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Origin of the Universe by Stephen Hawking
Text of 'Origin of the Universe' by S.W. Hawking
(Copyright 1988 Stephen W. Hawking. All rights reserved.)
[Note: This is taken from the text used by Professor Hawking's speech
synthesizer. While most of the spelling and punctuation peculiarities
required by the computer translator have been corrected, some may
still exist (especially names).]
The problem of the origin of the universe, is a bit like the old question:
Which came first, the chicken, or the egg. In other words, what agency created
the universe. And what created that agency. Or perhaps, the universe, or the
agency that created it, existed forever, and didn't need to be created.
Up to recently, scientists have tended to shy away from such questions,
feeling that they belonged to metaphysics or religion, rather than to science.
However, in the last few years, it has emerged that the Laws of Science may
hold even at the beginning of the universe. In that case, the universe could
be self contained, and determined completely by the Laws of Science.
The debate about whether, and how, the universe began, has been going on
throughout recorded history. Basically, there were two schools of thought.
Many early traditions, and the Jewish, Christian and Islamic religions, held
that the universe was created in the fairly recent past. For instance, Bishop
Usher calculated a date of four thousand and four BC, for the creation of the
universe, by adding up the ages of people in the Old Testament. One fact that
was used to support the idea of a recent origin, was that the Human race is
obviously evolving in culture and technology. We remember who first performed
that deed, or developed this technique. Thus, the arguement runs, we can not
have been around all that long. Otherwise, we would have already progressed
more than we have. In fact, the biblical date for the creation, is not that
far off the date of the end of the last Ice Age, which is when modern humans
seem first to have appeared.
On the other hand, some people, such as the Greek philosopher, Aristotle, did
not like the idea that the universe had a beginning. They felt that would
imply Divine intervention. They prefered to believe that the universe, had
existed, and would exist, forever. Something that was eternal, was more
perfect than something that had to be created. They had an answer to the
argument about human progress, that I described. It was, that there had been
periodic floods, or other natural disasters, which repeatedly set the human
race right back to the beginning.
Both schools of thought held that the universe was essentially unchanging in
time. Either it had been created in its present form, or it had existed
forever, like it is today. This was a natural belief in those times, because
human life, and, indeed the whole of recorded history, are so short that the
universe has not changed significantly during them. In a static, unchanging
universe, the question of whether the universe has existed forever, or whether
it was created at a finite time in the past, is really a matter for
metaphysics or religion: either theory could account for such a universe.
Indeed, in 1781, the philosopher, Immanuel Kant, wrote a monumental, and very
obscure work, The Critique of Pure Reason. In it, he concluded that there were
equally valid arguements, both for believing that the universe had a beginning,
and for believing that it did not. As his title suggests, his conclusions were
based simply on reason. In other words, they did not take any account of
observations about the universe. After all, in an unchanging universe, what
was there to observe?
In the 19th century, however, evidence began to accumulate that the earth, and
the rest of the universe, were in fact changing with time. On the one hand,
geologists realized that the formation of the rocks, and the fossils in them,
would have taken hundreds or thousands of millions of years. This was far
longer than the age of the Earth, according to the Creationists.
On the other hand, the German physicist, Boltzmann, discovered the so-called
Second Law of Thermodynamics. It states that the total amount of disorder in
the universe (which is measured by a quantity called entropy), always
increases with time. This, like the argument about human progress, suggests
that the universe can have been going only for a finite time. Otherwise, the
universe would by now have degenerated into a state of complete disorder, in
which everything would be at the same temperature.
Another difficulty with the idea of a static universe, was that according to
Newton's Law of Gravity, each star in the universe ought to be attracted
towards every other star. So how could they stay at a constant distance from
each other. Wouldn't they all fall together. Newton was aware of this
problem about the stars attracting each other. In a letter to Richard Bentley,
a leading philosopher of the time, he agreed that a finite collection of stars
could not remain motionless: they would all fall together, to some central
point. However, he argued that an infinite collection of stars, would not fall
together: for there would not be any central point for them to fall to. This
argument is an example of the pitfalls that one can encounter when one talks
about infinite systems. By using different ways to add up the forces on each
star, from the infinite number of other stars in the universe, one can get
different answers to the question: can they remain at constant distance from
each other. We now know that the correct proceedure, is to consider the case
of a finite region of stars. One then adds more stars, distributed roughly
uniformly outside the region. A finite collection of stars will fall together.
