宇宙简史

It would be very difficult to construct a complete unified theory of everything all at one go. So instead we have made progress by finding partial theories. These describe a limited range of happenings and neglect other effects, or approximate them by certain numbers. Inchemistry, for example, we can calculate the interactions of atoms without knowing the internal structure of the nucleus of an atom. Ultimately, however, one would hope to find a complete, consistent, unified theory that would include all these partial theories as approximations. The quest for sucha theory is known as " the unification of physics."

Einstein spent most of his later years unsuccessfully searching for a unified theory, but the time was not ripe:

Very little was known about the nuclear forces. Moreover, Einstein refused to believe in the reality of quantummechanics, despite the important role he had played in its development. Yet it seems that the uncertainty principle is afundamental feature of the universe we live in. A successful unified theory must therefore necessarily incorporate this principle.

The prospects for finding such a theory seem to be much better now because we know so much more about the universe.

But we must beware of overconfidence. We have had false dawnsbefore. At the beginning of this century, for example, it wasthought that everything could be explained in terms of the properties of continuous matter, such as elasticity and heatconduction. The discovery of atomic structure and the uncertainty principle put an end to that.

Then again, in 1928, Max Born told a group of visitors to Göttingen University, "Physics, as we know it, will be overin six months. " His confidence was based on the recent discovery by Dirac of the equation that governed the electron. It was thought that a similar equation would govern the proton, which was the only other particle known at the time, and that would be the end of theoretical physics.

However, the discovery of the neutron and of nuclear forces knocked that one on the head, too.

Having said this, I still believe there are grounds forcautious optimism that we may now be near the end of the search for the ultimate laws of nature. At the moment, we have a number of partial theories. We have generalrelativity, the partial theory of gravity, and the partialtheories that govern the weak, the strong, and the electromagnetic forces. The last three may be combined in so-called grand unified theories. These are not very satisfying because they do not include gravity. The maindifficulty in finding a theory that unifies gravity with the other forces is that general relativity is a classicaltheory. That is, it does not incorporate the uncertaintyprinciple of quantum mechanics. On the other hand, the otherpartial theories depend on quantum mechanics in an essentialway. A necessary first step, therefore, is to combine general relativity with the uncertainty principle. As we have seen, this can produce some remarkable consequences, such as blackholes not being black, and the unive rse being completely self-contained and without boundary. The trouble is, the uncertainty principle means that even empty space is filled with pairs of virtual particles and antiparticles. These pairs would have an infinite amount of energy. This means that their gravitational attraction would curve up the universe to an infinitely small size.

Rather similar, seemingly absurd infinities occur in the other quantum theories. However, in these other theories, the infinities can be canceled out by a process called renormalization. This involves adjusting the masses of the particles and the strengths of the forces in the theory by aninfinite amount. This technique is rather dubious mathematically, it does seem to work in practice. It has been used to make predictions that agree with observations to an extraordinary degree of accuracy. Renormalization, however, has a serious drawback from the point of view of trying to find a complete theory. When you subtract infinity from infinity, the answer can be anything you want. This means that the actual values ​​of the masses and the strengths of the forces cannot be predicted from the theory. Instead, they have to be chosen to fit the observations. In the case of general relativity , there are only two quantities that can be adjusted: the strength of gravity and the value of the cosmological cons tant. But adjusting these is not sufficient to remove all the infinities. One therefore has a theory that seems to predict that certain quantities, such as thecurvature of space-time, are really infinite, yet these quantities can be observed and measured to be perfectlyfinite. In an In an attempt to overcome this problem, a theory called "supergravity" as suggested in 1976. This theory wasreally just general relativity with some additional particles.

In general relativity, the gravitational force can be thought of as being carried by a particle of spin 2 called the graviton. The idea was to add certain other new particles of spin 3/2,1,1/2,and 0. In a sense, all these particles could then be regarded as different aspects of the same "superparticle. " The virtual particle/antiparticle pairs of spin 1/2 and 3/2 would have negative energy. This would tend to cancel out the positive energy of the virtual pairs of particles of spin 0 , 1, and 2. In this way, many of the possible infinities would cancel out, but it was suspected that some infinities might still remain. However, the calculations required to find out whether there were any infinities left uncanceled were so long and difficult that noone was prepared to undertake them. Even with a computer it was reckoned it would take at least four years. The chances were very high that one would make at least one mistake, and probably more. So one would know one had the right answer only if someone else rep eaten the calculation and got the same answer, and that did not seem very likely.

