Wormholes and Time Travel (Part 1)

A Briefer History of Time – Stephen Hawking

The last chapter discussed why we see time go forward: why disorder increases and why we remember the past but not the future. Time was treated as if it were a straight railway line on which one could only go one way or the other.

But what if the railway line had loops and branches so that a train could keep going forward but come back to a station it had already passed? In other words, might it be possible for someone to travel into the future or the past?

H. G. Wells in The Time Machine explored these possibilities as have countless other writers of science fiction. Yet many of the ideas of science fiction, like submarines and travel to the moon, have become matters of science fact. So what are the prospects for time travel?

The first indication that the laws of physics might really allow people to travel in time came in 1949 when Kurt Gödel discovered a new space- time allowed by general relativity. Gödel was a mathematician who was famous for proving that it is impossible to prove all true statements, even if you limit yourself to trying to prove all the true statements in a subject as apparently cut and dried as arithmetic. Like the uncertainty principle, Gödel’s incompleteness theorem may be a fundamental limitation on our ability to understand and predict the universe, but so far at least it hasn’t seemed to be an obstacle in our search for a complete unified theory.

Gödel got to know about general relativity when he and Einstein spent their later years at the Institute for Advanced Study in Princeton. His space-time had the curious property that the whole universe was rotating. One might ask: “Rotating with respect to what?” The answer is that distant matter would be rotating with respect to directions that little tops or gyroscopes point in.

This had the side effect that it would be possible for someone to go off in a rocket ship and return to earth before he set out. This property really upset Einstein, who had thought that general relativity wouldn’t allow time travel. However, given Einstein’s record of ill-founded opposition to gravitational collapse and the uncertainty principle, maybe this was an encouraging sign. The solution Gödel found doesn’t correspond to the universe we live in because we can show that the universe is not rotating. It also had a non-zero value of the cosmological constant that Einstein introduced when he thought the universe was unchanging. After Hubble discovered the expansion of the universe, there was no need for a cosmological constant and it is now generally believed to be zero. However, other more reasonable space-times that are allowed by general relativity and which permit travel into the past have since been found. One is in the interior of a rotating black hole.

Another is a space-time that contains two cosmic strings moving past each other at high speed. As their name suggests, cosmic strings are objects that are like string in that they have length but a tiny cross section. Actually, they are more like rubber bands because they are under enormous tension, something like a million million million million tons. A cosmic string attached to the earth could accelerate it from 0 to 60 mph in 1/30th of a second. Cosmic strings may sound like pure science fiction but there are reasons to believe they could have formed in the early universe as a result of symmetry-breaking of the kind discussed in Chapter 5. Because they would be under enormous tension and could start in any configuration, they might accelerate to very high speeds when they straighten out.

The Gödel solution and the cosmic string space-time start out so distorted that travel into the past was always possible. God might have created such a warped universe but we have no reason to believe he did.

Observations of the microwave background and of the abundances of the light elements indicate that the early universe did not have the kind of curvature required to allow time travel. The same conclusion follows on theoretical grounds if the no boundary proposal is correct. So the question is: if the universe starts out without the kind of curvature required for time travel, can we subsequently warp local regions of space-time sufficiently to allow it?

A closely related problem that is also of concern to writers of science fiction is rapid interstellar or intergalactic travel. According to relativity, nothing can travel faster than light. If we therefore sent a spaceship to our nearest neighboring star, Alpha Centauri, which is about four light- years away, it would take at least eight years before we could expect the travelers to return and tell us what they had found. If the expedition were to the center of our galaxy, it would be at least a hundred thousand years before it came back. The theory of relativity does allow one consolation. This is the so-called twins paradox mentioned in Chapter 2.

Because there is no unique standard of time, but rather observers each have their own time as measured by clocks that they carry with them, it is possible for the journey to seem to be much shorter for the space travelers than for those who remain on earth. But there would not be much joy in returning from a space voyage a few years older to find that everyone you had left behind was dead and gone thousands of years ago.

