single aspect of general relativity as far as Star Trek is concerned. The complexity of the theory means that we still have not yet fully understood all its consequences; therefore we cannot rule out various exotic possibilities. It is these exotic possibilities that are the grist of Star Trek's mill. In fact, we shall see that all these possibilities rely on one great unknown that permeates everything, from wormholes and black holes to time machines.
The first implication of the fact that spacetime need not be flat which will be important to the adventures of the Enterprise is that time itself becomes an even more dynamic quantity than it was in special relativity. Time can flow at different rates for different observers even if they are not moving relative to each other. Think of the ticks of a clock as the ticks on a ruler made of rubber. If I were to stretch or bend the ruler, the spacing between the ticks would differ from point to point. If this spacing represents the ticks of a clock, then clocks located in different places can tick at different rates. In general relativity, the only way to “bend” the ruler is for a gravitational field to be present, which in turn requires the presence of matter.
To translate this into more pragmatic terms: if I put a heavy iron ball near a clock, it should change the rate at which the clock ticks. Or more practical still, if I sleep with my alarm clock tucked next to my body's rest mass, I will be awakened a little later than I would otherwise, at least as far as the rest of the world is concerned.
A famous experiment done in the physics laboratories at Harvard University in 1960 first demonstrated that time can depend on where you are. Robert Pound and George Rebka showed that the frequency of gamma radiation measured at its source, in the basement of the building, differed from the frequency of the radiation when it was received 74 feet higher, on the building's roof (with the detectors having been carefully calibrated so that any observed difference would not be detector-related). The shift was an incredibly small amount about 1 part in a million billion. If each cycle of the gamma-ray wave is like the tick of an atomic clock, this experiment implies that a clock in the basement will appear to be running more slowly than an equivalent atomic clock on the roof. Time slows on the lower floor because this is closer to the Earth than the roof is, so the gravitational field, and hence the spacetime curvature, is larger there. As small as this effect was, it was precisely the value predicted by general relativity, assuming that spacetime is curved near the Earth.
The second implication of curved space is perhaps even more exciting as far as space travel is concerned. If space is curved, then a straight line need not be the shortest distance between two points. Here's an example. Consider a circle on a piece of paper. Normally, the shortest distance between two points A and B located on opposite sides
of the circle is given by the line connecting them through the center of the circle:
If, instead, one were to travel around the circle to get from A to B, the journey would be about 1 1/2 times as long. However, let me draw this circle on a rubber sheet, and distort the central region:
Now, when viewed in our three-dimensional perspective, it is clear that the journey from A to B taken through the center of the region will be much longer than that taken by going around the circle. Note that if we took a snapshot of this from above, so we would have only a two-dimensional perspective, the line from A to B through the center would look like a straight line. More relevant perhaps, if a tiny bug (or two-dimensional beings, of the type encountered by the Enterprise) were to follow the trajectory from A to B through the center by crawling along the surface of the sheet, this trajectory would appear to be straight. The bug would be amazed to find that the straight line through the center between A and B was no longer the shortest distance between these two points. If the bug were intelligent, it would be forced to the conclusion that the two-dimensional space it lived in was curved. Only by viewing the embedding of this sheet in the underlying three-dimensional space can we observe the curvature directly.
Now, remember that we live within a four-dimensional spacetime that can be curved, and we can no more perceive the curvature of this space directly than the bug crawling on the surface of the sheet can detect the curvature of the sheet. I think you know where I am heading: If, in curved space, the shortest distance between two points need not be a straight line, then it might be possible to traverse what appears along the line of sight to be a huge distance, by finding instead a shorter route through curved spacetime.
These properties I have described are the stuff that Star Trek dreams are made of. Of course, the question is: How many of these dreams may one day come true?
WORMHOLES: FACT AND FANCY: The Bajoran wormhole in Deep Space Nine is perhaps the most famous wormhole in Star Trek, although there have been plenty of others, including the dangerous wormhole that Scotty could create by imbalancing the matter-antimatter mix in the Enterprise's warp drive; the unstable Barzan wormhole, through which a Ferengi ship was lost in the Next Generation episode "The
Price"; and the temporal wormhole that the Voyager encountered in its effort to get back home from the far edge of the galaxy.