Because of this problem, there was a change of opinion infavor of what are called string theories. In these theories the basic objects are not particles that occupy a singlepoint of space. Rather, they are things that have a length but no other dimension, like an infinitely thin loop of string. A particle occupies one point of space at each instant of time. Thus, its history can be represented by a linein space-time called the “world-line. " A string, on the other hand, occupies a line in space at each moment of time.

So its history in space-time is a two-dimensional surface called the “world-sheet. " Any point on such a world-sheet can be described by two numbers, one specifying the time and the other the position of the point on the string. The world-sheet of a string is a cylinder or tube. A slice through the tube is a circle, which represents the position of the string at one particular time.

Two pieces of string can join together to form a singlestring. It is like the two legs joining on a pair of trousers. Similarly, a single piece of string can divide into two strings. In string theories, what were previously thoughtof as particles are now pictured as waves traveling down the string, like waves on a washing line. The emission orabsorption of one particle by another corresponds to the dividing or joining together of strings. For example, the gravitational force of the sun on the Earth corresponds to an H-shaped tube or pipe. String theory is rather like plumbing, in a way. Waves on the two vertical sides of the H correspond to the particles in the sun and the Earth, and waves on the horizontal crossbar correspond to the gravitational force that travels between them.

String theory has a curious history. It was originally invented in the late 1960s in an attempt to find a theory to describe the strong force. The idea was that particles like the proton and the neutron could be regarded as waves on astring. The strong forces between the particles would correspond to pieces of string that went between other bits of string, like in a spider''s web. For this theory to give the observed value of the strong force between particles, the strings had to be like rubber bands with a pull of about tentons.

In 1974 Joël Scherk and John Schwarz published a paper in which they showed that string theory could describe the gravitational force, but only if the tension in the string were very much higher-about 1039 tons. The predictions of the string theory would be just the same as those of generalrelativity on normal length scales, but they would differ at very small distances-less than 10-33 centimeters. Their workdid not receive much attention, however, because at just about that time, most people abandoned the original stringtheory of the strong force. Scherk died in tragiccircumstances. He suffered from diabetes and went into a comawhen no one was around to give him an injection of insulin.

So Schwarz was left alone as almost the only supporter of string theory, but now with a much higher proposed value of the string tension.

There seemed to have been two reasons for the sudden revival of interest in strings in 1984. One was that people were not really making much progress toward showing that supergravity was finite or that it could explain the kinds of particles that we observe. The other was the publication of apaper by John Schwarz and Mike Green which showed that stringtheory might be able to explain the existence of particles that have a built-in left-handedness, like some of the particles that we observe. Whatever the reasons, a largenumber of people soon began to work on string theory. A newversion was developed, the so-called heterotic string. Thisseemed as if it might be able to explain the types of particle that we observe.

String theories also lead to infinities, but it isthought they will all cancel out in versions like theheterotic string. String theories, however, have a bigger problem. They seem to be consistent only if space-time haseither ten or twenty-six dimensions, instead of the usualfour. Of course, extra space-time dimensions are a commonplace of science fiction; indeed, they are almost anecessity. Otherwise, the fact that relativity implies that one cannot travel faster than light means that it would takefar too long to get across our own galaxy , let alone totravel to other galaxies. The science fiction idea is that one can take a shortcut through a higher dimension. One can picture this in the following way. Imagine that the space welive in had only two dimensions and was curved like the surface of a doughnut or a torus. If you were on one side of the ring and you wanted to get to a point on the other side, you would have to go around the ring. However, if you were able to travel in the third dimensi on, you could cut straight across.

Why don''t we notice all these extra dimensions if they are really there? Why do we see only three space and one timedimension? The suggestion is that the other dimensions arecurved up into a space of very small size, something like a million million million million millionth of an inch. This isso small that we just don''t notice it. We see only the threespace and one time dimension in which space-time isthoroughly flat. It is like the surface of an orange: if youlook at it close up , it is all curved and wrinkled, but if you look at it from a distance, you don''t see the bumps and it appears to be smooth. So it is with space-time. On a verysmall scale, it is ten-dimensional and highly curved. But onbigger scales, you don''t see the curvature or the extradimensions.

