Even though Stephen Hawking turned fifty in 1992 (coincidentally, the year in which the first edition of this book was published) and had forecast the death of physics twelve years earlier, he has continued to be involved in scientific research since then. But like many grand old men of science (a description which, against all the odds, is now an entirely apt one for Hawking), in his later years he has turned his attention to ideas at the wilder fringes of scientific respectability. During the middle part of the 1990s, Hawking’s research contributions largely involved the paradoxes and possibilities of time travel—a field he entered not as a pioneer, but following in the footsteps of his old friend and scientific sparring partner, Kip Thorne.
You may be surprised to learn that the subject of time travel is a respectable area of research at all, even at the wilder fringes of respectability. If so, you are not alone. When one of us wrote a book about time travel1 and it was reviewed in the pages of the astronomical magazine Observatory, the magazine received an irate letter from two engineers at the University of Hull, castigating the editors
for lending credence to such ridiculous notions by even acknowledging the existence of the book. But everything in that book, and everything we have to tell you in this chapter, is based on solid, respectable science, jumping off from the work of Thorne and the equally eminent Igor Novikov (formerly of the Soviet Union, now working in Denmark)—and, of course, of Hawking himself. Building a time machine may not yet be a practicable engineering prospect, but the possibility that natural time machines may exist is one that an increasing number of scientists are now taking very seriously indeed.
The physical description of a working time machine that has intrigued Hawking and other researchers recently is closely related to the physics of baby universes, described in Chapter 13. On that scenario, matter that collapses into a black hole and toward a singularity in our Universe can somehow be shunted sideways in space-time, emerging to form a new expanding universe, in its own set of space-time dimensions. But what we did not spell out in our earlier discussion is that in principle the original black hole and the new baby universe are still connected by the cosmological equivalent of an umbilical cord, a tunnel through space-time that the cosmologists prosaically refer to as a “wormhole.” In the context of baby universes, such a wormhole would have a diameter comparable to the smallest quantum of length (the Planck length, about 10-35 m) and since no information could get out of the black hole marking the end of the wormhole in our Universe, the connection seems to be only of academic interest.
But there is another way of looking at wormholes, one that has long been a favorite of science fiction writers. The equations of the general theory of relativity also allow for the existence of a more modest kind of wormhole, which links two places in our own Universe. Einstein himself, working with Nathan Rosen at Princeton in the 1930s, worked out the appropriate mathematical
description of such a wormhole, which is known as an Einstein-Rosen bridge.
The usual problems with wormholes apply to an Einstein-Rosen bridge, which is, in effect, a wormhole linking two black holes in our Universe—a shortcut through space-time. Such a wormhole could form naturally, the equations say; but the gravity of the black holes at either end of the tunnel would snap the wormhole shut faster than light could travel along it, closing it before there was time for anything to get from one end to the other.
This result was so well known that for fifty years no relativists bothered to study the equations describing such wormholes in detail. But that didn’t stop the SF writers leaping on the idea and using it as a basis for moving their characters (and spaceships) around the Universe more or less instantaneously. The idea is that if you had an Einstein-Rosen bridge connecting a region of space near our Sun with a region of space on the other side of the Galaxy, a spaceship could dive in one end and come out of the other end essentially instantaneously, without the bother of covering all the intervening space at something less than the speed of light. But what those SF writers carefully swept under the carpet was the evidence that any such tunnel through space would only be open for a fraction of a second and would in any case only be as wide as the Planck length, so that their spaceships (and any passengers) would be distinctly crushed by their journey.
All of that changed, as Kip Thorne recounts in his book Black Holes and Time Warps,2 in the mid-1980s, when the noted scientist Carl Sagan decided to turn his hand to fiction. Like other SF writers, Sagan wanted to use the idea of a tunnel through space to get round the speed-of-light barrier. But being a scientist, he wanted at least to pay lip service to the problem of the rapid collapse of a wormhole and give his readers some scientific double-talk to provide a fictional “explanation” of why the tunnel they were traveling
through did not collapse. He turned to Kip Thorne for advice on how he might provide this necessary verbal camouflage, and Thorne took up the challenge.
At the end of the 1984-1985 academic year, Thorne realized that what would be needed to hold a wormhole open would be to thread it with so-called “exotic matter.” Exotic matter gets its name because it has a bizarre property—negative pressure, or negative tension. If you squeeze ordinary matter, it is compressed; but if you squeeze exotic matter, it expands (it doesn’t just resist your squeeze; it really does expand). You might think that this is hardly a step forward, since nobody has ever seen exotic matter. And yet cosmologists believe that it might occur naturally in the Universe, in the form of what is known as cosmic string.
