The Origin of the Universe*

Jorge Aliaga Cacho

By Stephen Hawking

The problem of the universe's origin is a bit like the old question: which came first, the chicken or the eggs? 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. Until recently, scientists have tended to shy away from such questions, feeling that they belong to metaphysics or religion rather than to science. In the last few years, however, 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. (In the seventeenth century Bishop Ussher calculated a date of 4004 BC for the creation of the universe, a figure arrived at 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 the recognition that the human race is obviously evolving in culture and technology. We remember who first performed that deed or developed this technique. Thus the argument runs, that we cannot have been around all that long; otherwise, we would already have progressed more than we have. In fact, the biblical date for the creation is not that far from the date of the last ice age, which is when modern humans seem first to have appeared. 

On the other hand, there were people such as the Greek philosopher Aristotle who did not like the idea that the universe had a beginning. They felt that would imply divine intervention. They preferred to believe that the universe had existed and would exist forever. Something eternal was more perfect than something that was created. They had an answer to the argument about human progress described above: periodic floods or other natural disasters had repeatedly set the human race right back to the beginning.

Both schools of thought held that the universe was essentially unchanging with time. Either it was created in its present form, or it has endured forever as it is today. This was a natural belief, because human life - indeed, the whole of recorded history - is so brief that during it the universe has not changed significantly. In a static, unchanging universe, the question of whether it has existed forever or whether it was created at a finite time in the past really matters 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 which he concluded that there were equally valid arguments 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 of the universe. After all in any account of observations of the universe, what was there to observe?

In the nineteenth century, however, evidence began to accumulate that the Earth and the rest of the universe were in fact changing with time. Geologists realized that the formation of the rocks and the fossils in them would have taken hundreds or thousands or millions of years. This was far longer than the age of the earth as calculated by the creationists. Further evidence was provided by de so-called second law of thermodynamics, formulated by the German physicist Ludwig Boltzmann. 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 for human progress, suggests that the universe can have been going only for a finite time. Otherwise, it 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. If so, how could stay motionless, at a constant distance from each other? Wouldn't they all fall together?

Newton was aware of this problem. 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 all fall together to some central point. However, he argued, 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 of whether the stars can remain at constant distances from each other. We now know that the corner procedure is to consider the case of a 'finite' region of stars and then to add more stars, distributed roughly uniformly outside the region. A 'finite' collection of stars will fall together, and according to Newton's law, adding more stars outside the region will non stop the collapse. Thus, an infinite collection of stars cannot 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 the recession.

Despite the difficulties with the idea of a static and unchanging universe, no one in the seventeenth, 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 cannot really hold it against Newton, because he lived 250 years before the observational discovery of the expansion of the universe. But Einstein should have known better. The theory of general relativity he formulated in 1915 predicted that the universe was expanding. But he remained so convinced of a static universe that he added an element to his theory to reconcile ith with Newton's theory and balance gravity.

The discovery of the expansion of the universe by Edwin Hubble iin 1929 completely changes the discussion about its origin. If you take the present notion of the galaxies and run it back in time, it would seem that they should all have on top of each other at some moment between ten and twenty thousand million years ago. At this time, a singularity called the big band, the density of the universe and the curvatures of space-time 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. But science could not explain why it was as it was after the big bang.

Not surprisingly, many scientists were unhappy with this conclusion. There were thus several attempts to avoid the conclusion that there must have been a big bang, singularity and hence a beginning of time. 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 in between from matter that was continually being created. The universe existed and would continue to exist forever in more or less the same state as it is today.