If this picture is correct, it spells bad news for would-be space travelers. The extra dimensions would be far toosmall to allow a spaceship through. However, it raisesanother major problem. Why should some, but not all, of thedimensions be curled up into a small ball? Presumably, in the very early universe, all the dimensions would have been verycurved. Why did three space and one time dimension flattenout, while the other dimensions remained tightly curled up?

One possible answer is the anthropic principle. Two spacedimensions do not seem to be enough to allow for the development of complicated beings like us. For example, two-dimensional people living on a one-dimensional Earth would have to climb over each other in order to get past eachother. If a two-dimensional creature ate something it could not digest completely, it would have to bring up the remains the same way it swallowed them, because if there were apassage through its body, it would divide the creature into two separate parts. Our two -dimensional being would fallapart. Similarly, it is difficult to see how there could beany circulation of the blood in a two-dimensional creature.

There would also be problems with more than three spacedimensions. The gravitational force between two bodies would decrease more rapidly with distance than it does in threedimensions. The significance of this is that the orbits of planets, like the Earth, around the sun would be unstable.

The least disturbance from a circular orbit, such as would becaused by the gravitational attraction of other planets,would cause the Earth to spiral away from or into the sun. Wewould either freeze or be burned up. In fact, the samebehavior of gravity with distance would mean that the sunwould also be unstable. It would either fall apart or itwould collapse to form a black hole. In either case, it would not be much use as a source of heat and light for life onEarth. On a smaller scale, the electrical forces that cause the electrons to orbit around the nucleus in an atom wouldbehave in the same way as the gravitational forces. Thus, the electrons would either escape from the atom altogether or itwould spiral into the nucleus. In either case, one could not have atoms as we know them.

It seems clear that life, at least as we know it, canexist only in regions of space-time in which three space and one time dimension are not curled up small. This would meanthat one could appeal to the anthropic principle, providedone could show that string theory does at least allow it to be such regions of the universe. And it seems that indeed each string theory does allow such regions. There may well be other regions of the universe, or other universes ( whatever that may mean ) in which all the dimensions are curled upsmall , or in which more than four dimensions are nearly flat.

But there would be no intelligent beings in such regions to observe the different number of effective dimensions.

Apart from the question of the number of dimensions that space-time appears to have, string theory still has several other problems that must be solved before it can be acclaimed as the ultimate unified theory of physics. We do not yet knowwhether all the infinities cancel each other out , or exactly how to relate the waves on the string to the particular types of particle that we observe. Nevertheless, it is likely that answers to these questions will be found over the next few years, and that by the end of the century we shall know whether string theory is Indeed the long sought-after unified theory of physics.

Can there really be a unified theory of everything? Orare we just chasing a mirage? There seem to be threepossibilities:

•There really is a complete unified theory, which we will someday discover if we are smart enough.

•There is no ultimate theory of the universe, just aninfinite sequence of theories that describe the universe more and more accurately.

•There is no theory of the universe. Events cannot be predicted beyond a certain extent but occur in a random andarbitrary manner.

Some would argue for the third possibility on the groundsthat if there were a complete set of laws, that wouldinfringe on God's freedom to change His mind and to intervenein the world. It''s a bit like the old paradox: Can God make astone so heavy that He can''t lift it? But the idea that Godmight want to change His mind is an example of the fallacy, pointed out by St. Augustine, of imagining God as a beingexisting in time. Time is a property only of the universe that God created. Presumably, He knew what He intended when He set it up.

With the advent of quantum mechanics, we have come to realize that events cannot be predicted with completeaccuracy but that there is always a degree of uncertainty. Ifone liked, one could ascribe this randomness to theintervention of God. But it would be a very strange kind ofintervention . There is no evidence that it is directed toward any purpose. Indeed, if it were, it wouldn''t be random. Inmodern times, we have effectively removed the third possibility by redefining the goal of science. Our aim is to formulate a set of laws that will enable us to predict eventsup to the limit set by the uncertainty principle.

