Page 70 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 8

Figure 8:1

The history of the universe in real time, however, would look very different. At about ten or twenty thousand million
years ago, it would have a minimum size, which was equal to the maximum radius of the history in imaginary time. At
later real times, the universe would expand like the chaotic inflationary model proposed by Linde (but one would not
now have to assume that the universe was created somehow in the right sort of state). The universe would expand to
a very large size Figure 8:1 and eventually it would collapse again into what looks like a singularity in real time. Thus,
in a sense, we are still all doomed, even if we keep away from black holes. Only if we could picture the universe in
terms of imaginary time would there be no singularities.

If the universe really is in such a quantum state, there would be no singularities in the history of the universe in
imaginary time. It might seem therefore that my more recent work had completely undone the results of my earlier
work on singularities. But, as indicated above, the real importance of the singularity theorems was that they showed
that the gravitational field must become so strong that quantum gravitational effects could not be ignored. This in turn
led to the idea that the universe could be finite in imaginary time but without boundaries or singularities. When one
goes back to the real time in which we live, however, there will still appear to be singularities. The poor astronaut
who falls into a black hole will still come to a sticky end; only if he lived in imaginary time would he encounter no
singularities.

This might suggest that the so-called imaginary time is really the real time, and that what we call real time is just a
figment of our imaginations. In real time, the universe has a beginning and an end at singularities that form a
boundary to space-time and at which the laws of science break down. But in imaginary time, there are no
singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real is just
an idea that we invent to help us describe what we think the universe is like. But according to the approach I
described in Chapter 1, a scientific theory is just a mathematical model we make to describe our observations: it
exists only in our minds. So it is meaningless to ask: which is real, “real” or “imaginary” time? It is simply a matter of
which is the more useful description.

One can also use the sum over histories, along with the no boundary proposal, to find which properties of the
universe are likely to occur together. For example, one can calculate the probability that the universe is expanding at
nearly the same rate in all different directions at a time when the density of the universe has its present value. In the
simplified models that have been examined so far, this probability turns out to be high; that is, the proposed no
boundary condition leads to the prediction that it is extremely probable that the present rate of expansion of the
universe is almost the same in each direction. This is consistent with the observations of the microwave background
radiation, which show that it has almost exactly the same intensity in any direction. If the universe were expanding
faster in some directions than in others, the intensity of the radiation in those directions would be reduced by an

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