# The Cosmological Argument (part 5)

September 09, 2007 Time: 00:23:45We have been looking at the scientific evidence for the beginning of the universe. We saw that the standard Big Bang model postulates the origin of the universe out of nothing at some point in the finite past in confirmation of the standard Judeo-Christian doctrine of the creation of the universe out of nothing. But many scientists unhappy with this have proposed alternative models to try to avoid the prediction of the origin of the universe out of nothing in the standard model. Last time we saw the failure of the steady state theory, the oscillating universe theory, the vacuum fluctuation universe theories, and the chaotic inflationary universe theory to avoid the beginning predicted by the standard model. Now we want to turn to a couple more recently proposed models that try to avoid the beginning of the universe.

At the close of their discussion of Andrei Linde’s chaotic inflationary model that we talked about last time, Alexander Vilenkin and Arvind Borde say with respect to Linde's metaphysical question, “What was there before the singularity?” that “The most promising way to deal with this problem is probably to treat the Universe quantum mechanically and describe it by a wave function rather than by a classical spacetime.”[1] What are they talking about? They are talking about developing a quantum theory of gravity; that is to say, they are trying to marry Einstein's General Theory of Relativity to quantum theory – the theory of the subatomic realm. This is a project which has eluded physicists up until now. No one has been able to craft a quantum theory of gravitation. But this represents the sort of Holy Grail of contemporary physics. Certain theorists are speculating that perhaps the marriage of quantum theory and General Relativity Theory will enable us to avoid the beginning of the universe predicted by the standard Big Bang cosmology. These theories are enormously speculative because there is no quantum theory of gravitation. So in one sense all of this is built on air. In fact, Vilenkin candidly calls this an exercise in “metaphysical cosmology.”[2] These are just as much philosophy as they are science.

One of the most famous quantum gravity models that has been developed is the one formulated by Stephen Hawking, the famous Cambridge physicist who has Lou Gehrig's disease and whose picture has been on the cover of many famous news magazines, and then his colleague James Hartle from the University of California at Santa Barbara. On the Hartle-Hawking model, they proposed to eliminate the initial singularity by rounding off the initial surface of space-time so that it does not look like a cone having a sharp edge or point but rather something like a badminton birdie which is rounded off. On the standard Big Bang model, space-time is sort of like a cone. As you go back in time space shrinks down to an initial cosmological singularity which represents the boundary to space and time. On the Hartle-Hawking model, by contrast, as you go back in time the universe is sort of rounded off so that there is no initial space-time point. Rather, the beginning of space and time is rather like the surface of a globe, like the North Pole or the South Pole. There isn’t any edge that you come to at which space and time would come to an end.

The way in which they achieve this rounding off of space-time is by introducing imaginary numbers for the time variable in Einstein's equations. Imaginary numbers are numbers which are multiples of the square root of negative one. As you think about it, any number squared (like 2^{2} or 3^{2} or -2^{2} or -3^{2)} is always a positive number. So there is no real number that is the square root of -1.[3] So mathematicians call these imaginary numbers. These imaginary numbers can serve as useful mathematical tricks or useful tools in doing certain sorts of mathematical equations. What happens when you introduce imaginary numbers into the equations for the gravitational field is that the singularity goes away and you have this rounded surface for the beginning of space and time.

Hawking thinks that this has profound theological implications. Listen to what he says:

The idea that space and time may form a closed surface without boundary . . . has profound implications for the role of God in the affairs of the universe . . . . So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end. What place, then, for a creator?[4]

Hawking does not deny the existence of God, but he does think his model eliminates the need for a Creator of the universe because on his model there is no beginning point at which the universe begins to exist.

The key to assessing Hawking’s theological claim will be your physical interpretation of these quantum gravity models. By postulating a finite time (even if it is imaginary) on a closed geometrical surface (namely, that bottom hemisphere) rather than an open geometrical surface and an infinite time, these models actually seem to support, rather than deny, the beginning of the universe. Such theories, if they are successful, will enable us to describe the beginning of the universe without having an initial singular point. As John Barrow points out, “This type of quantum universe has not always existed; it comes into being just as the classical cosmologies could, but it does not start at a Big Bang where physical quantities are infinite . . . .”[5] Barrow points out that these models are “often described as giving a picture of ‘creation out of nothing,’” but he says the only caveat is that in this case “there is no definite . . . point of creation.”[6] On the standard model, there is a definite point at which the universe begins, but on the Hartle-Hawking model you don’t have that initial point. But nevertheless, the model has a finite past and therefore begins to exist. Hartle and Hawking themselves construe their model as giving the probability for the universe “to appear from nothing,” and Hawking has said that on this model the universe “would quite literally be created out of nothing: not just out of the vacuum, but out of absolutely nothing at all, because there is nothing outside the universe.”[7] Taken at face value, these statements entail the beginning of the universe.

