A Brief history of time

Ptolemy’s model provided a reasonably accurate system for predicting the positions of heavenly bodies in the sky. But in order to predict these positions correctly,

A simpler model, however, was proposed in 1514 by a Polish priest, Nicholas Copernicus.

As far as Kepler was concerned, elliptical orbits were merely an ad hoc hypothesis, and a rather repugnant one at that, because ellipses were clearly less perfect than circles.

An explanation was provided only much later, in 1687, when Sir Isaac Newton published his Philosophiae Naturalis Principia Mathematica, probably the most important single work ever published in the physical sciences. In it Newton not only put forward a theory of how bodies move in space and time, but he also developed the complicated mathematics needed to analyze those motions. In addition, Newton postulated a law of universal gravitation according to which each body in the universe was attracted toward every other body by a force that was stronger the more massive the bodies and the closer they were to each other. It was this same force that caused objects to fall to the ground.

Newton went on to show that, according to his law, gravity causes the moon to move in an elliptical orbit around the earth and causes the earth and the planets to follow elliptical paths around the sun. The Copernican model got rid of Ptolemy’s celestial spheres, and with them, the idea that the universe had a
natural boundary.

It is an interesting reflection on the general climate of thought before the twentieth century that no one had
suggested that the universe was expanding or contracting. It was generally accepted that either the universe
had existed forever in an unchanging state, or that it had been created at a finite time in the past more or less as we observe it today.

Another objection to an infinite static universe

that in an infinite static universe nearly every line of sight would end on the surface of a star. Thus one would expect that the whole sky would be as bright as the sun, even at night.

The only way of avoiding the conclusion that the whole of the night sky should be as bright as the
surface of the sun would be to assume that the stars had not been shining forever but had turned on at some
finite time in the past

St. Augustine accepted a date of about 5000 BC for the Creation of the universe according to the book of Genesis. (It is interesting that this is not so far from the end of the last Ice Age, about 10,000 BC, which is when archaeologists tell us that civilization really began

The questions of whether the universe had a beginning in time and whether it is limited in space were later
extensively examined by the philosopher Immanuel Kant in his monumental (and very obscure) work Critique of Pure Reason, published in 1781

They are both based on his unspoken assumption that time continues back forever, whether or not the universe had existed forever.

But in 1929, Edwin Hubble made the landmark observation that wherever you look, distant galaxies are moving rapidly away from us. In other words, the universe is expanding.

Hubble’s observations suggested that there was a time, called the big bang, when the universe was infinitesimally small and infinitely dense

An expanding universe does not preclude a creator, but it does place limits on when he might have carried out his job! In order to talk about the nature of the universe and to discuss questions such as whether it has a beginning or an end, you have to be clear about what a scientific theory is. I shall take the simpleminded view that a theory is just a model of the universe, or a restricted part of it, and a set of rules that relate quantities in the model to observations that we make. It exists only in our minds and does not have any other reality (whatever that might mean). A theory is a good theory if it satisfies two requirements. It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations.

Newton’s theory of gravity was based on an even simpler model, in which bodies attracted each other with a force that was proportional to a quantity called their mass and inversely proportional to the square of the distance between them. Yet it predicts the motions of the sun, the moon, and the planets to a high degree of accuracy. Any physical theory is always provisional, in the sense that it is only a hypothesis: you can never prove it. No matter how many times the results of experiments agree with some theory, you can never be sure that the next time the result will not contradict the theory. On the other hand, you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory.

