Page 77 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 10
CHAPTER 10

WORMHOLES AND TIME TRAVEL

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
Godel discovered a new space-time allowed by general relativity. Godel 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, Godel’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.

Godel 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 Godel 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 Godel 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

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