According to Newton's Law of Gravity, adding more stars outside the region,
will not stop the collapse. Thus, an infinite collection of stars, can not
remain in a motionless state. If they are not moving relative to each other at
one time, the attraction between them, will cause them to start falling
towards each other. Alternatively, they can be moving away from each other,
with gravity slowing down the velocity of recession.
Despite these difficulties with the idea of a static and unchanging universe,
no one in the seventeenth, eighteenth, nineteenth or early twentieth centuries,
suggested that the universe might be evolving with time. Newton and Einstein,
both missed the chance of predicting, that the universe should be either
contracting, or expanding. One can not really hold it against Newton, because
he was two hundred and fifty years before the observational discovery of the
expansion of the universe. But Einstein should have known better. Yet when he
formulated the General Theory of Relativity to reconcile Newton's theory with
his own Special Theory of Relativity, he added a so-called, ``cosmological
constant''. This had a repulsive gravitational effect, which could balance the
attractive effect of the matter in the universe. In this way, it was possible
to have a static model of the universe.
Einstein later said: The cosmological constant was the greatest mistake of my
life. That was after observations of distant galaxies, by Edwin Hubble in the
1920's, had shown that they were moving away from us, with velocities that
were roughly proportional to their distance from us. In other words, the
universe is not static, as had been previously thought: it is expanding. The
distance between galaxies is increasing with time.
The discovery of the expansion of the universe, completely changed the
discussion about its origin. If you take the present motion of the galaxies,
and run it back in time, it seems that they should all have been on top of
each other, at some moment, between ten and twenty thousand million years ago.
At this time, which is called the Big Bang, the density of the universe, and
the curvature of spacetime, would have been infinite. Under such conditions,
all the known laws of science would break down. This is a disaster for science.
It would mean that science alone, could not predict how the universe began.
All that science could say is that: The universe is as it is now, because it
was as it was then. But Science could not explain why it was, as it was, just
after the Big Bang.
Not surprisingly, many scientists were unhappy with this conclusion. There
were thus several attempts to avoid the Big Bang. One was the so-called
Steady State theory. The idea was that, as the galaxies moved apart from each
other, new galaxies would form in the spaces inbetween, from matter that was
continually being created. The universe would have existed, and would continue
to exist, forever, in more or less the same state as it is today.
The Steady State model required a modification of general relativity, in order
that the universe should continue to expand, and new matter be created. The
rate of creation needed was very low: about one particle per cubic kilometre
per year. Thus, this would not be in conflict with observation.
The theory also predicted that the average density of galaxies, and similar
objects, should be constant, both in space and time. However, a survey of
extra-galactic sources of radio waves, was carried out by Martin Ryle and his
group at Cambridge. This showed that there were many more faint sources, than
strong ones. On average, one would expect that the faint sources were the
more distant ones. There were thus two possibilities: Either, we were in a
region of the universe, in which strong sources were less frequent than the
average. Or, the density of sources was higher in the past, when the light
left the more distant sources. Neither of these possibilities was compatible
with the prediction of the Steady State theory, that the density of radio
sources should be constant in space and time. The final blow to the Steady
State theory was the discovery, in 1965, of a background of microwaves.
These had the characteristic spectrum of radiation emited by a hot body,
though, in this case, the term, hot, is hardly appropriate, since the
temperature was only 2.7 degrees above Absolute Zero. The universe is a cold,
dark place! There was no reasonable mechanism, in the Steady State theory, to
generate microwaves with such a spectrum. The theory therefore had to be
abandoned.
Another idea to avoid a singularity, was suggested by two Russians, Lifshitz
and Khalatnikov. They said, that maybe a state of infinite density, would
occur only if the galaxies were moving directly towards, or away from, each
other. Only then, would the galaxies all have met up at a single point in the
past. However, one might expect that the galaxies would have had some small
sideways velocities, as well as their velocity towards or away from each other.
