difficult, however: the black hole would have the mass of a mountain compressed into less than a million millionth of an
inch, the size of the nucleus of an atom! If you had one of these black holes on the surface of the earth, there would be
no way to stop it from falling through the floor to the center of the earth. It would oscillate through the earth and back,
until eventually it settled down at the center. So the only place to put such a black hole, in which one might use the
energy that it emitted, would be in orbit around the earth – and the only way that one could get it to orbit the earth
would be to attract it there by towing a large mass in front of it, rather like a carrot in front of a donkey. This does not
sound like a very practical proposition, at least not in the immediate future.
But even if we cannot harness the emission from these primordial black holes, what are our chances of observing
them? We could look for the gamma rays that the primordial black holes emit during most of their lifetime. Although the
radiation from most would be very weak because they are far away, the total from all of them might be detectable. We
do observe such a background of gamma rays: Figure 7:5 shows how the observed intensity differs at different
frequencies (the number of waves per second). However, this background could have been, and probably was,
generated by processes other than primordial black holes. The dotted line in Figure 7:5 shows how the intensity should
vary with frequency for gamma rays given off by primordial black holes, if there were on average 300 per cubic
light-year. One can therefore say that the observations of the gamma ray background do not provide any positive
evidence for primordial black holes, but they do tell us that on average there cannot be more than 300 in every cubic
light-year in the universe. This limit means that primordial black holes could make up at most one millionth of the
matter in the universe.
Figure 7:5
With primordial black holes being so scarce, it might seem unlikely that there would be one near enough for us to
observe as an individual source of gamma rays. But since gravity would draw primordial black holes toward any matter,
they should be much more common in and around galaxies. So although the gamma ray background tells us that there
can be no more than 300 primordial black holes per cubic light-year on average, it tells us nothing about how common
they might be in our own galaxy. If they were, say, a million times more common than this, then the nearest black hole
to us would probably be at a distance of about a thousand million kilometers, or about as far away as Pluto, the farthest
known planet. At this distance it would still be very difficult to detect the steady emission of a black hole, even if it was
ten thousand megawatts. In order to observe a primordial black hole one would have to detect several gamma ray
quanta coming from the same direction within a reasonable space of time, such as a week. Otherwise, they might
simply be part of the background. But Planck’s quantum principle tells us that each gamma ray quantum has a very
high energy, because gamma rays have a very high frequency, so it would not take many quanta to radiate even ten
thousand megawatts. And to observe these few coming from the distance of Pluto would require a larger gamma ray
detector than any that have been constructed so far. Moreover, the detector would have to be in space, because
gamma rays cannot penetrate the atmosphere.
Of course, if a black hole as close as Pluto were to reach the end of its life and blow up, it would be easy to detect the
final burst of emission. But if the black hole has been emitting for the last ten or twenty thousand million years, the
chance of it reaching the end of its life within the next few years, rather than several million years in the past or future,
is really rather small! So in order to have a reasonable chance of seeing an explosion before your research grant ran
out, you would have to find a way to detect any explosions within a distance of about one light-year. In fact bursts of
gamma rays from space have been detected by satellites originally constructed to look for violations of the Test Ban
Treaty. These seem to occur about sixteen times a month and to be roughly uniformly distributed in direction across
the sky. This indicates that they come from outside the Solar System since otherwise we would expect them to be
concentrated toward the plane of the orbits of the planets. The uniform distribution also indicates that the sources are
either fairly near to us in our galaxy or right outside it at cosmological distances because otherwise, again, they would
be concentrated toward the plane of the galaxy. In the latter case, the energy required to account for the bursts would
be far too high to have been produced by tiny black holes, but if the sources were close in galactic terms, it might be
possible that they were exploding black holes. I would very much like this to be the case but I have to recognize that
there are other possible explanations for the gamma ray bursts, such as colliding neutron stars. New observations in
the next few years, particularly by gravitational wave detectors like LIGO, should enable us to discover the origin of the
gamma ray bursts.
Even if the search for primordial black holes proves negative, as it seems it may, it will still give us important
information about the very early stages of the universe. If the early universe had been chaotic or irregular, or if the
pressure of matter had been low, one would have expected it to produce many more primordial black holes than the
limit already set by our observations of the gamma ray background. Only if the early universe was very smooth and
uniform, with a high pressure, can one explain the absence of observable numbers of primordial black holes.
The idea of radiation from black holes was the first example of a prediction that depended in an essential way on both
the great theories of this century, general relativity and quantum mechanics. It aroused a lot of opposition initially
because it upset the existing viewpoint: “How can a black hole emit anything?” When I first announced the results of
my calculations at a conference at the Rutherford-Appleton Laboratory near Oxford, I was greeted with general
incredulity. At the end of my talk the chairman of the session, John G. Taylor from Kings College, London, claimed it
was all nonsense. He even wrote a paper to that effect. However, in the end most people, including John Taylor, have
come to the conclusion that black holes must radiate like hot bodies if our other ideas about general relativity and
quantum mechanics are correct. Thus, even though we have not yet managed to find a primordial black hole, there is
fairly general agreement that if we did, it would have to be emitting a lot of gamma rays and X rays.
