Stephen Hawking

by A Brief History Of Time (lit)

  The fourth category is the strong nuclear force, which holds the quarks together in the proton and neutron, and holds the protons and neutrons together in the nucleus of an atom. It is believed that this force is carried by another spin-1 particle, called the gluon, which interacts only with itself and with the quarks. The strong nuclear force has a curious property called confinement: it always binds particles together into combinations that have no color. One cannot have a single quark on its own because it would have a color (red, green, or blue). Instead, a red quark has to be joined to a green and a blue quark by a “string” of gluons (red + green + blue = white). Such a triplet constitutes a proton or a neutron. Another possibility is a pair consisting of a quark and an antiquark (red + antired, or green + antigreen, or blue + antiblue = white). Such combinations make up the particles known as mesons, which are unstable because the quark and antiquark can annihilate each other, producing electrons and other particles. Similarly, confinement prevents one having a single gluon on its own, because gluons also have color. Instead, one has to have a collection of gluons whose colors add up to white. Such a collection forms an unstable particle called a glueball.

  The fact that confinement prevents one from observing an isolated quark or gluon might seem to make the whole notion of quarks and gluons as particles somewhat metaphysical. However, there is another property of the strong nuclear force, called asymptotic freedom, that makes the concept of quarks and gluons well defined. At normal energies, the strong nuclear force is indeed strong, and it binds the quarks tightly together. However, experiments with large particle accelerators indicate that at high energies the strong force becomes much weaker, and the quarks and gluons behave almost like free particles.

  Figure 5:2

  Figure 5:2 shows a photograph of a collision between a high-energy proton and antiproton. The success of the unification of the electromagnetic and weak nuclear forces led to a number of attempts to combine these two forces with the strong nuclear force into what is called a grand unified theory (or GUT). This title is rather an exaggeration: the resultant theories are not all that grand, nor are they fully unified, as they do not include gravity. Nor are they really complete theories, because they contain a number of parameters whose values cannot be predicted from the theory but have to be chosen to fit in with experiment. Nevertheless, they may be a step toward a complete, fully unified theory. The basic idea of GUTs is as follows: as was mentioned above, the strong nuclear force gets weaker at high energies. On the other hand, the electromagnetic and weak forces, which are not asymptotically free, get stronger at high energies. At some very high energy, called the grand unification energy, these three forces would all have the same strength and so could just be different aspects of a single force. The GUTs also predict that at this energy the different spin-½ matter particles, like quarks and electrons, would also all be essentially the same, thus achieving another unification.

  The value of the grand unification energy is not very well known, but it would probably have to be at least a thousand million million GeV. The present generation of particle accelerators can collide particles at energies of about one hundred GeV, and machines are planned that would raise this to a few thousand GeV. But a machine that was powerful enough to accelerate particles to the grand unification energy would have to be as big as the Solar System – and would be unlikely to be funded in the present economic climate. Thus it is impossible to test grand unified theories directly in the laboratory. However, just as in the case of the electromagnetic and weak unified theory, there are low-energy consequences of the theory that can be tested.

  The most interesting of these is the prediction that protons, which make up much of the mass of ordinary matter, can spontaneously decay into lighter particles such as antielectrons. The reason this is possible is that at the grand unification energy there is no essential difference between a quark and an antielectron. The three quarks inside a proton normally do not have enough energy to change into antielectrons, but very occasionally one of them may acquire sufficient energy to make the transition because the uncertainty principle means that the energy of the quarks inside the proton cannot be fixed exactly. The proton would then decay. The probability of a quark gaining sufficient energy is so low that one is likely to have to wait at least a million million million million million years (1 followed by thirty zeros). This is much longer than the time since the big bang, which is a mere ten thousand million years or so (1 followed by ten zeros). Thus one might think that the possibility of spontaneous proton decay could not be tested experimentally. However, one can increase one’s chances of detecting a decay by observing a large amount of matter containing a very large number of protons. (If, for example, one observed a number of protons equal to 1 followed by thirty-one zeros for a period of one year, one would expect, according to the simplest GUT, to observe more than one proton decay.)

  A number of such experiments have been carried out, but none have yielded definite evidence of proton or neutron decay. One experiment used eight thousand tons of water and was performed in the Morton Salt Mine in Ohio (to avoid other events taking place, caused by cosmic rays, that might be confused with proton decay). Since no spontaneous proton decay had been observed during the experiment, one can calculate that the probable life of the proton must be greater than ten million million million million million years (1 with thirty-one zeros). This is longer than the lifetime predicted by the simplest grand unified theory, but there are more elaborate theories in which the predicted lifetimes are longer. Still more sensitive experiments involving even larger quantities of matter will be needed to test them.