This might have made it possible for there to have been an earlier contracting
phase, in which the galaxies somehow managed to avoid hitting each other. The
universe might then have re-expanded, without going through a state of
infinite density.
When Lifshitz and Khalatnikov made their suggestion, I was a research student,
looking for a problem with which to complete my PhD thesis. Two years earlier,
I had been diagnosed as having ALS, or motor neuron disease. I had been given
to understand that I had only two or three years to live. In this situation,
it didn't seem worth working on my PhD, because I didn't expect to finish it.
However, two years had gone by, and I was not much worse. Moreover, I had
become engaged to be married. In order to get married, I had to get a job. And
in order to get a job, I needed to finish my thesis.
I was interested in the question of whether there had been a Big Bang
singularity, because that was crucial to an understanding of the origin of the
universe. Together with Roger Penrose, I developed a new set of mathematical
techniques, for dealing with this and similar problems. We showed that if
General Relativity was correct, any reasonable model of the universe must
start with a singularity. This would mean that science could predict that the
universe must have had a beginning, but that it could not predict how the
universe should begin: for that one would have to appeal to God.
It has been interesting to watch the change in the climate of opinion on
singularities. When I was a graduate student, almost no one took singularities
seriously. Now, as a result of the singularity theorems, nearly everyone
believes that the universe began with a singularity. In the meantime, however,
I have changed my mind: I still believe that the universe had a beginning, but
that it was not a singularity.
The General Theory of Relativity, is what is called a classical theory. That
is, it does not take into account the fact that particles do not have
precisely defined positions and velocities, but are smeared out over a small
region by the Uncertainty Principle of quantum mechanics. This does not
matter in normal situations, because the radius of curvature of spacetime, is
very large compared to the uncertainty in the position of a particle. However,
the singularity theorems indicate that spacetime will be highly distorted,
with a small radius of curvature, at the beginning of the present expansion
phase of the universe. In this situation, the uncertainty principle will be
very important. Thus, General Relativity brings about its own downfall, by
predicting singularities. In order to discuss the beginning of the universe,
we need a theory which combines General Relativity with quantum mechanics.
We do not yet know the exact form of the correct theory of quantum gravity.
The best candidate we have at the moment, is the theory of Superstrings, but
there are still a number of unresolved difficulties. However, there are
certain features that we expect to be present, in any viable theory. One is
Einstein's idea, that the effects of gravity can be represented by a spacetime,
that is curved or distorted by the matter and energy in it. Objects try to
follow the nearest thing to a straight line, in this curved space. However,
because it is curved, their paths appear to be bent, as if by a gravitational
field.
Another element that we expect to be present in the ultimate theory, is
Richard Feynman's proposal that quantum theory can be formulated, as a Sum
Over Histories. In it simplest form, the idea is that a particle has every
possible path, or history, in space time. Each path or history has a
probability that depends on its shape. For this idea to work, one has to
consider histories that take place in ``imaginary'' time, rather than the real
time in which we perceive ourselves as living. Imaginary time may sound like
something out of science fiction, but it is a well defined mathematical
concept. It can be thought of as a direction of time that is at right angles
to real time, in some sense. One adds up the probabilities for all the
particle histories with certain properties, such as passing through certain
points at certain times. One then has to extrapolate the result, back to the
real space time in which we live. This is not the most familiar approach to
quantum theory, but it gives the same results as other methods.
In the case of quantum gravity, Feynman's idea of a ``Sum over Histories''
would involve summing over different possible histories for the universe.
That is, different curved space times.
One has to specify what class of
possible curved spaces should be included in the Sum over Histories. The
choice of this class of spaces, determines what state the universe is in.
If the class of curved spaces that defines the state of the universe, included
spaces with singularities, the probabilities of such spaces would not be
determined by the theory. Instead, they would have to be assigned in some
arbitrary way. What this means, is that science could not predict the
probabilities of such singular histories for spacetime. Thus, it could not
predict how the universe should behave. However, it is possible that the
universe is in a state defined by a sum that includes only non singular curved
spaces. In this case, the laws of science would determine the universe
completely: one would not have to appeal to some agency external to the
universe, to determine how it began. In a way, the proposal that the state of
the universe is determined by a sum over non singular histories only, is like
the drunk looking for his key under the lamp post: it may not be where he
lost it, but it is the only place in which he might find it. Similarly, the
universe may not be in the state defined by a sum over non singular histories,
but it is the only state in which science could predict how the universe
should be.
