Stephen Hawking (42 page)

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
laughingstock 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 spacetime 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 around 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 spacetime. 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
The Illustrated Brief History of Time
,
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 = mc
²
), 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 around and around 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
seconds. 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
seconds 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
seconds 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
seconds, 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.