  Even though it is very difficult to observe spontaneous proton decay, it may be that our very existence is a consequence of the reverse process, the production of protons, or more simply, of quarks, from an initial situation in which there were no more quarks than antiquarks, which is the most natural way to imagine the universe starting out. Matter on the earth is made up mainly of protons and neutrons, which in turn are made up of quarks. There are no antiprotons or antineutrons, made up from antiquarks, except for a few that physicists produce in large particle accelerators. We have evidence from cosmic rays that the same is true for all the matter in our galaxy: there are no antiprotons or antineutrons apart from a small number that are produced as particle/ antiparticle pairs in high-energy collisions. If there were large regions of antimatter in our galaxy, we would expect to observe large quantities of radiation from the borders between the regions of matter and antimatter, where many particles would be colliding with their anti-particles, annihilating each other and giving off high-energy radiation.

  We have no direct evidence as to whether the matter in other galaxies is made up of protons and neutrons or antiprotons and anti-neutrons, but it must be one or the other: there cannot be a mixture in a single galaxy because in that case we would again observe a lot of radiation from annihilations. We therefore believe that all galaxies are composed of quarks rather than antiquarks; it seems implausible that some galaxies should be matter and some antimatter.

  Why should there be so many more quarks than antiquarks? Why are there not equal numbers of each? It is certainly fortunate for us that the numbers are unequal because, if they had been the same, nearly all the quarks and antiquarks would have annihilated each other in the early universe and left a universe filled with radiation but hardly any matter. There would then have been no galaxies, stars, or planets on which human life could have developed. Luckily, grand unified theories may provide an explanation of why the universe should now contain more quarks than antiquarks, even if it started out with equal numbers of each. As we have seen, GUTs allow quarks to change into antielectrons at high energy. They also allow the reverse processes, antiquarks turning into electrons, and electrons and antielectrons turning into antiquarks and quarks. There was a time in the very early universe when it was so hot that the particle energies would have been high enough for these transformations to take place.
But why should that lead to more quarks than antiquarks? The reason is that the laws of physics are not quite the same for particles and antiparticles.

  Up to 1956 it was believed that the laws of physics obeyed each of three separate symmetries called C, P, and T. The symmetry C means that the laws are the same for particles and antiparticles. The symmetry P means that the laws are the same for any situation and its mirror image (the mirror image of a particle spinning in a right-handed direction is one spinning in a left-handed direction). The symmetry T means that if you reverse the direction of motion of all particles and antiparticles, the system should go back to what it was at earlier times; in other words, the laws are the same in the forward and backward directions of time. In 1956 two American physicists, Tsung-Dao Lee and Chen Ning Yang, suggested that the weak force does not in fact obey the symmetry P. In other words, the weak force would make the universe develop in a different way from the way in which the mirror image of the universe would develop. The same year, a colleague, Chien-Shiung Wu, proved their prediction correct. She did this by lining up the nuclei of radioactive atoms in a magnetic field, so that they were all spinning in the same direction, and showed that the electrons were given off more in one direction than another. The following year, Lee and Yang received the Nobel Prize for their idea. It was also found that the weak force did not obey the symmetry C. That is, it would cause a universe composed of antiparticles to behave differently from our universe. Nevertheless, it seemed that the weak force did obey the combined symmetry CP. That is, the universe would develop in the same way as its mirror image if, in addition, every particle was swapped with its antiparticle! However, in 1964 two more Americans, J. W. Cronin and Val Fitch, discovered that even the CP symmetry was not obeyed in the decay of certain particles called K-mesons. Cronin and Fitch eventually received the Nobel Prize for their work in 1980. (A lot of prizes have been awarded for showing that the universe is not as simple as we might have thought!)

  There is a mathematical theorem that says that any theory that obeys quantum mechanics and relativity must always obey the combined symmetry CPT. In other words, the universe would have to behave the same if one replaced particles by antiparticles, took the mirror image, and also reversed the direction of time. But Cronin and Fitch showed that if one replaces particles by antiparticles and takes the mirror image, but does not reverse the direction of time, then the universe does not behave the same. The laws of physics, therefore, must change if one reverses the direction of time – they do not obey the symmetry T.

  Certainly the early universe does not obey the symmetry T: as time runs forward the universe expands – if it ran backward, the universe would be contracting. And since there are forces that do not obey the symmetry T, it follows that as the universe expands, these forces could cause more antielectrons to turn into quarks than electrons into antiquarks. Then, as the universe expanded and cooled, the antiquarks would annihilate with the quarks, but since there would be more quarks than antiquarks, a small excess of quarks would remain. It is these that make up the matter we see today and out of which we ourselves are made. Thus our very existence could be regarded as a confirmation of grand unified theories, though a qualitative one only; the uncertainties are such that one cannot predict the numbers of quarks that will be left after the annihilation, or even whether it would be quarks or antiquarks that would remain. (Had it been an excess of antiquarks, however, we would simply have named antiquarks quarks, and quarks antiquarks.)