In 1983, Jim Hartle and I, proposed that the state of the universe should be
given by a Sum over a certain class of Histories. This class consisted of
curved spaces, without singularities, and which were of finite size, but which
did not have boundaries or edges. They would be like the surface of the Earth,
but with two more dimensions. The surface of the Earth has a finite area, but
it doesn't have any singularities, boundaries or edges. I have tested this by
experiment. I went round the world, and I didn't fall off.
The proposal that Hartle and I made, can be paraphrased as: The boundary
condition of the universe is, that it has no boundary. It is only if the
universe is in this ``no boundary'' state, that the laws of science, on their
own, determine the probabilities of each possible history. Thus, it is only in
this case that the known laws would determine how the universe should behave.
If the universe is in any other state, the class of curved spaces, in the
``Sum over Histories'', will include spaces with singularities. In order to
determine the probabilities of such singular histories, one would have to
invoke some principle other than the known laws of science. This principle
would be something external to our universe. We could not deduce it from
within the universe. On the other hand, if the universe is in the ``no
boundary'' state, we could, in principle, determine completely how the universe
should behave, up to the limits set by the Uncertainty Principle.
It would clearly be nice for science if the universe were in the ``no
boundary'' state, but how can we tell whether it is? The answer is, that the
no boundary proposal makes definite predictions, for how the universe should
behave. If these predictions were not to agree with observation, we could
conclude that the universe is not in the ``no boundary'' state. Thus, the ``no
boundary'' proposal is a good scientific theory, in the sense defined by the
philosopher, Karl Popper: it can be falsified by observation.
If the observations do not agree with the predictions, we will know that there
must be singularities in the class of possible histories. However, that is
about all we would know. We would not be able to calculate the probabilities
of the singular histories. Thus, we would not be able to predict how the
universe should behave. One might think that this unpredictability wouldn't
matter too much, if it occurred only at the Big Bang. After all, that was ten
or twenty billion years ago. But if predictability broke down in the very
strong gravitational fields in the Big Bang, it could also break down whenever
a star collapsed. This could happen several times a week, in our galaxy alone.
Thus, our power of prediction would be poor, even by the standards of weather
forecasts.
Of course, one could say that one didn't care about a breakdown in
predictability, that occurred in a distant star. However, in quantum theory,
anything that is not actually forbidden, can and ~will happen. Thus, if the
class of possible histories includes spaces with singularities, these
singularities could occur anywhere, not just at the Big Bang and in collapsing
stars. This would mean that we couldn't predict anything. Conversely, the
fact that we are able to predict events, is experimental evidence against
singularities, and for the ``no boundary'' proposal.
So what does the no boundary proposal, predict for the universe. The first
point to make, is that because all the possible histories for the universe are
finite in extent, any quantity that one uses as a measure of time, will have a
greatest and a least value. So the universe will have a beginning, and an end.
However, the beginning will not be a singularity. Instead, it will be a bit
like the North Pole of the Earth. If one takes degrees of latitude on the
surface of the Earth to be the anallogue of time, one could say that the
surface of the Earth began at the North Pole. Yet the North Pole is a
perfectly ordinary point on the Earth. There's nothing special about it, and
the same laws hold at the North Pole, as at other places on the Earth.
Similarly, the event that we might choose to label, as ``the beginning of the
universe'', would be an ordinary point of spacetime, much like any other, the
laws of science would hold at the beginning, as elsewhere.