The idea that gives rise to wormholes is exactly the one I just described. If spacetime is curved, then perhaps there are different ways of connecting two points so that the distance between them is much shorter than that which would be measured by traveling in a “straight line” through curved space. Because curved-space phenomena in four dimensions are impossible to visualize, we once again resort to a two-dimensional rubber sheet, whose curvature we can observe by embedding it in three-dimensional space.
If the sheet is curved on large scales, one might imagine that it looks something like this:
Clearly, if we were to poke a pencil down at A and stretch the sheet until we touched B, and then sewed together the two parts of the sheet, like so:
we would create a path from A to B that was far shorter than the path leading around the sheet from one point to another. Notice also that the sheet appears flat near A and also near B. The curvature that brings these two points close enough together to warrant joining them by a tunnel is due to the global bending of the sheet over large distances. A little bug (even an intelligent one) at A, confined to crawl on the sheet, would have no idea that B was as “close” as it was, even if it could do some local experiments around A to check for a curvature of the sheet.
As you have no doubt surmised, the tunnel connecting A and B in this figure is a two-dimensional analogue of a three-dimensional wormhole, which could, in principle, connect distant regions of space-time. As exciting as this possibility is, there are several deceptive aspects of the picture which I want to bring to your attention. In the first place, even though the rubber sheet is shown embedded in a three-dimensional space in order for us to “see” the curvature of the sheet, the curved sheet can exist without the three-dimensional space around it needing to exist. Thus, while a wormhole could exist joining A and B, there is no sense in which A and B are “close” without the wormhole being present. It is not as if one is free to leave the rubber sheet and move from A to B through the three-dimensional space in which the sheet is embedded. If the three-dimensional space is not there, the rubber sheet is all there is to the universe.
Thus, imagine that you were part of an infinitely advanced civilization (but not as advanced as the omnipotent Q beings, who seem to transcend the laws of physics) that had the power to build wormholes in space. Your wormhole building device would effectively be like the pencil in the example I just gave. If you had the power to produce huge local curvatures in space, you would have to poke around blindly in the hope that somehow you could connect two regions of space that, until the instant a wormhole was established, would remain very distant from each other. In no way whatsoever would these two regions be close together until the wormhole produced a bridge. The bridge-building process itself is what changes the global nature of spacetime.
Because of this, making a wormhole is not to be taken lightly. When Premier Bhavani of Barzan visited the Enterprise to auction off the rights to the Barzan wormhole, she exclaimed, “Before you is the first and only stable wormhole known to exist!” Alas, it wasn't stable; indeed, the only wormholes whose mathematical existence has been consistently established in the context of general relativity are transitory. Such wormholes are created as two microscopic “singularities” regions of spacetime where, the curvature becomes infinitely sharp find each other and momentarily join. However, in a time shorter than the time it would take a space traveler to pass through such a worm-hole, it closes up, leaving once again two disconnected singularities. The unfortunate explorer would be crushed to bits in one singularity or the other before being able to complete the voyage through the wormhole.
The problem of how to keep the mouth of a wormhole open has been hideously difficult to resolve in mathematical detail, but is quite easily stated in physical terms: Gravity sucks! Any kind of normal matter or energy will tend to collapse under its own gravitational attraction unless something else stops it. Similarly, the mouth of a wormhole will pinch off in nothing flat under normal circumstances.
So, the trick is to get rid of the normal circumstances. In recent years, the Caltech physicist Kip Thorne, among others, has argued that the only way to keep wormholes open is to thread them with “exotic material.” By this is meant material that will be measured, at least by certain observers, to have “negative” energy. As you might expect (although naive expectations are notoriously suspect in general relativity), such material would tend to “blow” not “suck,” as far as gravity is concerned.
Not even a diehard trekker might be willing to suspend disbelief long enough to accept the idea of matter with “negative energy”; however, as noted, in curved space one's normal expectations are often suspect. When you compound this with the exotica forced upon us by the laws of quantum mechanics, which govern the behavior of matter on small scales, quite literally almost all bets are off.