Cosmic string is hypothetical material left over from the Big Bang, in the form of tubes of energy much narrower than an atom but possibly stretching across the entire Universe. It is a by-product of the era of the Big Bang itself, and the best way to think of it is as a piece of the Big Bang “frozen” and trapped inside a tube with a diameter of just 10-14 that of an atomic nucleus. Because the string contains the energy density of the Universe as it was about 10-35 seconds after the moment of creation, even though it is so narrow each centimeter of cosmic string would contain the equivalent of 10 trillion tons of mass. A loop of cosmic string a meter long would weigh as much as the Earth.
There is no direct proof that cosmic strings exist or ever have existed, but there is some circumstantial evidence—such objects could have provided the “seeds” on which galaxies grew when the Universe was young. The gravitational influence of loops of string would make clouds of gas clump together, eventually getting big enough to carry on the job of galaxy formation unaided.
And, you may have guessed, cosmic string has another strange property. It operates under negative tension. If you pull a piece of
cosmic string, it will shrink; but if you squeeze it, it will stretch. It is just the stuff to hold wormholes open with; the more the gravity of the black holes involved tries to squeeze the wormhole shut, the more the cosmic string will expand and hold it open.
Sagan was delighted with Thorne’s suggestions on how to hold a traversable star gate open, and the explanation duly appeared in his novel, Contact, published in 1985. At the time, few readers realized that the “mumbo-jumbo” describing the structure of the wormhole through which Sagan’s characters traveled was actually the most up-to-date scientific theory about wormholes, at the cutting edge of research. But what is really surprising, with hindsight, is that neither Thorne nor Sagan immediately appreciated that the equations Thorne had found which allowed for the existence of a traversable wormhole would apply equally well to time travel as to space travel. The point, of course, is that Einstein’s equations of the general theory of relativity describe space-time, not just space alone. A wormhole (an Einstein-Rosen bridge) can link different parts of space-time in our own Universe. This means that it can link different regions of space at the same time (allowing instantaneous space travel). It can also link the same place at different times (allowing instantaneous time travel). Or, indeed, it can link different places at different times, allowing the intrepid voyager to travel through both space and time, simultaneously and instantaneously. Thorne only realized the full power of the work he had started out on as a favor to Sagan when he went to a symposium in Chicago in December 1986, and one of the other participants pointed out the implications of the work for time travel.
This posed Thorne with what he thought was a real dilemma. He had two students, Michael Morris and Ulvi Yurtsever, who were eager to work on the theory of wormholes. But Thorne worried that they might blight their careers by publishing papers about time travel and become a laughing stock in the scientific community. It
wasn’t until 1988 that the three of them published a paper on time travel, in the journal Physical Review Letters (vol. 61, p. 1446), and even when the paper appeared Thorne instructed the staff at the Caltech public relations department to turn their job on its head— not only were they not allowed to publicize the paper, but they had to try to suppress any publicity for the work!
Of course, this didn’t work. News about the paper, and the evidence that the laws of the general theory of relativity—the best theory of space-time that we have—do not forbid time travel, spread quickly. The effect was exactly the opposite of what Thorne had feared. His own career received a boost, and the careers of his two students were kick-started triumphantly. Over in Russia, Igor Novikov had been thinking along similar lines but had been afraid to publish for fear of being ridiculed; encouraged by the reception for the Caltech work, he presented his own ideas in public, and time travel studies became respectable.
Hawking was one of the researchers who joined this cottage industry in the 1990s. We should emphasize that none of this work is directed at developing any practical means of time travel, even in the far future. Any civilization that wanted to build a time machine would have to be able to manipulate stellar mass black holes, as well as having access to a supply of cosmic string. The relativists today are more concerned about the implications that wormholes that form time machines might exist naturally in the Universe, perhaps left over from the Big Bang itself. Even if the wormholes were only big enough for particles like electrons and protons to travel through them, there would be serious implications for our understanding of the way the Universe works.
So the efforts of the theorists in the 1990s concentrated on two approaches to the problem. First, they tried to prove that time travel really is impossible and that Thorne and his colleagues were mistaken when they claimed otherwise. This approach has failed; there
is still no evidence that the laws of physics forbid time travel, only that they make it very difficult to build a time machine. But the second approach is intriguingly different and is where Hawking really comes into the story of time travel, although he is also one of the people who would like to be able to prove that it is impossible. The aim is to show that the Universe is set up in such a way that the only kind of time travel that can actually occur does not disturb the status quo.