From the analogy with the surface of the Earth, one might expect that the end
of the universe would be similar to the beginning, just as the North Pole is
much like the South Pole. However, the North and South Poles correspond to the
beginning and end of the history of the universe, in imaginary time, not the
real time that we experience. If one extrapolates the results of the ``Sum over
Histories'' from imaginary time to real time, one finds that the beginning of
the universe in real time can be very different from its end. It is difficult
to work out the details, of what the no boundary proposal predicts for the
beginning and end of the universe, for two reasons. First, we don't yet know
the exact laws that govern gravity according to the Uncertainty Principle of
quantum mechanics. Though we know the general form and many of the properties
that they should have. Second, even if we knew the precise laws, we could not
use them to make exact predictions. It would be far too difficult, to solve
the equations exactly. Nevertheless, it does seem possible to get an
approximate idea, of what the no boundary condition would imply. Jonathan
Halliwell and I, have made such an approximate calculation. We treated the
universe as a perfectly smooth and uniform background, on which there were
small perturbations of density. In real time, the universe would appear to
begin its expansion at a minimum radius. At first, the expansion would be
what is called inflationary. That is, the universe would double in size every
tiny fraction of a second, just as prices double every year in certain
countries. The world record for economic inflation, was probably Germany after
the First World War. The price of a loaf of bread, went from under a mark, to
millions of marks in a few months. But that is nothing compared to the
inflation that seems to have occurred in the early universe: an increase in
size by a factor of at least a million million million million million times,
in a tiny fraction of a second. Of course, that was before the present
government.
This inflation was a good thing, in that it produced a universe that was
smooth and uniform on a large scale, and was expanding at just the critical
rate to avoid recollapse. The inflation was also a good thing in that it
produced all the contents of the universe, quite literally out of nothing.
When the universe was a single point, like the North Pole, it contained
nothing. Yet there are now at least 10 to the 80 particles in the part of the
universe that we can observe. Where did all these particles come from? The
answer is, that Relativity and quantum mechanics, allow matter to be created
out of energy, in the form of particle anti particle pairs. So, where did the
energy come from, to create the matter? The answer is, that it was borrowed,
from the gravitational energy of the universe. The universe has an enormous
debt of negative gravitational energy, which exactly balances the positive
energy of the matter. During the inflationary period, the universe borrowed
heavily from its gravitational energy, to finance the creation of more matter.
The result was a triumph for Reagan economics: a vigorous and expanding
universe, filled with material objects. The debt of gravitational energy, will
not have to be repaid until the end of the universe.
The early universe could not have been exactly homogeneous and uniform,
because that would violate the Uncertainty Principle of quantum mechanics.
Instead, there must have been departures from uniform density. The no
boundary proposal, implies that these differences in density, would start off
in their ground state. That is, they would be as small as possible, consistent
with the Uncertainty Principle. However, during the inflationary expansion,
they would be amplified. After the period of inflationary expansion was over,
one would be left with a universe that was expanding slightly faster in some
places, than in others. In regions of slower expansion, the gravitational
attraction of the matter, would slow down the expansion still further.
Eventually, the region would stop expanding, and would contract to form
galaxies and stars. Thus, the no boundary proposal, can account for all the
complicated structure that we see around us. However, it does not make just a
single prediction for the universe. Instead, it predicts a whole family of
possible histories, each with its own probability. There might be a possible
history in which Walter Mondale won the last presidential election, though
maybe the probability is low.
The no boundary proposal, has profound implications for the role of God in the
affairs of the universe. It is now generally accepted, that the universe
evolves according to well defined laws. These laws may have been ordained by
God, but it seems that He does not intervene in the universe, to break the
laws. However, until recently, it was thought that these laws did not apply to
the beginning of the universe. It would be up to God to wind up the clockwork,
and set the universe going, in any way He wanted. Thus, the present state of
the universe, would be the result of God's choice of the initial conditions.
The situation would be very different, however, if something like the no
boundary proposal were correct. In that case, the laws of physics would hold,
even at the beginning of the universe. So God would not have the freedom to
choose the initial conditions. Of course, God would still be free to choose
the laws that the universe obeyed. However, this may not be much of a choice.
There may only be a small number of laws, which are self consistent, and which
lead to complicated beings, like ourselves, who can ask the question: What is
the nature of God? Even if there is only one, unique set of possible laws, it
is only a set of equations. What is it that breathes fire into the equations,
and makes a universe for them to govern. Is the ultimate unified theory so
compelling, that it brings about its own existence. Although Science may solve
the problem of ~how the universe began, it can not answer the question: why
does the universe bother to exist? Maybe only God can answer that.
THE END
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