The existence of radiation from black holes seems to imply that gravitational collapse is not as final and irreversible as
we once thought. If an astronaut falls into a black hole, its mass will increase, but eventually the energy equivalent of
that extra mass will be returned to the universe in the form of radiation. Thus, in a sense, the astronaut will be
“recycled.” It would be a poor sort of immortality, however, because any personal concept of time for the astronaut
would almost certainly come to an end as he was torn apart inside the black hole! Even the types of particles that were
eventually emitted by the black hole would in general be different from those that made up the astronaut: the only
feature of the astronaut that would survive would be his mass or energy.
The approximations I used to derive the emission from black holes should work well when the black hole has a mass
greater than a fraction of a gram. However, they will break down at the end of the black hole’s life when its mass gets
very small. The most likely outcome seems to be that the black hole will just disappear, at least from our region of the
universe, taking with it the astronaut and any singularity there might be inside it, if indeed there is one. This was the
first indication that quantum mechanics might remove the singularities that were predicted by general relativity.
However, the methods that I and other people were using in 1974 were not able to answer questions such as whether
singularities would occur in quantum gravity. From 1975 onward I therefore started to develop a more powerful
approach to quantum gravity based on Richard Feynrnan’s idea of a sum over histories. The answers that this
approach suggests for the origin and fate of the universe and its contents, such as astronauts, will be de-scribed in the
next two chapters. We shall see that although the uncertainty principle places limitations on the accuracy of all our
predictions, it may at the same time remove the fundamental unpredictability that occurs at a space-time singularity.
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PREVIOUS NEXT
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CHAPTER 8
THE ORIGIN AND FATE OF THE UNIVERSE
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Einstein’s general theory of relativity, on its own, predicted that space-time began at the big bang singularity and
would come to an end either at the big crunch singularity (if the whole universe recollapsed), or at a singularity inside
a black hole (if a local region, such as a star, were to collapse). Any matter that fell into the hole would be destroyed
at the singularity, and only the gravitational effect of its mass would continue to be felt outside. On the other hand,
when quantum effects were taken into account, it seemed that the mass or energy of the matter would eventually be
returned to the rest of the universe, and that the black hole, along with any singularity inside it, would evaporate
away and finally disappear. Could quantum mechanics have an equally dramatic effect on the big bang and big
crunch singularities? What really happens during the very early or late stages of the universe, when gravitational
fields are so strong that quantum effects cannot be ignored? Does the universe in fact have a beginning or an end?
And if so, what are they like?
Throughout the 1970s I had been mainly studying black holes, but in 1981 my interest in questions about the origin
and fate of the universe was reawakened when I attended a conference on cosmology organized by the Jesuits in
the Vatican. The Catholic Church had made a bad mistake with Galileo when it tried to lay down the law on a
question of science, declaring that the sun went round the earth. Now, centuries later, it had decided to invite a
number of experts to advise it on cosmology. At the end of the conference the participants were granted an audience
with the Pope. He told us that it was all right to study the evolution of the universe after the big bang, but we should
not inquire into the big bang itself because that was the moment of Creation and therefore the work of God. I was
glad then that he did not know the subject of the talk I had just given at the conference – the possibility that
space-time was finite but had no boundary, which means that it had no beginning, no moment of Creation. I had no
desire to share the fate of Galileo, with whom I feel a strong sense of identity, partly because of the coincidence of
having been born exactly 300 years after his death!
In order to explain the ideas that I and other people have had about how quantum mechanics may affect the origin
and fate of the universe, it is necessary first to understand the generally accepted history of the universe, according
to what is known as the “hot big bang model.” This assumes that the universe is described by a Friedmann model,
right back to the big bang. In such models one finds that as the universe expands, any matter or radiation in it gets
cooler. (When the universe doubles in size, its temperature falls by half.) Since temperature is simply a measure of
the average energy – or speed – of the particles, this cooling of the universe would have a major effect on the matter
in it. At very high temperatures, particles would be moving around so fast that they could escape any attraction
toward each other due to nuclear or electromagnetic forces, but as they cooled off one would expect particles that
attract each other to start to clump together. Moreover, even the types of particles that exist in the universe would
depend on the temperature. At high enough temperatures, particles have so much energy that whenever they collide
many different particle/antiparticle pairs would be produced – and although some of these particles would annihilate
on hitting antiparticles, they would be produced more rap-idly than they could annihilate. At lower temperatures,
however, when colliding particles have less energy, particle/antiparticle pairs would be produced less quickly – and
annihilation would become faster than production.
At the big bang itself the universe is thought to have had zero size, and so to have been infinitely hot. But as the
universe expanded, the temperature of the radiation decreased. One second after the big bang, it would have fallen
to about ten thousand million degrees. This is about a thousand times the temperature at the center of the sun, but
temperatures as high as this are reached in H-bomb explosions. At this time the universe would have contained
mostly photons, electrons, and neutrinos (extremely light particles that are affected only by the weak force and
gravity) and their antiparticles, together with some protons and neutrons. As the universe continued to expand and
the temperature to drop, the rate at which electron/antielectron pairs were being produced in collisions would have
fallen below the rate at which they were being destroyed by annihilation. So most of the electrons and antielectrons
would have annihilated with each other to produce more photons, leaving only a few electrons left over. The
neutrinos and antineutrinos, however, would not have annihilated with each other, because these particles interact
with themselves and with other particles only very weakly. So they should still be around today. If we could observe
them, it would provide a good test of this picture of a very hot early stage of the universe. Unfortunately, their
energies nowadays would be too low for us to observe them directly. However, if neutrinos are not massless, but
have a small mass of their own, as suggested by some recent experiments, we might be able to detect them
