Three Roads to Quantum Gravity (29 page)

But there is an even better piece of evidence for the same conclusion. It is right in front of us, and so familiar that it is difficult at first to understand that it also is a structure of enormous improbability. This is space itself. The simple fact that the world consists of a three-dimensional space, which is almost Euclidean in its geometry, and which extends for huge distances on all sides, is itself an extraordinarily improbable circumstance. This may seem absurd, but this is only because we have become so mentally dependent on the Newtonian view of the world. For how probable the arrangement of the universe is cannot be answered a priori. Rather, it depends on the theory we have about what space is. In Newton’s theory we posit that the world lives in an infinite three-dimensional space. On this assumption, the probability of us perceiving a three-dimensional space around us, stretching infinitely in all directions, is 1. But of course we know that space is not exactly Euclidean, only approximately so. On large scales space is curved because gravity bends light rays. Since this
directly contradicts a prediction of Newton’s theory, we can deduce that, with probability 1, Newton’s theory is false.

It is a little harder to pose the question in Einstein’s theory of spacetime, as that theory has an infinite number of solutions. In many of them space is approximately flat, but in many of them it is not. Given that there are an infinite number of examples of each, it is not straightforward to ask how probable it would be, were the solution chosen at random, that the resulting universe would look almost like three-dimensional Euclidean space.

It is easier to ask the question in a quantum theory of gravity. To ask it we need a form of the theory that does not assume the existence of any classical background geometry for space. Loop quantum gravity is an example of such a theory. As I explained in Chapters 9 and 10, it tells us that there is an atomic structure to space, described in terms of the spin networks invented by Roger Penrose. As we saw there, each possible quantum state for the geometry of space can be described as a graph such as that shown in
Figures 24
to
27
. We can then pose the question this way: how probable is it that such a graph represents a geometry for space that would be perceived by observers like us, living on a scale hugely bigger than the Planck scale, to be an almost Euclidean three-dimensional space? Well, each node of a spin network graph corresponds to a volume of roughly the Planck length on each side. There are then 10
⁹⁹
nodes inside every cubic centimetre. The universe is at least 10
²⁷
centimetres in size, so it contains at least 10
¹⁸⁰
nodes. The question of how probable it is that space looks like an almost flat Euclidean three-dimensional space all the way up to cosmological scales can then be posed as follows: how probable is it that a spin network with 10
¹⁸⁰
nodes would represent such a flat Euclidean geometry?

The answer is, exceedingly improbable! To see why, an analogy will help. To represent an apparently smooth, featureless three-dimensional space, the spin network has to have some kind of regular arrangement, something like a crystal. There is nothing special about any position in Euclidean space that distinguishes it from any other position. The same must be true, at least to a good approximation, of the quantum
description of such a space. Such a spin network must then be something like a metal. A metal looks smooth because the atoms in it have a regular arrangement, consisting of almost perfect crystals that contain huge numbers of atoms. So the question we are asking is analogous to asking how probable it is that all the atoms in the universe would arrange themselves in a crystalline structure like the atoms in a metal, stretching from one end of the universe to another. This is, of course, exceedingly improbable. But there are about 10
⁷⁵
spin network nodes inside every atom, so the probability that all of them are arranged regularly is less than 1 part in 10
⁷⁵
- smaller still.

It may be that this is an underestimate and the probability is not quite so small. There is one way of ensuring that all the atoms in the universe arrange themselves in a perfect crystal, which is to freeze the universe down to a temperature of absolute zero, and compacted so as to give it a density high enough for hydrogen gas to form a solid. So perhaps the spin network representing the geometry of the world is arranged regularly because it is frozen.

We can ask how probable this is. We can reason that if the universe were formed completely by chance it would have a temperature which is some reasonable fraction of the maximum possible temperature. The maximum possible temperature is the temperature that a gas would have if each atom was as massive as the Planck mass and moved at a fair fraction of the speed of light. The reason is that if the temperature were raised beyond point, the Planck temperature, the molecules would all collapse into black holes. Now, for the atoms of space to have a regular arrangement the temperature must be much, much less than this maximum temperature. In fact, the temperature of the universe is less than 10
^-32
times the Planck temperature. So the probability that a universe, chosen randomly, would have this temperature is less than 1 part in 10
³²
. So we conclude that it is at least this improbable that the universe is as cold as it is.

Whichever way we make the estimate, we conclude that if space really has a discrete atomic structure, then it is extraordinarily improbable that it would have the completely smooth and regular arrangement we observe it to have. So this
is indeed something that requires explanation. If the explanation is not to be that some outside agency chose the state of the universe, there must have been some mechanism of self-organization that, acting in our past, drove the world into this incredibly improbable state. Cosmologists have been worrying about this problem for some time. One solution which has been proposed is called inflation. This is a mechanism by which the universe can blow itself up exponentially fast until it becomes the flat, almost Euclidean universe we observe today. Inflation solves part of the problem, but it itself requires certain improbable conditions. When inflation begins to act, the universe must already be smooth on a scale of at least 10
⁵
times the Planck scale. And - at least as far as we know - inflation requires the fine tuning of two parameters. One of these is the cosmological constant, which must be smaller than its natural value in a quantum theory of gravity by a factor of at least 10
⁶⁰
. The other is the strength of a certain force, which in many versions of inflation must be no greater than 10
^-6
. The net result is that for inflation to act we require a situation with a probability of at most 10
^-81
. Even if we leave the cosmological constant out of it, we still require a situation whose probability is at most 10
^-21
. So inflation may be part of the answer, but it cannot be the complete answer.