BLACK HOLES AND DR. HAWKING: Enter Stephen Hawking. He first became well known among physicists
working on general relativity for his part in proving general theorems related to singularities in spacetime, and then, in the 1970s, for his remarkable theoretical discoveries about the behavior of black holes. These objects are formed from material that has collapsed so utterly that the local gravitational field at their surface prevents even light from escaping.
Incidentally, the term “black hole,” which has so captivated the popular imagination, was coined by the theoretical physicist John Archibald Wheeler of Princeton University, in the late fall of 1967. The date here is very interesting, because, as far as I can determine, the first Star Trek episode to refer to a black hole, which it called a “black star,” was aired in 1967 before Wheeler ever used the term in public. When I watched this episode early in the preparation of this book, I found it amusing that the Star Trek writers had gotten the name wrong. Now I realize that they very nearly invented it!
Black holes are remarkable objects for a variety of reasons. First, all black holes eventually hide a spacetime singularity at their center, and anything that falls into the black hole must inevitably encounter it. At such a singularityan infinitely curved “cusp” in spacetimethe laws of physics as we know them break down. The curvature near the singularity is so large over such a small region that the effects of gravity are governed by the laws of quantum mechanics. Yet no one has yet been able to write down a theory that consistently accommodates both general relativity (that is, gravity) and quantum mechanics. Star Trek writers correctly recognized this tension between quantum mechanics and gravity, as they usually refer to all spacetime singularities as “quantum singularities.” One thing is certain, however: by the time the gravitational field at the center of a black hole reaches a strength large enough for our present picture of physics to break down, any ordinary physical object will be torn apart beyond recognition. Nothing could survive intact.
You may notice that I referred to a black hole as “hiding” a singularity at its center. The reason is that at the outskirts of a black hole is a mathematically defined surface we call the “event horizon,” which shields our view of what happens to objects that fall into the hole. Inside the event horizon, everything must eventually hit the ominous singularity. Outside the event horizon, objects can escape. While an observer unlucky enough to fall into a black hole will notice nothing special at all as he or she (soon to be “it”) crosses the event horizon, an observer watching the process from far away sees something very different. Time slows down for the observer freely falling in the vicinity of the event horizon, relative to an observer located far away. As a result, the falling observer appears from the outside to slow down as he or she nears the event horizon. The closer the falling observer gets to the event horizon, the slower is his or her clock relative to the outside observer's. While it may take the falling observer a few moments (local time) to cross the event horizonwhere, I repeat, nothing special happens and nothing special sitsit will take an eternity as observed by someone on the outside. The infalling object appears to become frozen in time.
Moreover, the light emitted by any infalling object gets harder and harder to see from the outside. As an object approaches the event horizon, the object gets dimmer and dimmer (because the observable radiation from it gets shifted to frequencies below the visible). Finally, even if you could see, from the outside, the object's transit of the event horizon (which you cannot, in any finite amount of time), the object would disappear completely once it passed the horizon, because any light it emitted would be trapped inside, along with the object. Whatever falls inside the event horizon is lost forever to the outside world. It appears that this lack of communication is a one- way street: an observer on the outside can send signals into the black hole, but no signal can ever be returned.
For these reasons, the black holes encountered in Star Trek tend to produce impossible results. The fact that the event horizon is not a tangible object, but rather a mathematical marker that we impose on our description of a black hole to delineate the region inside from that outside, means that the horizon cannot have a “crack,” as required by the crew of the Voyager when they miraculously escape from a black hole's interior. (Indeed, this notion is so absurd that it makes it onto my ten-best list of Star Trek mistakes described in the last chapter.) And the “quantum singularity life-forms” encountered by the crew of the Enterprise as they, and a nearby Romulan Warbird, travel backward and forward in time have a rather unfortunate nesting place for their young: apparently they place them inside natural black holes (which they incorrectly mistake the “artificial” quantum singularity inside the Romulan engine core for). This may be a safe nursery, but it must be difficult to retrieve your children afterward. I remind you that nothing inside a black hole can ever communicate with anything outside one.