In practice, what often happens is that a new theory is devised that is really an extension of the previous theory

The eventual goal of science is to provide a single theory that describes the whole universe. However, the
approach most scientists actually follow is to separate the problem into two parts. First, there are the laws that tell us how the universe changes with time. (If we know what the universe is like at any one time, these physical laws tell us how it will look at any later time.) Second, there is the question of the initial state of the universe. Some people feel that science should be concerned with only the first part; they regard the question of the initial situation as a matter for metaphysics or religion.

we break the problem up into bits and invent a number of partial theories

classic example again is the Newtonian theory of gravity, which tells us that the gravitational
force between two bodies depends only on one number associated with each body, its mass, but is otherwise
independent of what the bodies are made of

Today scientists describe the universe in terms of two basic partial theories – the general theory of relativity
and quantum mechanics. They are the great intellectual achievements of the first half of this century. The
general theory of relativity describes the force of gravity and the large-scale structure of the universe, that is, the structure on scales from only a few miles to as large as a million million million million (1 with twenty-four zeros after it) miles, the size of the observable universe. Quantum mechanics, on the other hand, deals with phenomena on extremely small scales, such as a millionth of a millionth of an inch. Unfortunately, however, these two theories are known to be inconsistent with each other – they cannot both be correct.

Now, if you believe that the universe is not arbitrary, but is governed by definite laws, you ultimately have to
combine the partial theories into a complete unified theory that will describe everything in the universe

The ideas about scientific theories outlined above assume we are rational beings who are free to observe

However, provided the universe has evolved in a regular way, we might expect that the reasoning abilities that
natural selection has given us would be valid also in our search for a complete unified theory, and so would not
lead us to the wrong conclusions.

The discovery of a complete unified theory, therefore, may not aid the survival of our species. It
may not even affect our lifestyle

Our present ideas about the motion of bodies date back to Galileo and Newton. Before them people believed
Aristotle, who said that the natural state of a body was to be at rest and that it moved only if driven by a force or impulse. It followed that a heavy body should fall faster than a light one, because it would have a greater pull toward the earth.

no one until Galileo bothered to see whether bodies of different weight did in fact fall at different speeds. It is said that Galileo demonstrated that Aristotle’s belief was false by dropping weights from the leaning tower of Pisa

Galileo’s measurements indicated that each body increased its speed at the same rate, no matter what its weight

Of course a lead weight would fall faster than a feather, but that is only because a feather is slowed down by air resistance

Galileo’s measurements were used by Newton as the basis of his laws of motion

It also meant that whenever a body is not acted on by any force, it will keep on moving in a straight line at the same speed.

What happens to a body when a force does act on it is given by Newton’s second law. This states that the body will accelerate, or change its speed, at a rate that is proportional to the force. (For example, the acceleration is twice as great if the force is twice as great.) The acceleration is also smaller the greater the mass (or quantity of matter) of the body. (The same force acting on a body of twice the mass will produce half the acceleration.)

Newton discovered a law to describe the force of gravity, which states that every body attracts every other body with a force that is proportional to the mass of each body. Thus the force between two bodies would be twice as strong if one of the bodies (say, body A) had its mass doubled.

a body of twice the weight will have twice the force of gravity pulling it down, but it will also have twice the mass. According to Newton’s second law, these two effects will exactly cancel each other, so the acceleration will be the same in all cases. Newton’s law of gravity also tells us that the farther apart the bodies, the smaller the force. Newton’s law of gravity says that the gravitational attraction of a star is exactly one quarter that of a similar star at half the distance.

big difference between the ideas of Aristotle and those of Galileo and Newton is that Aristotle believed in a
preferred state of rest. he thought that the earth was at rest. But it follows from Newton’s laws that there is no unique standard of rest. One could equally well say that body A was at rest and body B was moving at constant speed with respect to body A, or that body B was at rest and body A was moving.

The lack of an absolute standard of rest meant that one could not determine whether two events that took place at different times occurred in the same position in space.

Newton was very worried by this lack of absolute position, or absolute space, as it was called, because it did
not accord with his idea of an absolute God

Both Aristotle and Newton believed in absolute time.