When Hawking said in the question a moment ago that I cited that you don’t have any place for a creator because on his model there is no beginning point or edge, what he must mean is that on his model there is no beginning point and hence no point of creation. But having a beginning does not imply having a beginning point. Even on the standard model which has a beginning point, sometimes theorists will just “cut out” the initial singular point. But that doesn’t mean that therefore on these models space and time no longer begins to exist and that you’ve thus solved the problem of the origin of the universe. You wouldn’t say, for example, that a performance of Beethoven’s Fifth Symphony had no beginning if you just took away the initial instant of the symphony.[8] It would still have a beginning in the sense of being finite in the past, even if it didn’t have a beginning point.

I think we can say that time begins to exist just in case for any finite temporal interval of time that you pick there are only a finite number of equal intervals prior to that. So, for example, if we divided time into, say, hours – to say that time had a beginning means that there are only a finite number of hours prior to any arbitrary hour that you pick in the history of the universe. On that definition, these quantum gravity models have a beginning because time is not infinite in the past. Thus these models actually imply the beginning of the universe.

It is significant that this use of imaginary quantities is a characteristic of all of these quantum gravity models of the universe. Why is that? Very simply, because the use of imaginary numbers are just mathematical tricks but don’t represent physically significant quantities. They are used for example in quantum mechanics or in electrical mechanics to grease the equations to get certain results. But when you get to the end of the process, you always convert back into real numbers in order to get a physically significant result. What Hawking does is simply refuse to convert back to real numbers at the end of the process. But if you convert back to real numbers what you discover is that the singularity is there all the time. As Hawking says, “Only if we could picture the universe in terms of imaginary time would there be no singularities . . . . When one goes back to the real time in which we live, however, there will still appear to be singularities.”[9] What Hawking's model represents is really just a re-description of a universe with a singular beginning point in imaginary numbers which suppresses the singularity in that description. But it doesn’t really avoid the beginning of the universe because once you convert back to real numbers which are necessary for a significant physical result you find that in fact the singularity was there all the time.

hus, whether its origin was at a singular point or not, the fact that the universe began to exist remains a prediction of any of these quantum gravity models like Hawking and Hartle have proposed. So far from avoiding the beginning of the universe, these models actually imply the beginning of the universe.

We finally come to the extreme edge of current cosmology – what we might call string cosmology. These models of the origin of the universe are based upon an alternative to the standard model of elementary particle theory. Elementary particle theory is the theory of the basic constituents, or building blocks, of matter. On the standard model, matter is composed out of tiny little particles called quarks. But on string theory (or sometimes as it is called, M-theory) the fundamental building blocks of matter are not little particles like quarks. Rather, they are tiny vibrating strings of energy. So this is called string theory.

String theory is so embryonic and complicated that its equations haven’t even all been stated yet, much less solved. But that hasn’t deterred certain cosmologists from trying to use string theory to avoid the beginning of the universe predicted by standard Big Bang cosmology. The most celebrated of these scenarios in the popular press has been the so-called Ekpyrotic scenario championed by Paul Steinhardt of Princeton University.[10] The cover story of the Scientific American magazine was on these Ekpyrotic models of the universe as a means of avoiding the initial singularity and the beginning of the universe predicted by the standard Big Bang model.

These Ekpyrotic scenarios have already gone through a number of revisions as deficiencies in them have been exposed. In the most recent revision called the cyclic Ekpyrotic model, we are asked to envision two 3-dimensional membranes (sometimes these are called *branes* for short) existing in a 5-dimensional space. These 3-dimensional membranes which exist in this higher 5-dimensional state are supposed to be parallel to each other and to be in an eternal process of approaching one another and colliding and then receded from one another. Then they re-approach, collide, and recede from one another in an eternal cycle. That is why it is called a cyclic Ekpyrotic model. Each time the two membranes collide and spank together that causes one of the membranes to expand. That membrane is our universe. So with each collision, the expansion of our universe is renewed, keeps on going, thus the universe never had a beginning, never came to exist. Even though our 3-dimensional universe is expanding, this whole 5-dimensional setup is eternal and never had a beginning.

It hardly needs to be said that this is little different than science fiction. It is so speculative, its speculation builds upon speculation. There are all kinds of problems with it but some of these are so technical that I don’t think I will go into them. Let me just mention one of the problems. What this model really amounts to is our old friend the oscillating model writ large in 5-dimensions. As such it faces the same problem that the oscillating model did; namely, it is impossible for the universe to go through a singularity from a contraction and come back to a new bounce. Rather, the universe would just end at the end of one of the cycles. So this model has not been able to deliver on its promises to explain the large scale structure of the observable universe. In light of all of these problems, Andrei Linde has recently complained that while this cyclic Ekpyrotic scenario is very popular among journalists, it has remained “unpopular among scientists.”