For the universe to continue to expand and new matter to be created, the steady state model required a modification of general relativity, but the rate of creation needed was very low: about one particle per cubic kilometre per year, which would not 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 sources of radio waves outside our galaxies, carried out by Martin Ryle and his group at Cambridge, showed that there were many more faint sources than strong ones. On average, one would expect the faint sources to be the more distan ones. There were thus two possibilities: either we are in a region of the universe in which strong sources are less frequent than the average, or the density of sources was higher in the past when the light left the more distant sources on its journey towards us. 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 theory was the discovery in 1964 by Arno Penzias and Robert Wilson of a background of microwave radiation from far beyond our galaxie. This had the characteristic spectrum of radiation emitted 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 that would avoid a Big Bang singularity was suggested by two Russian scientists, Evgenii Lifshitz and Isaac Khalatnikov, in 1963. They said that a state of infinite density might occur only if the galaxies were moving directly towards or away from each other; only then would they all have met up at a single point in the past. However, the galaxies would also have had some small sideways velocities, and this might have made it possible for there to have been an earlier contracting phase of the universe, in which the galaxies might have come very close together but 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. I was interested in the question of whether there has 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 is correct, any reasonable model of the universe must start with a singularity. This would mean that science could not 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 chain in the climate of opinions on singularities. When I was a graduate student, almost no one took them seriously. Now as a result of the singularity theorems, nearly everyone believes that the universe began with a singularity, at which the laws of physics broke down. However, I now think that although there is a singularity, the laws of physics can still determine how the universe began. 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 uncertain principle of quantum mechanics that does not allow us to measure simultaneously, both the position and the velocity. This does not matter in normal situations, because the radius of curvature of space-time is very large compared to the uncertainty in the position of a particle. However, the singularity theorems indicate that space-time 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. To discuss the beginning of the universe, we need a theory that combines general relativity with quantum mechanics.

The theory is quantum gravity. We do not yet know the exact form the correct theory of quantum gravity will take. The best candidate we have at the moment is the theory of superstrings, but there are still several unresolved difficulties. However, certain features can be expected to be present in any viable theory. One is Einstein`s idea that the effects of gravity can be represented by a space-time that is curved or distorted -warped- 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 its simplest form, the idea is that every particle has every possible path, or history, in space-time. Each path or history has a probability that depends on its shape. History has a probability that depends on its shape. For this idea to work, one must consider histories that take place in imaginary time, rather than in the real time we perceive ourselves living. Imaginary time may sound like something from science fiction, but it is a well-defined mathematical concept. In a sense, it can be thought of as a direction of time, rather than in the real time we perceive ourselves as living. Imaginary time may sound like something out of science fiction, but it is a well-defined concept. In a sense, it can be thought of as a direction of time that is at right angles to real-time. 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. These would represent the history of the universe and everything in it. 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, the probabilities would have to be assigned in some arbitrary way. This means that science could not predict the probabilities of such singular histories for space-time. Thus, it could not predict how the universe should behave. It is possible, however, 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 only non-singular histories 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 where 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 Hattle 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, which were of finite size but which did not have boundaries or edges. They would be like the earth's surface 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 around 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, only in this case would the known laws 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. 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 our 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 of the uncertainty principle.

It would clearly, be nice for science if the universe were in a 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 a 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 disproved or falsified by observation.

If the observations do not agree with the predictions, we will know thof at 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. Our power of prediction would be poor even by the standards of weather forecasts.

Of course, one could say one need not care about the 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 can 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 of the universe are finite in extent, any quantity that one uses as a measure of time will have the greatest and least value. Thus, the universe will have a beginning and an end. The beginning in real-time will be the big bang singularity. Instead, it will be a bit like the North Pole of the Earth. If one takes degrees of latitude on the surface the Earth begins at the North Pole. Yet the North Pole is a perfectly ordinary point on the earth. There is nothing special about it, and the same laws hold at the North Pole as the other places on the earth. Similarly, the event that we might choose to label as 'the beginning of the universe in imaginary time' would be an ordinary point of space-time, much like any other. The laws of science would be held 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 in 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.

Jonathan Halliwell and I have made an approximate calculation of what the no-boundary condition would imply. We treated the universe as a perfectly smooth and uniform background, on which there were small perturbations of density. In the real-time, the universe would appear to begin its expansion at a very small in a certain 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, where the price of a loaf of bread went from under a mark to millions of marks in a few months. But this 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.

The 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 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/antiparticle pairs. And where did the energy come from to create this 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 Keynesian economics: a vigorous and expanding universe, filled with material objects. The debt of gravitational energy will not have to be paid until the end of the universe.

The early universe could not have been completely 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. During the inflationary expansiòn, however, the differences 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 structures 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 the Labour Party won the last election in Britain, 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. Until recently, however, 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 had the freedom to choose the initial conditions. Of course, He would still have been free to choose the laws that the universe obeyed. However, this may not have been 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?

And even if there is only one unique set of possible laws, it is only a set of equations. What is 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 cannot answer the question: why does the universe bother to exist? I don't know the answer to that.