Roemer’s achievement, in not only proving that light travels at a finite speed, but also in measuring that speed, was remarkable – coming as it did eleven years before Newton’s publication of Principia Mathematica. A proper theory of the propagation of light didn’t come until 1865, when the British physicist James Clerk Maxwell succeeded in unifying the partial theories that up to then had been used to describe the forces of electricity and magnetism. Maxwell’s equations predicted that there could be wavelike disturbances in the combined electromagnetic field, and that these would travel at a fixed speed, like ripples on a pond. If the wavelength of these waves (the distance between one wave crest and the next) is a meter or more, they are what we now call radio waves. Shorter wavelengths are known as microwaves (a few centimeters) or infrared (more than a ten-thousandth of a centimeter). Visible light has a wavelength of between only forty and eighty millionths of a centimeter. Even shorter wavelengths are known as ultraviolet, X rays, and gamma rays.

Albert Einstein, pointed out that the whole idea of an ether was unnecessary, providing one
was willing to abandon the idea of absolute time

The fundamental postulate of the theory of relativity, as it was called, was that the laws of science should be
the same for all freely moving observers, no matter what their speed.

best known are the equivalence of mass and energy, summed up in Einstein’s
famous equation E=mc2 (where E is energy, m is mass, and c is the speed of light), and the law that nothing
may travel faster than the speed of light. Because of the equivalence of energy and mass, the energy which an
object has due to its motion will add to its mass. In other words, it will make it harder to increase its speed

t can in fact never reach the
speed of light, because by then its mass would have become infinite, and by the equivalence of mass and
energy, it would have taken an infinite amount of energy to get it there. For this reason, any normal object is
forever confined by relativity to move at speeds slower than the speed of light. Only light, or other waves that
have no intrinsic mass, can move at the speed of light.

speed of the light is just the distance it has traveled divided by the time it has taken

In relativity, on the other hand, all observers must agree on how fast light travels. They still, however, do not agree on the distance the light has traveled, so they must therefore now also disagree over the time it has taken In other words, the theory of relativity put an end to the idea of absolute time!

In effect, the meter is defined to be the distance traveled by light in 0.000000003335640952 second, as measured by a cesium clock

We must accept that time is not completely separate from and independent of space, but is combined with it to form an object called space-time.

In fact, one may describe the whole universe in terms of a collection of overlapping patches. In each
patch, one can use a different set of three coordinates to specify the position of a point.

Einstein made the revolutionary suggestion that gravity is not a force like other forces, but is a consequence of the fact that space-time is not flat, as had been previously assumed: it is curved, or “warped,” by the distribution of mass and energy in it. Bodies like the earth are not made to move on curved orbits by a force called gravity; instead, they follow the nearest thing to a straight path in a curved space, which is called a geodesic.

The mass of the sun curves space-time in such a way that although the earth follows a straight path in
four-dimensional space-time, it appears to us to move along a circular orbit in three-dimensional space

the theory predicts that the light cones of points near the sun would be slightly bent inward, on account of the mass of the sun. not until 1919 that a British expedition, observing an eclipse from West Africa,
showed that light was indeed deflected by the sun, just as predicted by the theory

Another prediction of general relativity is that time should appear to slower near a massive body like the earth. This is because there is a relation between the energy of light and its frequency (that is, the number of waves of light per second): the greater the energy, the higher frequency. As light travels upward in the earth’s gravitational field, it loses energy, and so its frequency goes down. (This means that the length of time between one wave crest and the next goes up.) To someone high up, it would appear that everything down below was making longer to happen. This prediction was tested in 1962, using a pair of very accurate clocks mounted at the top and bottom of a water tower. The clock at the bottom, which was nearer the earth, was found to run slower, in exact agreement with general relativity.

Newton’s laws of motion put an end to the idea of absolute position in space. The theory of relativity gets rid of absolute time. Consider a pair of twins. Suppose that one twin goes to live on the top of a mountain while the other stays at sea level. The first twin would age faster than the second.