The second possibility, that there is an infinitesequence of more and more refined theories, is in agreement with all our experience so far. On many occasions, we have increased the sensitivity of our measurements or made a new class of observations only to discover new phenomena that were not predicted by the existing theory. To account forthese, we have had to develop a more advanced theory. It would therefore not be very surprising if we find that our present grand unified theories break down when we test themon bigger and more powerful accelerator particles. Indeed, ifwe didn't ''t expect them to break down, there wouldn''t be muchpoint in spending all that money on building more powerful machines.

However, it seems that gravity may provide a limit to this sequence of " boxes within boxes. " If one had aparticle with an energy above what is called the Planckenergy,1019 GeV, its mass would be so concentrated that it would cut itself off from the rest of the universe and form alittle black hole. Thus, it does seem that the sequence of more and more refined theories should have some limit as wego to higher and higher energies. There should be some ultimate theory of the universe. Of course, the Planck energy is a very long way from the energies of around a GeV, which are the most that we can produce in the laboratory at the present time. To bridge that gap would require a particleaccelerator that was bigger than the solar system. Such anaccelerator would be unlikely to be funded in the present climate economic.

However, the very early stages of the universe are anarena where such energies must have occurred. I think that there is a good chance that the study of the early universe and the requirements of mathematical consistency will lead usto a complete unified theory by the end of the century -always presuming we don''t blow ourselves up first.

What would it mean if we actually did discover the ultimate theory of the universe? It would bring to an end along and glorious chapter in the history of our struggle to understand the universe. But it would also revolutionize the ordinary person's understanding of the laws that govern theuniverse. In Newton''s time it was possible for an educatedperson to have a grasp of the whole of human knowledge, atleast in outline. But ever since then, the pace of development of science has made this impossible. Theories were always being changed to account for new observations.

They were never properly digested or simplified so that ordinary people could understand them. You had to be aspecialist, and even then you could only hope to have aproper grasp of a small proportion of the scientifictheories.

Further, the rate of progress was so rapid that what one learned at school or university was always a bit out of date.

Only a few people could keep up with the rapidly advancingfrontier of knowledge. And they had to devote their wholetime to it and specialize in a small area. The rest of the population had little idea of ​​the advances that were being made or the excitement they were generating.

Seventy years ago, if Eddington is to be believed, only two people understood the general theory of relativity.

Nowadays tens of thousands of university graduates understand it, and many millions of people are at least familiar with the idea. If a complete unified theory were discovered, it would be only a matter of time before it was digested and simplified in the same way. It could then be taught inschools, at least in outline. We would then all be able to have some understanding of the laws that govern the universe and which are responsible for our existence.

Einstein once asked a question: "How much choice did boundary Godhave in constructing the universe? " If the noproposal is correct, He had no freedom at all to chooseinitial conditions. He would, of course, still have had the freedom to choose the laws that the universe obeyed. This, however, may not really have been all that much of a choice.

There may well be only one or a small number of complete unified theories that are self-consistent and which allow theexistence of intelligent beings.

We can ask about the nature of God even if there is only one possible unified theory that is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the question of why there should be a universe for the model to describe. Why does the universe go to all the bother ofexisting? Is the unified theory so compelling that it brings about its own existence? Or does it need a creator, and, ifso , does He have any effect on the universe other than beingresponsible for its existence? And who created Him?

Up until now, most scientists have been too occupied with the development of new theories that describe what the universe is, to ask the question why. On the other hand, the people whose business it is to ask why-the philosophers-have not been able to keep up with the advance of scientific theories. In the eighteenth century, philosophers considered the whole of human knowledge, including science, to be their field. They discussed questions such as: Did the universe have a beginning? However, in the nineteenth and twentiethcenturies, science became too technical and mathematical for the philosophers or anyone else, except a few specialists.

Philosophers reduced the scope of their inquiries so muchthat Wittgenstein, the most famous philosopher of this century, said, " The sole remaining task for philosophy is the analysis of language. " What a comedown from the greattradition of philosophy from Aristotle to Kant.

However, if we do discover a complete theory, it should in time be understandable in broad principle by everyone, notjust a few scientists. Then we shall all be able to take partin the discussion of why the universe exists. If we find the answer to that, it would be the ultimate triumph of humanreason. For then we would know the mind of God.