Nevertheless, black holes, for all their interesting properties, need not be that exotic. The only black holes we have any evidence for in the universe today result from the collapse of stars much more massive than the Sun. These collapsed objects are so dense that a teaspoon of material inside would weigh many tons. However, it is another remarkable property of black holes that the more massive they are, the less dense they need be when they form. For example, the density of the black hole formed by the collapse of an object 100 million times as massive as our Sun need only be equal to the density of water. An object of larger mass will collapse to form a black hole at a point when it is even less dense. If you keep on extrapolating, you will find that the density required to form a black hole with a mass equal to the mass of the observable universe would be roughly the same as the average density of matter in the universe! We may be living inside a black hole.
In 1974, Stephen Hawking made a remarkable discovery about the nature of black holes. They aren't completely black! Instead, they will emit radiation at a characteristic temperature, which depends on their mass. While the nature of this radiation will give no information whatsoever on what fell into the black hole, the idea that radiation could be emitted from a black hole was nevertheless astounding, and appeared to violate a number of theoremssome of which Hawking had earlier provedholding that matter could only fall into black holes, not out of them. This remains true, except for the source of the black-hole radiation, which is not normal matter. Instead, it is empty space, which can behave quite exoticallyespecially in the vicinity of a black hole.
Ever since the laws of quantum mechanics were made consistent with the special theory of relativity, shortly after the Second World War, we have known that empty space is not so empty. It is a boiling, bubbling sea of quantum fluctuations. These fluctuations periodically spit out elementary particle pairs, which exist for time intervals so short that we cannot measure them directly, and then disappear back into the vacuum from which they came. The uncertainty principle of quantum mechanics tells us that there is no way to directly probe empty space over such short time intervals and thus no way to preclude the brief existence of these so-called virtual particles. But although they cannot be measured directly, their presence does affect certain physical processes that we can measure, such as the rate and energy of transitions between certain energy levels in atoms. The predicted effect
of virtual particles agrees with observations as well as any prediction known in physics.
This brings us back to Hawking's remarkable result about black holes. Under normal circumstances, when a quantum fluctuation creates a virtual particle pair, the pair will annihilate and disappear back into the vacuum in a time short enough so that the violation of conservation of energy (incurred by the pair's creation from nothing) is not observable. However, when a virtual particle pair pops out in the curved space near a black hole, one of the particles may fall into the hole, and then the other can escape and be observed. This is because the particle that falls into the black hole can in principle lose more energy in the process than the amount required to create it from nothing. It thus contributes “negative energy” to the black hole, and the black hole's own energy is therefore decreased. This satisfies the energy-conservation law's balance-sheet, making up for the energy that the escaping particle is observed to have. This is how the black hole emits radiation. Moreover, as the black hole's own energy decreases bit by bit in this process, there is a concomitant decrease in its mass. Eventually, it may completely evaporate, leaving behind only the radiation it produced in its lifetime.
Hawking and many others have gone beyond a consideration of quantum fluctuations of matter in a background curved space to something even more exotic and less well defined. If quantum mechanics applies not merely to matter and radiation but to gravity as well, then on sufficiently small scales quantum fluctuations in spacetime itself must occur. Unfortunately, we have no workable theory for dealing with such processes, but this has not stopped a host of tentative theoretical investigations of phenomena that might result. One of the most interesting speculations is that quantum mechanical processes might allow the spontaneous creation not just of particles but of whole new baby universes. The quantum mechanical formalism describing how this might occur is, at least mathematically, very similar to the wormhole solutions discovered in ordinary general relativity. Via such “Euclidean” wormholes, a temporary “bridge” is created, from which a new universe springs. The possibilities of Euclidean wormhole processes and baby universes are sufficiently exciting that quantum fluctuations were mentioned during Hawking's poker game with Einstein and Newton in the Next Generation episode “Descent.” 1 If the Star Trek writers were confused, they had a right to be. These issues are unfortunately currently very murky. Until we discover the proper mathematical framework to treat such quantum gravitational processes, all such discussions are shots in the dark.
What is most relevant to us here is not the phenomenon of black-hole evaporation, or even baby universes, as interesting as they may be, but rather the discovery that quantum fluctuations of empty space can, at least in the presence of strong gravitational fields, become endowed with properties reminiscent of those required to hold open a worm-hole. The central question, which also has no definitive answer yet, is whether quantum fluctuations near a wormhole can behave sufficiently exotically to allow one to keep a wormhole open.