For the vast majority of stars, there is only one characteristic
feature that we can observe – the color of their light. Newton discovered that if light from the sun passes
through a triangular-shaped piece of glass, called a prism, it breaks up into its component colors (its spectrum)
as in a rainbow

In fact, the light emitted by any opaque object that is glowing red hot has a characteristic spectrum
that depends only on its temperature – a thermal spectrum. This means that we can tell a star’s temperature
from the spectrum of its light.) Moreover, we find that certain very specific colors are missing from stars’
spectra, and these missing colors may vary from star to star. Since we know that each chemical element
absorbs a characteristic set of very specific colors, by matching these to those that are missing from a star’s
spectrum, the wavelength (or distance from one wave crest to the next with the longest wavelengths appearing at the red end of the spectrum and the shortest wavelengths at the blue end.

This relationship between wavelength and speed, which is called the Doppler effect, is an everyday experience. Listen to a car passing on the road:

More surprising still was the finding that Hubble published in 1929: even the size of a galaxy’s red shift is not random, but is directly proportional to the galaxy’s distance from us. Or, in other words, the farther a galaxy is, the faster it is moving away! And that meant that the universe could not be static, as everyone previously had thought, is in fact expanding; the distance between the different galaxies is changing all the time.
The discovery that the universe is expanding

if the rocket has more than a certain critical speed (about seven miles per second), gravity will not be strong enough to pull it back,

it might seem that if we observe all other galaxies to be moving away from us, then we must be at the center of the universe. There is, however, an alternate explanation: the universe might look the same in every direction as seen from any other galaxy too

The situation is rather like a balloon with a number of spots painted on it being steadily blown up. As the balloon expands, the distance between any two spots increases, but there is no spot that can be said to be the center of the expansion

Many people do not like the idea that time has a beginning, probably because it smacks of divine intervention. (The Catholic Church, on the other hand, seized on the big bang model and in 1951officially pronounced it to be in accordance with the Bible.)


The doctrine of scientific determinism was strongly resisted by many people, who felt that it infringed God’s freedom to intervene in the world,

According to the laws we believed at the time, a hot body ought to give off electromagnetic waves (such as radio waves, visible light, or X rays) equally at all frequencies. For example, a hot body should radiate the same amount of energy in waves with frequencies between one and two million million waves a second as in waves with frequencies between two and three million million waves a second. Now since the number of waves a second is unlimited, this would mean that the total energy radiated would be infinite.
In order to avoid this obviously ridiculous result, the German scientist Max Planck suggested in 1900 that light, X rays, and other waves could not be emitted at an arbitrary rate, but only in certain packets that he called quanta. Moreover, each quantum had a certain amount of energy that was greater the higher the frequency of the waves, so at a high enough frequency the emission of a single quantum would require more energy than was available. Thus the radiation at high frequencies would be reduced, and so the rate at which the body lost energy would be finite. The quantum hypothesis explained the observed rate of emission of radiation from hot bodies very well, but its implications for determinism were not realized until 1926, when another German scientist, Werner Heisenberg, formulated his famous uncertainty principle. In order to predict the future position and velocity of a particle, one has to be able to measure its present position and velocity accurately. The obvious way to do this is to shine light on the particle. Some of the waves of light will be scattered by the particle and this will indicate its position. However, one will not be able to determine the position of the particle more accurately than the distance between the wave crests of light, so one needs
to use light of a short wavelength in order to measure the position of the particle precisely. Now, by Planck’s quantum hypothesis, one cannot use an arbitrarily small amount of light; one has to use at least one quantum. This quantum will disturb the particle and change its velocity in a way that cannot be predicted. moreover, the more accurately one measures the position, the shorter the wavelength of the light that one needs and hence the higher the energy of a single quantum. So the velocity of the particle will be disturbed by a larger amount. In other words, the more accurately you try to measure the position of the particle, the less accurately you can measure its speed, and vice versa. Heisenberg showed that the uncertainty in the position of the particle times the uncertainty in its velocity times the mass of the particle can never be smaller than a certain quantity, which is known as Planck’s constant. Moreover, this limit does not depend on the way in which one tries to measure the position or velocity of the particle, or on the type of particle:
Heisenberg’s uncertainty principle is a fundamental, inescapable property of the world.

in general, quantum mechanics does not predict a single definite result for an observation. Instead, it predicts a number of different possible outcomes and tells us how likely each of these is.

