《时间简史―从大爆炸到黑洞》 ――史蒂芬?霍金

A Brief History of Time - Stephen Hawking... Chapter 5
important, and I shall return to it later in the chapter.
In quantum mechanics, the forces or interactions between matter particles are all supposed to be carried by particles of
integer spin

A Brief History of Time - Stephen Hawking... Chapter 5
proposed theories that unified this interaction with the electromagnetic force, just as Maxwell had unified electricity and
magnetism about a hundred years earlier. They suggested that in addition to the photon, there were three other spin-1
particles, known collectively as massive vector bosons, that carried the weak force. These were called W+ (pronounced
W plus), W- (pronounced W minus), and Zo (pronounced Z naught), and each had a mass of around 100 GeV (GeV
stands for gigaelectron-volt, or one thousand million electron volts). The Weinberg-Salam theory exhibits a property
known as spontaneous symmetry breaking. This means that what appear to be a number of completely different particles
at low energies are in fact found to be all the same type of particle, only in different states. At high energies all these
particles behave similarly. The effect is rather like the behavior of a roulette ball on a roulette wheel. At high energies
(when the wheel is spun quickly) the ball behaves in essentially only one way

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-? 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

A Brief History of Time - Stephen Hawking... Chapter 5
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!)

A Brief History of Time - Stephen Hawking... Chapter 5
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

A Brief History of Time - Stephen Hawking... Chapter 6
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

A Brief History of Time - Stephen Hawking... Chapter 6
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
hostility of other scientists, particularly Eddington, his former teacher and the leading authority on the structure of stars,
persuaded Chandrasekhar to abandon this line of work and turn instead to other problems in astronomy, such as the
motion of star clusters. However, when he was awarded the Nobel Prize in 1983, it was, at least in part, for his early
work on the limiting mass of cold stars.
Chandrasekhar had shown that the exclusion principle could not halt the collapse of a star more massive than the
Chandrasekhar limit, but the problem of understanding what would happen to such a star, according to general
relativity, was first solved by a young American, Robert Oppenheimer, in 1939. His result, however, suggested that
there would be no observational consequences that could be detected by the telescopes of the day. Then World War II
intervened and Oppenheimer himself became closely involved in the atom bomb project. After the war the problem of
gravitational collapse was largely forgotten as most scientists became caught up in what happens on the scale of the
atom and its nucleus. In the 1960s, however, interest in the large-scale problems of astronomy and cosmology was
revived by a great increase in the number and range of astronomical observations brought about by the application of
modern technology. Oppenheimer’s work was then rediscovered and extended by a number of people.
The picture that we now have from Oppenheimer’s work is as follows. The gravitational field of the star changes the
paths of light rays in space-time from what they would have been had the star not been present. The light cones, which
indicate the paths followed in space and time by flashes of light emitted from their tips, are bent slightly inward near the
surface of the star. This can be seen in the bending of light from distant stars observed during an eclipse of the sun. As
the star contracts, the gravitational field at its surface gets stronger and the light cones get bent inward more. This
makes it more difficult for light from the star to escape, and the light appears dimmer and redder to an observer at a
distance. Eventually, when the star has shrunk to a certain critical radius, the gravitational field at the surface becomes
so strong that the light cones are bent inward so much that light can no longer escape Figure 6:1.

Figure 6:1
According to the theory of relativity, nothing can travel faster than light. Thus if light cannot escape, neither can anything
else; everything is dragged back by the gravitational field. So one has a set of events, a region of space-time, from
which it is not possible to escape to reach a distant observer. This region is what we now call a black hole. Its boundary
is called the event horizon and it coincides with the paths of light rays that just fail to escape from the black hole.
In order to understand what you would see if you were watching a star collapse to form a black hole, one has to
remember that in the theory of relativity there is no absolute time. Each observer has his own measure of time. The time
for someone on a star will be different from that for someone at a distance, because of the gravitational field of the star.