(By the way, once again, I find the Star Trek writers remarkably prescient in their choice of nomenclature. The Bajoran and Barzan wormholes are said to involve “verteron” fields. I have no idea whether this name was plucked out of a hat or not. However, since virtual particlesthe quantum fluctuations in otherwise empty space are currently the best candidate for Kip Thorne's “exotic matter,” I think the Star Trek writers deserve credit for their intuition, if that's what it was.)
More generally, if quantum fluctuations in the vacuum can be exotic, is it possible that some other nonclassical configuration of matter and radiationlike, say, a warp core breach, or perhaps Scotty's “intermix” imbalance in the warp drivemight also fill the bill? Questions such as this remain unanswered. While by no means circumventing the incredible implausibility of stable wormholes in the real universe, they do leave open the larger question of whether wormhole travel is impossible or merely almost impossible. The wormhole issue is not just one of science fact versus science fiction: it is a key that can open doors which many would prefer to leave closed.
TIME MACHINES REVISITED: Wormholes, as glorious as they would be for tunneling through vast distances in space, have an even more remarkable potential, glimpsed most recently in the Voyager episode “Eye of the Needle.” In this episode, the Voyager crew discovered a small wormhole leading back to their own “alpha quadrant” of the galaxy. After communicating through it, they found to their horror that it led not to the alpha quadrant they knew and loved but to the alpha quadrant of a generation earlier. The two ends of the wormhole connected space at two different times!
Well, this is another one of those instances in which the Voyager writers got it right. If wormholes exist, they can
and will be time machines! This startling realization has grown over the last decade, as various theorists, for lack of anything more interesting to do, began to investigate the physics of wormholes a little more seriously. Worm- hole time machines are easy to design: perhaps the simplest example (due again to Kip Thorne) is to imagine a wormhole with one end fixed and the other end moving at a fast but sublight speed through a remote region of the galaxy. In principle, this is possible even if the length of the wormhole remains unchanged. In my earlier two- dimensional wormhole drawing, just drag the bottom half of the sheet to the left, letting space “slide” past the bottom mouth of the wormhole while this mouth stays fixed relative to the wormhole's other mouth:
Because the bottom mouth of the wormhole will be moving with respect to the space in which it is situated, while the top mouth will not, special relativity tells us that clocks will tick at different rates at each mouth. On the other hand, if the length of the wormhole remains fixed, then as long as one is inside the wormhole the two ends appear to be at rest relative to each other. In this frame, clocks at either end should be ticking at the same rate. Now slide the bottom sheet back to where it used to be, so that the bottom mouth of the wormhole ends up back where it started relative to the background space. Let's say that this process takes a day, as observed by someone near the bottom mouth. But for an observer near the top mouth, this same process could appear to have taken ten days. If this second observer were to peer through the top mouth to look at the observer located near the bottom mouth, he would see on the wall calendar next to the observer a date nine days earlier! If he now decides to go through the worm-hole for a visit, he will travel backward in time.
If stable wormholes exist, we must therefore concede that time machines are possible. We now return finally to Einstein's remarks early in the last chapter. Can time travel, and thus stable wormholes, and thus exotic matter with negative energy, be “excluded on physical grounds”?
Wormholes are after all merely one example of time machines that have been proposed in the context of general relativity. Given our previous discussion about the nature of the theory, it is perhaps not so surprising that time travel becomes a possibility. Let's recall the heuristic description of Einstein's equations which I gave earlier:
The left-hand side of this equation fixes the geometry of spacetime. The right-hand side fixes the matter and energy distribution. Generally we would ask: For a given distribution of matter and energy, what will be the resulting curvature of space? But we can also work backward: For any given geometry of space, including one with “closed timelike curves”that is, the “causality loops,” which allow you to return to where you began in space and time, like the loop the Enterprise was caught in before, during, and after crashing into the Boze-man Einstein's equations tell you exactly what distribution of matter and energy must be present. So in principle you can design any kind of time-travel universe you want; Einstein's equations will tell you what matter and energy distribution is necessary. The key question then simply becomes: Is such a matter and energy distribution physically possible?