But let’s not get into all those technical difficulties. I think the more important point is this: It turns out that just like the chaotic inflationary model that we discussed last time, the cyclic Ekpyrotic universe cannot be eternal in the past. In September of 2001, Borde and Vilenkin in cooperation of Alan Guth (the father of inflationary cosmology) were able to generalize their earlier results which show that inflationary models cannot be eternal in the past. They were able to extend these conclusions to other models of the universe. Specifically they said “our argument can be straight forwardly extended to cosmology in higher dimensions, specifically brane cosmology.” So according to Vilenkin, “It follows from our theorem that the cyclic universe is past incomplete” – that is to say, it goes back to an initial singularity. The need for the initial singularity has not been eliminated. Therefore, even despite its other problems, if those can be solved the cycle Ekpyrotic scenario cannot be past eternal.

That brings us right up to the current edge of cosmological speculation today. As I said last time, the history of 20^{th} century cosmology has in a sense been a history of the failure of one theory after another to avert the beginning of the universe predicted by the standard Big Bang model. So when people say to you, “You can’t trust this scientific evidence, it comes and goes,” that is a half truth.[11] What comes and goes are all of these theoretical attempts to try to avoid the beginning of the universe predicted by the standard model, but the standard model first proposed back in 1920s by Friedman and Lemaitre continues to survive. So it has been one confirmation after another of the prediction of the standard model that the universe began to exist. Laypeople who think the results of contemporary cosmology are fleeting and uncertain have mistaken the enduring stability of the standard model for the transitory and fleeting quality of all of these challenges to the standard model that have been proposed over the decades.

Science is always provisional, and therefore the evidence is always tentative and our conclusions are tentative. Nevertheless, I think it is hard to deny that the best evidence does stubbornly continue to indicate that the universe began to exist.

We can be confident that because of the philosophical and theological implications of the beginning of the universe that alternative models will continue to be proposed. Those attempts are to be welcomed and encouraged. I think we have no reason to expect that these new models that will be proposed in the future will be any more successful in averting the beginning of the universe then all of their failed predecessors. As they come and go with each successive failure, they confirm the beginning of the universe as predicted in the standard Big Bang theory. Meanwhile, the origin of the universe cannot just be wished away. The demand “Why the universe exists” is pressed upon us by the current results of Big Bang cosmology. There is no other model of the universe which is as mathematically consistent or consistently corroborated by the evidence as the standard Big Bang theory. Therefore, it seems to me that we have good evidence for premise (2) of the cosmological argument that the universe began to exist.

Reflecting upon the current situation, the British physicist P. C. W. Davies says,

'What caused the big bang?' . . . One might consider some supernatural force, some agency beyond space and time as being responsible for the big bang, or one might prefer to regard the big bang as an event without a cause. It seems to me that we don't have too much choice. Either . . . something outside of the physical world . . . or . . . an event without a cause.[12]

But we’ve already seen in our discussion of premise (1) that whatever begins to exist has a cause. The idea that anything could come into existence uncaused out of nothing is worse than magic. Therefore, it seems to me that this evidence from the expansion of the universe provides powerful reason for thinking that the universe began to exist and that therefore the universe has a cause.

If this were not enough, there is actually additional scientific evidence for the beginning of the universe quite apart from the Big Bang. We will talk about that next time.[13]

[1] A. Borde and A. Vilenkin, "Eternal Inflation and the Initial Singularity," *Physical Review Letters* 72 (1994): 3307.

[2] A. Vilenkin, "Birth of Inflationary Universes," *Physical Review* D 27 (1983): 2854. See J. Hartle and S. Hawking, "Wave Function of the Universe," *Physical Review* D 28 (1983): 2960-75; A. Vilenkin, "Creation of the Universe from Nothing," *Physical Letters* 117B (1982): 25-28.

[3] 5:00

[4] Stephen Hawking, *A Brief History of Time* (New York: Bantam Books, 1988), p. 140-41.

[5] John D. Barrow, *Theories of Everything* (Oxford: Clarendon Press, 1991), p. 68.

[6] Ibid., pp. 67-68.

[7] Hartle and Hawking, "Wave Function of the Universe," p. 2961; Hawking and Penrose, *Nature of Space and Time*, p. 85.

[8] 10:06

[9] Hawking, *Brief History of Time*, pp. 138-39.

[10] 15:01

[11] 20:03

[12] Paul Davies, "The Birth of the Cosmos," in *God, Cosmos, Nature and Creativity*, ed. Jill Gready (Edinburgh: Scottish Academic Press, 1995), pp. 8-9.

[13] Total Running Time: 23:45 (Copyright © 2007 William Lane Craig)