This is known as the “chronology protection conjecture” (a term invented by Hawking), and you can see why it is important by pondering the implications of the “granny paradox,” a theme that has been exhaustively explored, in different variations, by the science fiction writers.
In the classic version of the paradox, a time traveler goes back in time and inadvertently (or even deliberately) causes the death of his maternal grandmother, before his own mother was born. So the time traveler himself could never have existed, in which case, his granny was never killed, and he did exist—and so on.
Physicists are uncomfortable when dealing with people (at least when dealing with people as experimental objects), but Novikov and Thorne have treated the puzzle in terms any physicist can feel at ease with (the possibilities of this variation on the theme were first pointed out to Thorne in a letter from Joe Polchinski, of the University of Texas in Austin). Imagine a wormhole that is bent round on itself so that it has two mouths alongside each other in space but at different times. One mouth is a few seconds in the past of the other. Now roll a billiard ball into the second mouth. The ball comes out of the first mouth a few seconds before it goes in the second mouth. This is already a neat trick; but with a little practice at rolling the ball on different trajectories into the second mouth, you can do something even more interesting. Arrange the path of the ball so that when it emerges from the first mouth it bumps into the
version of itself that is still traveling toward the second hole, knocking itself out of the way. So the ball never goes round the time loop, in which case, it did not knock itself out of the way, and it did enter the time tunnel—and so on.
The relevance of this puzzle is that it addresses subjects such as free will and determinism, and whether the Universe “knows” in advance the outcome of a scientific experiment—it asks how time itself works.
One resolution of the puzzle, familiar from science fiction and endorsed by some interpretations of quantum theory, is that there are many different parallel realities (perhaps an infinite number) existing side by side, in some sense, in a multidimensional space-time. On that picture, the granny who gets killed is the one in the universe next door (or a few blocks over), and although in that reality she has no children, in the first reality the original granny (from the perspective of the time traveler) grows up and has a daughter who has a son. This is the kind of time travel scenario explored in the Back to the Future series of movies. In the first of those movies, Marty has not changed the past to make his father a successful author; Marty himself (as becomes clear in Back to the Future II) has somehow slipped into a parallel reality, and in that reality his father always was a successful author (there ought, therefore, to be two Martys in the “new” reality, but even Steven Spielberg sometimes misses a trick!). This approach also has a family resemblance to the sum-over-histories approach to quantum mechanics, mentioned in Chapter 10,3 although now the different realities are each treated as “real” in their own right and are not averaged over.
The other resolution to the granny paradox is sometimes called the consistent histories approach, and says that even if people (or particles) can travel in time, whatever happens when they do so must be a self-consistent solution to the laws of physics. So you can’t go back in time and kill your granny when she was a little girl, because history already records that the killing did not occur. You
may try to do so, if you are nasty enough, but (as several SF writers have entertainingly suggested) if you do try, something will happen to deflect you from your intended course of action.
Hawking discusses both possibilities in his latest book,4 where he also points out a neat way to explain why we have not received any visitors from the future. After all, even though it might take thousands of years to develop the technology to travel in time, once a civilization had done so, wouldn’t the whole of the past be open to it for exploration? Perhaps not. A possible way to explain the absence of visitors from the future today is that a time machine would open up the entire future for exploration but would only allow time travelers to go back in time to the moment when the time machine first became operational. They could not go any further back because at earlier times the machine would not exist!
But the chronology protection conjecture may make all such speculation redundant, if it operates the way Hawking himself thinks it might.
This has to do with the way a time machine doesn’t only act as a time machine, but (as you may have noticed) as a matter duplicator. In the example of the billiard ball traveling round a time loop, there is a short period of time—a few seconds in our chosen example, but it could be as long as you like—in which there are two copies of the ball in the same present. The matter the second version of the ball is made of represents a substantial amount of energy (in line with Einstein’s equation, E = mc2), and a human being (let alone a spaceship) would represent much more energy. This energy requirement is another constraint on the construction of a practical time machine—you would have to supply an enormous amount of additional energy to send anything through the machine, equivalent to making a duplicate of the object being transmitted, although that might not be much of a problem to a civilization that could manipulate cosmic string.
