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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PREVIOUS NEXT
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CHAPTER 6
BLACK HOLES
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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 make 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.
Chandrasekhar realized, however, that there is a limit to the repulsion that the exclusion principle can provide. The
theory of relativity limits the maximum difference in the velocities of the matter particles in the star to the speed of light.
This means that when the star got sufficiently dense, the repulsion caused by the exclusion principle would be less than
the attraction of gravity. Chandrasekhar calculated that a cold star of more than about one and a half times the mass of
the sun would not be able to support itself against its own gravity. (This mass is now known as the Chandrasekhar
limit.) A similar discovery was made about the same time by the Russian scientist Lev Davidovich Landau.
This had serious implications for the ultimate fate of massive stars. If a star’s mass is less than the Chandrasekhar limit,
it can eventually stop contracting and settle down to a possible final state as a “white dwarf” with a radius of a few
thousand miles and a density of hundreds of tons per cubic inch. A white dwarf is supported by the exclusion principle
repulsion between the electrons in its matter. We observe a large number of these white dwarf stars. One of the first to
be discovered is a star that is orbiting around Sirius, the brightest star in the night sky.
Landau pointed out that there was another possible final state for a star, also with a limiting mass of about one or two
times the mass of the sun but much smaller even than a white dwarf. These stars would be supported by the exclusion
principle repulsion between neutrons and protons, rather than between electrons. They were therefore called neutron
stars. They would have a radius of only ten miles or so and a density of hundreds of millions of tons per cubic inch. At
the time they were first predicted, there was no way that neutron stars could be observed. They were not actually
detected until much later.
Stars with masses above the Chandrasekhar limit, on the other hand, have a big problem when they come to the end of
their fuel. In some cases they may explode or manage to throw off enough matter to reduce their mass below the limit
and so avoid catastrophic gravitational collapse, but it was difficult to believe that this always happened, no matter how
big the star. How would it know that it had to lose weight? And even if every star managed to lose enough mass to
avoid collapse, what would happen if you added more mass to a white dwarf 'or neutron star to take it over the limit?
Would it collapse to infinite density? Eddington was shocked by that implication, and he refused to believe
Chandrasekhar’s result. Eddington thought it was simply not possible that a star could collapse to a point. This was the
view of most scientists: Einstein himself wrote a paper in which he claimed that stars would not shrink to zero size. The