A Brief History of Time - Stephen Hawking... Chapter 6
Suppose an intrepid astronaut on the surface of the collapsing star, collapsing inward with it, sent a signal every
second, according to his watch, to his spaceship orbiting about the star. At some time on his watch, say 11:00, the star
would shrink below the critical radius at which the gravitational field becomes so strong nothing can escape, and his
signals would no longer reach the spaceship. As 11:00 approached his companions watching from the spaceship would
find the intervals between successive signals from the astronaut getting longer and longer, but this effect would be very
small before 10:59:59. They would have to wait only very slightly more than a second between the astronaut’s 10:59:58
signal and the one that he sent when his watch read 10:59:59, but they would have to wait forever for the 11:00 signal.
The light waves emitted from the surface of the star between 10:59:59 and 11:00, by the astronaut’s watch, would be
spread out over an infinite period of time, as seen from the spaceship. The time interval between the arrival of
successive waves at the spaceship would get longer and longer, so the light from the star would appear redder and
redder and fainter and fainter. Eventually, the star would be so dim that it could no longer be seen from the spaceship:
all that would be left would be a black hole in space. The star would, however, continue to exert the same gravitational
force on the spaceship, which would continue to orbit the black hole. This scenario is not entirely realistic, however,
because of the following problem. Gravity gets weaker the farther you are from the star, so the gravitational force on our
intrepid astronaut’s feet would always be greater than the force on his head. This difference in the forces would stretch
our astronaut out like spaghetti or tear him apart before the star had contracted to the critical radius at which the event
horizon formed! However, we believe that there are much larger objects in the universe, like the central regions of
galaxies, that can also undergo gravitational collapse to produce black holes; an astronaut on one of these would not be
torn apart before the black hole formed. He would not, in fact, feel anything special as he reached the critical radius,
and could pass the point of no return without noticing it However, within just a few hours, as the region continued to
collapse, the difference in the gravitational forces on his head and his feet would become so strong that again it would
tear him apart.
The work that Roger Penrose and I did between 1965 and 1970 showed that, according to general relativity, there must
be a singularity of infinite density and space-time curvature within a black hole. This is rather like the big bang at the
beginning of time, only it would be an end of time for the collapsing body and the astronaut. At this singularity the laws
of science and our ability to predict the future would break down. However, any observer who remained outside the
black hole would not be affected by this failure of predictability, because neither light nor any other signal could reach
him from the singularity. This remarkable fact led Roger Penrose to propose the cosmic censorship hypothesis, which
might be paraphrased as “God abhors a naked singularity.” In other words, the singularities produced by gravitational
collapse occur only in places, like black holes, where they are decently hidden from outside view by an event horizon.
Strictly, this is what is known as the weak cosmic censorship hypothesis: it protects observers who remain outside the
black hole from the consequences of the breakdown of predictability that occurs at the singularity, but it does nothing at
all for the poor unfortunate astronaut who falls into the hole.
There are some solutions of the equations of general relativity in which it is possible for our astronaut to see a naked
singularity: he may be able to avoid hitting the singularity and instead fall through a "wormhole” and come out in another
region of the universe. This would offer great possibilities for travel in space and time, but unfortunately it seems that
these solutions may all be highly unstable; the least disturbance, such as the presence of an astronaut, may change
them so that the astronaut could not see the singularity until he hit it and his time came to an end. In other words, the
singularity would always lie in his future and never in his past. The strong version of the cosmic censorship hypothesis
states that in a realistic solution, the singularities would always lie either entirely in the future (like the singularities of
gravitational collapse) or entirely in the past (like the , big bang). I strongly believe in cosmic censorship so I bet Kip
Thorne and John Preskill of Cal Tech that it would always hold. I lost the bet on a technicality because examples were
produced of solutions with a singularity that was visible from a long way away. So I had to pay up, which according to
the terms of the bet meant I had to clothe their nakedness. But I can claim a moral victory. The naked singularities were
unstable: the least disturbance would cause them either to disappear or to be hidden behind an event horizon. So they
would not occur in realistic situations.
The event horizon, the boundary of the region of space-time from which it is not possible to escape, acts rather like a
one-way membrane around the black hole: objects, such as unwary astronauts, can fall through the event horizon into
the black hole, but nothing can ever get out of the black hole through the event horizon. (Remember that the event
horizon is the path in space-time of light that is trying to escape from the black hole, and nothing can travel faster than
light.) One could well say of the event horizon what the poet Dante said of the entrance to Hell: “All hope abandon, ye
who enter here.” Anything or anyone who falls through the event horizon will soon reach the region of infinite density
and the end of time.
General relativity predicts that heavy objects that are moving will cause the emission of gravitational waves, ripples in
the curvature of space that travel at the speed of light. These are similar to light waves, which are ripples of the
electromagnetic field, but they are much harder to detect. They can be observed by the very slight change in separation
they produce between neighboring freely moving objects. A number of detectors are being built in the United States,

A Brief History of Time - Stephen Hawking... Chapter 6
Europe, and Japan that will measure displacements of one part in a thousand million million million (1 with twenty-one
zeros after it), or less than the nucleus of an atom over a distance of ten miles.
Like light, gravitational waves carry energy away from the objects that emit them. One would therefore expect a system
of massive objects to settle down eventually to a stationary state, because the energy in any movement would be
carried away by the emission of gravitational waves. (It is rather like dropping a cork into water: at first it bobs up and
down a great deal, but as the ripples carry away its energy, it eventually settles down to a stationary state.) For
example, the movement of the earth in its orbit round the sun produces gravitational waves. The effect of the energy
loss will be to change the orbit of the earth so that gradually it gets nearer and nearer to the sun, eventually collides with
it, and settles down to a stationary state. The rate of energy loss in the case of the earth and the sun is very low