Is it possible that some method of self-organization accounts for the fact that space looks perfectly smooth and regular, on scales hugely bigger than the Planck scale? This question has prompted some recent research, but as yet no clear answer has emerged. But if we are to avoid an appeal to religion, then this is a question that must have an answer.

So, in the end, the most improbable and hence the most puzzling aspect of space is its very existence. The simple fact that we live in an apparently smooth and regular three-dimensional world represents one of the greatest challenges to the developing quantum theory of gravity. If you look around at the world seeking mystery, you may reflect that one of the biggest mysteries is that we live in a world in which it is possible to look around, and see as far as we like. The great triumph of the quantum theory of gravity may be that it will explain to us why this is so. If it does not, then the mystic who
said that God is all around us will turn out to have been right. But if we find a scientific explanation of the existence of space, and so take the wind out of the sails of such a theistic mystic, there will still remain the mystic who preaches that God is nothing but the power of the universe as a whole to organize itself. In either case the greatest gift the quantum theory of gravity could give the world would be a renewed appreciation of the miracle that the world exists at all, together with a renewed faith that at least some small aspect of this mystery may be comprehended.

I
f I have done my job well I shall have left you with an understanding of the questions being asked by those of us who are aiming to complete the twentieth-century revolution in physics. One or another, or several, or none of the theories I have discussed may turn out to be right, but I hope that you will at least have gained an appreciation of what is at stake and what it will mean when we do finally find the quantum theory of gravity. My own view is that all the ideas I have discussed here will turn out to be part of the picture - that is why I have included them. I hope I have been sufficiently clear about my own views for you to have had no trouble distinguishing them from well established parts of science such as quantum theory and general relativity.

But above all, I hope you will have been persuaded that the search for fundamental laws and principles is one that is well worth supporting. For our community of researchers depends totally on the community at large for support in our endeavour. This reliance is twofold. First, it matters to us a great deal that we are not the only ones who care what space and time are, or where the universe came from. While I was writing my first book, I worried a lot over the time I was spending not doing science. But I found instead that I gained tremendous energy from all the interactions with ordinary people who take the time to follow what we do. Others I have spoken with have had the same experience. The most exciting thing about being in the position of conveying the cutting
edge of science to the public is discovering how many people out there care whether we succeed or fail in our work. Without this feedback there is a danger of becoming stale and complacent, and seeing our contributions only in terms of the narrow criteria of academic success. To avoid this we have to keep alive the feeling that our work brings us into contact with something true about nature. Many young scientists have this feeling, but in today’s competitive academic environment it is not easy to maintain it over a lifetime of research. There is perhaps no better way to rekindle this feeling than to communicate with people who bring to the conversation nothing more than a strong desire to learn.

The second reason why we depend on the public for support is that most of us produce nothing but this work. Since we have nothing to sell, we depend on the generosity of society to support our research. This kind of research is inexpensive, compared with medical research or experimental elementary particle physics, but this does not make it secure. The present-day political and bureaucratic environment in which science finds itself favours big, expensive science - projects that bring in the level of funding that boosts the careers of those who make the decisions about which kinds of science get supported. Nor is it easy for responsible people to commit funds to a high-risk field like quantum gravity, which has so far no experimental support to show for it. Finally, the politics of the academy acts to decrease rather than increase the variety of approaches to any problem. As more positions become earmarked for large projects and established research programs, there are correspondingly fewer positions available for young people investigating their own ideas. This has unfortunately been the trend in quantum gravity in recent years. This is not deliberate, but it is a definite effect of the procedures by which funding officers and deans measure success. Were it not for the principled commitment of a few funding officers and a few departmental heads and, not the least, a few private foundations, this kind of fundamental, high-risk/high-payoff research would be in danger of disappearing from the scene.

And quantum gravity is nothing if not high risk. The unfortunate lack of experimental tests means that relatively large groups of people may work for decades only to find that they have completely wasted their time, or at least done little but eliminate what at first seemed to be attractive possibilities for the theory. Measured sociologically, string theory seems very healthy at the moment, with perhaps a thousand practitioners; loop quantum gravity is robust but much less populous, with about a hundred investigators; other directions, such as Penrose’s twistor theory, are still pursued by only a handful. But thirty years from now all that will matter is which parts of which theory were right. And a good idea from one person is still worth hundreds of people working incrementally to advance a theory without solving its fundamental problems. So we cannot allow the politics of the academy too much influence here, or we shall all end up doing one thing. If that happens, then a century from now people may still be writing books about how quantum gravity is almost solved. If this is to be avoided, all the good ideas must be kept alive. Even more important is to maintain a climate in which young people feel there is a place for their ideas, no matter how initially unlikely or how far from the mainstream they may seem. As long as there is still room for the young scientist with the uncomfortable question and the bright idea, I see nothing to prevent the present rapid rate of progress from continuing until we have a complete theory of quantum gravity.

I should like to close this book by sticking out any part of my neck which is not yet exposed, and making a few predictions about how the problem of quantum gravity will in the end be solved. I believe that the huge progress we have made in the last twenty years is best illustrated by the fact that it is now possible to make an educated guess about how the last stages of the search for quantum gravity will go. Until recently we could have done no more than point to a few good ideas that were not obviously wrong. Now we have several proposals on the table that seem right enough and robust enough, and it is hard to imagine that they are completely wrong. The picture I have presented in this book was
assembled by taking all those ideas seriously. In the same spirit, I offer the following scenario of how the present revolution in physics will end.