  Grand unified theories do not include the force of gravity. This does not matter too much, because gravity is such a weak force that its effects can usually be neglected when we are dealing with elementary particles or atoms. However, the fact that it is both long range and always attractive means that its effects all add up. So for a sufficiently large number of matter particles, gravitational forces can dominate over all other forces. This is why it is gravity that determines the evolution of the universe. Even for objects the size of stars, the attractive force of gravity can win over all the other forces and cause the star to collapse. My work in the 1970s focused on the black holes that can result from such stellar collapse and the intense gravitational fields around them. It was this that led to the first hints of how the theories of quantum mechanics and general relativity might affect each other – a glimpse of the shape of a quantum theory of gravity yet to come.

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  CHAPTER 6

  BLACK HOLES

  The term black hole is of very recent origin. It was coined in 1969 by the American scientist John Wheeler as a graphic description of an idea that goes back at least two hundred years, to a time when there were two theories about light: one, which Newton favored, was that it was composed of particles; the other was that it was made of waves. We now know that really both theories are correct. By the wave/particle duality of quantum mechanics, light can be regarded as both a wave and a particle. Under the theory that light is made up of waves, it was not clear how it would respond to gravity. But if light is composed of particles, one might expect them to be affected by gravity in the same way that cannonballs, rockets, and planets are. At first people thought that particles of light traveled infinitely fast, so gravity would not have been able to slow them down, but the discovery by Roemer that light travels at a finite speed meant that gravity might have an important effect.

  On this assumption, a Cambridge don, John Michell, wrote a paper in 1783 in the Philosophical Transactions of the Royal Society of London in which he pointed out that a star that was sufficiently massive and compact would have such a strong gravitational field that light could not escape: any light emitted from the surface of the star would be dragged back by the star’s gravitational attraction before it could get very far. Michell suggested that there might be a large number of stars like this. Although we would not be able to see them because the light from them would not reach us, we would still feel their gravitational attraction. Such objects are what we now call black holes, because that is what they are: black voids in space. A similar suggestion was made a few years later by the French scientist the Marquis de Laplace, apparently independently of Michell. Interestingly enough, Laplace included it in only the first and second editions of his book The System of the World, and left it out of later editions; perhaps he decided that it was a crazy idea. (Also, the particle theory of light went out of favor during the nineteenth century; it seemed that everything could be explained by the wave theory, and according to the wave theory, it was not clear that light would be affected by gravity at all.)

  In fact, it is not really consistent to treat light like cannonballs in Newton’s theory of gravity because the speed of light is fixed. (A cannonball fired upward from the earth will be slowed down by gravity and will eventually stop and fall back; a photon, however, must continue upward at a constant speed. How then can Newtonian grav-ity affect light?) A consistent theory of how gravity affects light did not come along until Einstein proposed general relativity in 1915. And even then it was a long time before the implications of the theory for massive stars were understood.

  To understand how a black hole might be formed, we first need an understanding of the life cycle of a star. A star is formed when a large amount of gas (mostly hydrogen) starts to collapse in on itself due to its gravitational attraction. As it contracts, the atoms of the gas collide with each other more and more frequently and at greater and greater speeds – the gas heats up. Eventually, the gas will be so hot that when the hydrogen atoms collide they no longer bounce off each other, but instead coalesce to form helium. The heat released in this reaction, which is like a controlled hydrogen bomb explosion, is what makes the star shine. This additional heat also increases the pressure of the gas until it is sufficient to balance the gravitational attraction, and the gas stops contracting. It is a bit like a balloon – there is a balance between the pressure of the air inside, which is trying to make the balloon expand, and the tension in the rubber, which is trying to m
ake the balloon smaller. Stars will remain stable like this for a long time, with heat from the nuclear reactions balancing the gravitational attraction. Eventually, however, the star will run out of its hydrogen and other nuclear fuels. Paradoxically, the more fuel a star starts off with, the sooner it runs out. This is because the more massive the star is, the hotter it needs to be to balance its gravitational attraction. And the hotter it is, the faster it will use up its fuel. Our sun has probably got enough fuel for another five thousand million years or so, but more massive stars can use up their fuel in as little as one hundred million years, much less than the age of the universe. When a star runs out of fuel, it starts to cool off and so to contract. What might happen to it then was first understood only at the end of the 1920s.

  In 1928 an Indian graduate student, Subrahmanyan Chandrasekhar, set sail for England to study at Cambridge with the British astronomer Sir Arthur Eddington, an expert on general relativity. (According to some accounts, a journalist told Eddington in the early 1920s that he had heard there were only three people in the world who understood general relativity. Eddington paused, then replied, “I am trying to think who the third person is.”) During his voyage from India, Chandrasekhar worked out how big a star could be and still support itself against its own gravity after it had used up all its fuel. The idea was this: when the star becomes small, the matter particles get very near each other, and so according to the Pauli exclusion principle, they must have very different velocities. This makes them move away from each other and so tends to make the star expand. A star can therefore maintain itself at a constant radius by a balance between the attraction of gravity and the repulsion that arises from the exclusion principle, just as earlier in its life gravity was balanced by the heat.