We have already seen how this question arises in the context of wormholes. Stable wormholes require exotic matter with negative energy. Kurt Gšdel's time-machine solution in genera! relativity involves a universe with constant uniform energy density and zero pressure which spins but does not expand. More recently, a proposed time machine involving “cosmic strings” was shown to require a negative-energy configuration. In fact, it was recently proved that any configuration of matter in general relativity which might allow time travel must involve
exotic types of matter with negative energy as viewed by at least one observer.
It is interesting that almost all the episodes in Star Trek involving time travel or temporal distortions also involve some catastrophic form of energy release, usually associated with a warp core breach. For example, the temporal causality loop in which the Enterprise was trapped resulted only after (although the concepts of “before” and “after” lose their meaning in a causality loop) a collision with the Bozeman, which caused the warp core to breach and thereby caused the destruction of the Enterprise, a series of events that kept repeating over and over, until finally in one cycle the crew managed to avoid the collision. The momentary freezing of time aboard the Enterprise, discovered by Picard, Data, Troi, and LaForge in the episode “Timescape,” also appears to have been produced by a nascent warp core breach combined with a failure of the engine core aboard a nearby Romulan vessel. In “Time Squared,” a vast “energy vortex” propelled Picard back in time. In the original example of Star Trek time travel, “The Naked Time,” the Enterprise was thrown back three days following a warp core implosion. And the mammoth spacetime distortion in the final episode of The Next Generation, which travels backward in time and threatens to engulf the entire universe, was caused by the simultaneous explosion of three different temporal versions of the Enterprise, which converged at the same point in space.
So, time travel in the real universe, as in the Star Trek universe, seems to hinge on the possibility of exotic configurations of matter. Could some sufficiently advanced alien civilization construct a stable wormhole? Or can we characterize all mass distributions that might lead to time travel and then exclude them, as a set, “on physical grounds,” as Einstein might have wished? To date, we do not know the answer. Some specific time machines such as Gšdel's, and the cosmic-string-based systemhave been shown to be unphysical. While wormhole time travel has yet to be definitively ruled out, preliminary investigations suggest that the quantum gravitational fluctuations themselves may cause wormholes to self-destruct before they could lead to time travel.
Until we have a theory of quantum gravity, the final resolution of the issue of time travel is likely to remain unresolved. Nevertheless, several brave individuals, including Stephen Hawking, have already tipped their hand. Hawking is convinced that time machines are impossible, because of the obvious paradoxes that might result, and he has proposed a “chronology-protection conjecture,” to wit: “The laws of physics do not allow the appearance of closed timelike curves.”
I am personally inclined to agree with Hawking in this case. Nevertheless, physics is not done by fiat. As I have stated earlier, general relativity often outwits our naive expectations. As a warning, I provide two historical precedents. Twice before (that I know of), eminent theorists have argued that a proposed phenomenon in general relativity should be dismissed because the laws of physics must forbid it:
1. When the young astrophysicist Subrahmanyan Chandrasekhar proposed that stellar cores more massive than 1.4 times the mass of the Sun cannot, after burning all their nuclear fuel, settle down as white dwarfs but must continue to collapse due to gravity, the eminent physicist Sir Arthur Eddington dismissed the result in public, stating, “Various accidents may intervene to save the star, but I want more protection than that. I think there should be a law of nature to prevent a star from behaving in this absurd way!” At the time, much of the astrophysics community sided with Eddington. A half century later, Chandrasekhar shared the Nobel Prize for his insights, which have long since been verified.
2. Slightly over 20 years after Eddington dismissed Chan-drasekhar's claim, a remarkably similar event ocurred at a conference in Brussels. J. Robert Oppenheimer, the distinguished American theoretical physicist and father of the atomic bomb, had calculated that objects called neutron starsleft over after supernovae and even more dense than white dwarfscould not be larger than about twice the mass of the Sun without collapsing further to form what we would now call a black hole. The equally distinguished John Archibald Wheeler argued that this result was impossible, for precisely the reason Eddington had given for his earlier rejection of Chandrasekhar's claim: somehow the laws of physics must protect objects from such an absurd fate. Within a decade, Wheeler would completely capitulate and, ironically, would become known as the man who gave black holes their name.