One of the arguments proposed in an attempt to prove that time travel wormholes could not exist drew on this “photocopying” propensity of time machines. It said that if such a wormhole did exist, a beam of light (or even a few photons, the particles of light) shone into one mouth would go round and round the time loop, duplicating itself each time, and adding up to make an infinitely large blast of energy that would blow the time machine apart. Thorne convinced himself (and the other time travel researchers) that this would not happen, because each time the beam of light comes out of the mouth of the wormhole it is defocused and spread out to fill the Universe. Only a tiny fraction gets caught in the other mouth of the wormhole and repeats the round-trip.
But there is another kind of radiation that also has to be taken into account—the equivalent for a wormhole of the Hawking Radiation associated with a black hole. Quantum uncertainty, as we discussed in Chapter 9, allows the existence of vacuum fluctuations, usually temporary particles created out of nothing at all; these fluctuations can be promoted to become real particles in regions of intense gravity, like the surroundings of a wormhole. This obviously had to be taken into account in any satisfactory discussion of the physics of time machines. But the equations that describe the conditions that allow these quantum fluctuations to produce a shower of photons in a beam that would grow and circulate around a wormhole are horrendously complicated, and Thorne and his colleague Sung-Won Kim struggled with the puzzle throughout most of 1990.
The reason why they calculated the effects of photons, rather than any other particles, is not just because photons are simpler to work with but because they travel at the speed of light, so that they loop round and round a time tunnel faster than anything else can go. At first, Thorne and Kim found that, unlike ordinary light, the vacuum fluctuations effectively refocused themselves of their own accord. The vacuum radiation spraying out into the Universe from
one end of the whole would, the equations insisted, be bent back toward the other mouth, as if by a mysterious force, repeatedly traveling through the time loop and building up to disastrous levels. Then the two researchers decided that they were wrong. They thought they had discovered that the buildup of electromagnetic energy could only be infinite for “a vanishingly small interval of time.” Why should this matter? Because as we explained in Chapter 11, quantum physics tells us that even time has a kind of graininess and that there is no interval of time shorter than the Planck time, 10-45 sec. So there is no such thing as “a vanishingly small interval of time.”
When Thorne and Kim reworked their calculations making allowance for the graininess of time implied by the Planck time, they found that quantum effects would stop the disastrous buildup of radiation. So they wrote the work up in a paper that they submitted to the journal Physical Review, and at the same time sent copies of the paper to various colleagues around the world, including Hawking.
Hawking found the flaw in their argument. Although the Planck time is the smallest interval of time, as Einstein showed with his special theory of relativity, the measured length of a time interval depends on how the clock doing the measuring is moving. For the buildup of radiation in a wormhole, the relevant time is the time measured by someone sitting outside the wormhole and watching what is going on. For a clock traveling through the wormhole at high speed, the cutoff caused by the effects of quantum gravity does indeed stop the buildup of vacuum radiation 10-45 sec before the wormhole becomes a time machine. But to anybody sitting outside the wormhole and watching the buildup of radiation, this cutoff happens later—only 10-95 sec before the time machine starts to operate. Hawking’s revision of the timescale meant that there was potentially still time for the buildup of radiation to destroy the
wormhole before it could begin operating as a time machine. But nobody has yet been able to prove (or disprove) this conjecture.
The numbers involved are so tiny that it is mind-boggling to think that physicists can even begin to take note of these effects in their calculations. The number 10-95 is a decimal point followed by 94 zeroes and a 1. In order to be certain whether or not time machines can exist, we will need an understanding of quantum gravity, operating over such ridiculously small intervals of time as 10-95 sec, to explain what happens to the buildup of quantum fluctuations inside a wormhole. And this is why the subject of time travel is now of intense interest to physicists—not so much because they aim to prove or disprove that time machines can be built, but because they are still seeking a successful quantum theory of gravity, and by tackling puzzles such as the chronology protection conjecture they hope to be able to find which variations on the quantum gravity theme are worth pursuing. We are right back at the search for a theory of everything, the Holy Grail that always seems to lie just twenty tantalizing years into the future.
Hawking’s chronology protection conjecture can be summed up, in its latest form, as saying that whenever any civilization, no matter how advanced, tries to build a time machine, by whatever means, just before the device starts to operate in time machine mode a beam of vacuum fluctuation radiation akin to Hawking Radiation will build up inside the machine and destroy it. Although Thorne agrees that “we cannot know for sure until physicists have fathomed in depth the laws of quantum gravity,”5 it is significant that on this occasion he refuses to place a bet against Hawking and says that “Hawking is likely to be right.” The chronology protection conjecture is likely to be Hawking’s last significant contribution to science; appropriately, it may mark the end of time travel, if not the end of time.