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General relativity combines the time dimension with the three dimensions of
space to form what is called spacetime. The theory incorporates the effect of
gravity by saying that the distribution of matter and energy in the universe
warps and distorts spacetime, so that it is not flat. Objects in this spacetime
try to move in straight lines, but because spacetime is curved, their paths
appear bent. They move as if affected by a gravitational field.
As a rough analogy, not to be taken too literally, imagine a sheet of rubber.
One can place a large ball on the sheet to represent the Sun. The weight of the
ball will depress the sheet and cause it to be curved near the Sun. If one now
rolls little ball bearings on the sheet, they won't roll straight across to
the other side but instead will go around the heavy weight, like planets
orbiting the Sun.
The analogy is incomplete because in it only a two-dimensional section of space
(the surface of the rubber sheet) is curved, and time is left undisturbed, as it
is in Newtonian theory. However, in the theory of relativity, which agrees with
a large number of experiments, time and space are inextricably tangled up. One
cannot curve space without involving time as well. Thus time has a shape. By
curving space and time, general relativity changes them from being a passive
background against which events take place to being active, dynamic participants
in what happens. In Newtonian theory, where time existed independently of
anything else, one could ask: What did God do before He created the universe? As
Saint Augustine said, one should not joke about this, as did a man who said, "He was preparing Hell for those who pry too deep." It is a serious question
that people have pondered down the ages. According to Saint Augustine, before
God made heaven and earth, He did not make anything at all. In fact, this is
very close to modern ideas.
In general relativity, on the other hand, time and space do not exist
independently of the universe or of each other. They are defined by measurements
within the universe, such as the number of vibrations of a quartz crystal in a
clock or the length of a ruler. It is quite conceivable that time defined in
this way, within the universe, should have a minimum or maximum valuein other
words, a beginning or an end. It would make no sense to ask what happened before
the beginning or after the end, because such times would not be defined.
It was clearly important to decide whether the mathematical model of general
relativity predicted that the universe, and time itself, should have a beginning
or end. The general prejudice among theoretical physicists, including Einstein,
held that time should be infinite in both directions. Otherwise, there were
awkward questions about the creation of the universe, which seemed to be outside
the realm of science. Solutions of the Einstein equations were known in which
time had a beginning or end, but these were all very special, with a large
amount of symmetry. It was thought that in a real body, collapsing under its own
gravity, pressure or sideways velocities would prevent all the matter falling
together to the same point, where the density would be infinite. Similarly, if
one traced the expansion of the universe back in time, one would find that the
matter of the universe didn't all emerge from a point of infinite density.
Such a point of infinite density was called a singularity and would be a
beginning or an end of time.
In 1963, two Russian scientists, Evgenii Lifshitz and Isaac Khalatnikov, claimed
to have proved that solutions of the Einstein equations with a singularity all
had a special arrangement of matter and velocities. The chances that the
solution representing the universe would have this special arrangement were
practically zero. Almost all solutions that could represent the universe would
avoid having a singularity of infinite density:
Excerpted from The Universe in a Nutshell by Stephen Hawking Copyright 2001 by Stephen Hawking. Excerpted by permission of Bantam, a division of Random House, Inc. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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