Quantum mechanics therefore introduces an unavoidable element of unpredictability or randomness into
science. Einstein objected to this very strongly, despite the important role he had played in the development of these ideas. Einstein was awarded the Nobel Prize for his contribution to quantum theory. Nevertheless, Einstein never accepted that the universe was governed by chance; his feelings were summed up in his famous statement “God does not play dice.”

The only areas of physical science into which quantum mechanics has not yet been properly incorporated are gravity and the large-scale structure of the universe.

There is thus a duality between waves and particles in quantum mechanics: for some purposes it is helpful to think of particles as waves and for other purposes it is better to think of waves as particles

Any point on the screen will receive waves from the two slits. However, in general, the distance the light has to travel from the source to the screen via the two slits will be different. This will mean that the waves from the slits will not be in phase with each other when they arrive at the screen: in some places the waves will cancel each other out, and in others they will reinforce each other. The result is a characteristic pattern of light and dark fringes. The remarkable thing is that one gets exactly the same kind of fringes if one replaces the source of light by a source of particles such as electrons with a definite speed (this means that the corresponding waves have a definite length). It seems the more peculiar because if one only has one slit, one does not get any fringes, just a uniform distribution of electrons across the screen. One might therefore think that opening another slit would just increase the number of electrons hitting each point of the screen, but, because of interference, it actually decreases it in some places. If electrons are sent through the slits one at a time, one would expect each to pass through one slit or the other, and so behave just as if the slit it passed through were the only one there – giving a uniform distribution on the screen. In reality, however, even when the electrons are sent one at a time, the fringes still appear. Each electron, therefore, must be passing through both slits at the same time!

It revealed that an electron orbiting around the nucleus could be thought of as a wave, with a wavelength that depended on its velocity.

Up to about thirty years ago, it was thought that protons and neutrons were “elementary” particles, but experiments in which protons were collided with other protons or electrons at high speeds indicated that they were in fact made up of smaller particles. These particles were named quarks b

There are a number of different varieties of quarks: there are six “flavors,” which we call up, down, strange, charmed, bottom, and top. The first three flavors had been known since the 1960s but the charmed quark was discovered only in 1974, the bottom in 1977, and the top in 1995. Each flavor comes in three “colors,” red, green, and blue.

A proton or neutron is made up of three quarks, one of each color. A proton contains two up quarks and one down quark; a neutron contains two down and one up.

These particle energies are usually measured in units called electron volts

Using the wave/particle duality discussed in the last chapter, every-thing in the universe, including light and gravity, can be described in terms of particles.

It also predicted that the electron should have a partner: an anti-electron, or positron. The
discovery of the positron in 1932 confirmed Dirac’s theory and led to his being awarded the Nobel Prize for physics in 1933. We now know that every particle has an antiparticle, with which it can annihilate

In quantum mechanics, the forces or interactions between matter particles are all supposed to be carried by particles of integer spin – 0, 1, or 2

Force-carrying particles can be grouped into four categories according to the strength of the force that they carry and the particles with which they interact.

The first category is the gravitational force. This force is universal, that is, every particle feels the force of gravity, according to its mass or energy. Gravity is the weakest of the four forces by a long way; it is so weak that we would not notice it at all were it not for two special properties that it has: it can act over large distances, and it is always attractive.

In the quantum mechanical way of looking at the gravitational field, the force between two matter particles is pictured as being carried by a particle of spin 2 called the graviton.

The next category is the electromagnetic force, which interacts with electrically charged particles like electrons and quarks, but not with uncharged particles such as gravitons.

there are two kinds of electric charge, positive and negative.

The third category is called the weak nuclear force, which is responsible for radioactivity and which acts on all matter particles of spin-˝, but not on particles of spin 0, 1, or 2, such as photons and gravitons.

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 Zş (pronounced Z naught), and each had a mass of around 100 GeV (GeV stands for gigaelectron-volt, or one thousand million electron volts)

the discovery in 1983 at CERN (European Centre for Nuclear Research) of the three massive partners of the photon, with the correct predicted masses and other properties

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.