So in order to have any human interest in their stories, science fiction writers had to suppose that we would one day discover how to travel faster than light. What most of these authors don’t seem to have realized is that if you can travel faster than light, the theory of relativity implies you can also travel back in time, as the following limerick says: There was a young lady of Wight Who travelled much faster than light.

She departed one day, In a relative way, And arrived on the previous night. The point is that the theory of relativity says that there is no unique measure of time that all observers will agree on. Rather, each observer has his or her own measure of time. If it is possible for a rocket traveling below the speed of light to get from event A (say, the final of the 100- meter race of the Olympic Games in 2012) to event B (say, the opening of the 100,004th meeting of the Congress of Alpha Centauri), then all observers will agree that event A happened before event B according to their times.

Suppose, however, that the spaceship would have to travel faster than light to carry the news of the race to the Congress. Then observers moving at different speeds can disagree about whether event A occurred before B or vice versa. According to the time of an observer who is at rest with respect to the earth, it may be that the Congress opened after the race. Thus this observer would think that a spaceship could get from A to B in time if only it could ignore the speed-of-light speed limit. However, to an observer at Alpha Centauri moving away from the earth at nearly the speed of light, it would appear that event B, the opening of the Congress, would occur before event A, the 100-meter race. The theory of relativity says that the laws of physics appear the same to observers moving at different speeds.

This has been well tested by experiment and is likely to remain a feature even if we find a more advanced theory to replace relativity. Thus the moving observer would say that if faster-than-light travel is possible, it should be possible to get from event B, the opening of the Congress, to event A, the 100-meter race. If one went slightly faster, one could even get back before the race and place a bet on it in the sure knowledge that one would win.

There is a problem with breaking the speed-of-light barrier. The theory of relativity says that the rocket power needed to accelerate a spaceship gets greater and greater the nearer it gets to the speed of light.

We have experimental evidence for this, not with spaceships but with elementary particles in particle accelerators like those at Fermilab or CERN (European Centre for Nuclear Research). We can accelerate particles to 99.99 percent of the speed of light, but however much power we feed in, we can’t get them beyond the speed-of-light barrier.
Similarly with spaceships: no matter how much rocket power they have, they can’t accelerate beyond the speed of light.

That might seem to rule out both rapid space travel and travel back in time. However, there is a possible way out. It might be that one could warp space-time so that there was a shortcut between A and B. One way of doing this would be to create a wormhole between A and B. As its name suggests, a wormhole is a thin tube of space-time which can connect two nearly flat regions far apart.

There need be no relation between the distance through the wormhole and the separation of its ends in the nearly flat background. Thus one could imagine that one could create or find a wormhole that would lead from the vicinity of the Solar System to Alpha Centauri. The distance through the wormhole might be only a few million miles even though earth and Alpha Centauri are twenty million million miles apart in ordinary space. This would allow news of the 100-meter race to reach the opening of the Congress. But then an observer moving toward the earth should also be able to find another wormhole that would enable him to get from the opening of the Congress on Alpha Centauri back to earth before the start of the race. So wormholes, like any other possible form of travel faster than light, would allow one to travel into the past.

The idea of wormholes between different regions of space-time was not an invention of science fiction writers but came from a very respectable source. In 1935, Einstein and Nathan Rosen wrote a paper in which they showed that general relativity allowed what they called “bridges,” but which are now known as wormholes. The Einstein-Rosen bridges didn’t last long enough for a spaceship to get through: the ship would run into a singularity as the wormhole pinched off. However, it has been suggested that it might be possible for an advanced civilization to keep a wormhole open. To do this, or to warp space-time in any other way so as to permit time travel, one can show that one needs a region of space- time with negative curvature, like the surface of a saddle. Ordinary matter, which has a positive energy density, gives space-time a positive curvature, like the surface of a sphere. So what one needs, in order to warp space-time in a way that will allow travel into the past, is matter with negative energy density.

Energy is a bit like money: if you have a positive balance, you can distribute it in various ways, but according to the classical laws that were believed at the beginning of the century, you weren’t allowed to be overdrawn. So these classical laws would have ruled out any possibility of time travel. However, as has been described in earlier chapters, the classical laws were superseded by quantum laws based on the uncertainty principle.