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

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.

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.

Matter on the earth is made up mainly of protons and neutrons, which in turn are made up of quarks

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.

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

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

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.

How then can Newtonian grav-ity affect light?)

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.

Eventually, however, the star will run out of its hydrogen and other nuclear fuels

What might happen to it then was first understood only at the end of the 1920s.

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

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.

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.

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.

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,

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

Thus if light cannot escape, neither can anything else; everything is dragged back by the gravitational field

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

Roger Penrose and John Wheeler in particular. They argued that the rapid movements involved in a star’s collapse would mean that the gravitational waves it gave off would make it ever more spherical, and by the time it had settled down to a stationary state, it would be precisely spherical. According to this view, any non-rotating star, however complicated its shape and internal structure, would end up after gravitational collapse as a perfectly spherical black hole, whose size would depend only on its mass. Further calculations supported this view, and it soon came to be adopted generally

If the rotation is zero, the black hole is perfectly round and the solution is identical to the Schwarzschild solution. If the rotation is non-zero, the black hole bulges outward near its equator (just as the earth or the sun bulge due to their rotation), and the faster it rotates, the more it bulges

In 1963, however, Maarten Schmidt, an astronomer at the Palomar Observatory in California, measured the red shift of a faint starlike object in the direction of the source of radio waves called 3C273 (that is, source number 273 in the third Cambridge catalogue of radio sources). He found it was too large to be caused by a gravitational field: if it had been a gravitational red shift, the object would have to be so massive and so near to us that it would disturb the orbits of planets in the Solar System. This suggested that the red shift was instead caused by the expansion of the universe, which, in turn, meant that the object was a very
long distance away. And to be visible at such a great distance, the object must be very bright, must, in other words, be emitting a huge amount of energy.

A neutron star has a radius of about ten miles, only a few times the critical radius at which a star becomes a black hole. If a star could collapse to such a small size, it is not unreasonable to expect that other stars could collapse to even smaller size and become black holes.

One cannot, of course, immediately conclude that the companion is a black hole: it might merely be a star that is too faint to be seen. However, some of these systems, like the one called Cygnus X-1 Figure 6:2, are also strong sources of X-rays.

The best explanation for this phenomenon is that matter has been blown off the surface of the visible star. As it falls toward the unseen companion, it develops a spiral motion (rather like water running out of a bath), and it gets very hot, emitting X-rays

We also now have evidence for several other black holes in systems like Cygnus X-1 in our galaxy and in two neighboring galaxies called the Magellanic Clouds

The number of black holes may well be greater even than the number of visible stars, which totals about a hundred thousand million in our galaxy alone.

Very high-energy particles would be generated near the black hole by the in-falling matter. The magnetic field would be so strong that it could focus these particles into jets ejected outward along
the axis of rotation of the black hole, that is, in the directions of its north and south poles. Such jets are indeed observed in a number of galaxies and quasars

However, as we shall learn in the next chapter, black holes are not really black after all: they glow like a hot body, and the smaller they are, the more they glow. So, paradoxically, smaller black holes might actually turn out to be easier to detect than large ones!


So black holes ought to emit radiation. But by their very definition, black holes are objects that are not
supposed to emit anything.

Yakov Zeldovich and Alexander Starobinsky. They convinced me that, according to the quantum mechanical uncertainty principle, rotating black holes should create and emit particles.

I therefore set about devising a better mathematical treatment

Since then the calculations have been repeated in a number of different forms by other people. They all confirm that a black hole ought to emit particles and radiation as if it were a hot body with a temperature that depends only on the black hole’s mass: the higher the mass, the lower the temperature.
How is it possible that a black hole appears to emit particles when we know that nothing can escape from within its event horizon? The answer, quantum theory tells us, is that the particles do not come from within the black hole, but from the “empty” space just outside the black hole’s event horizon!

The positive energy of the outgoing radiation would be balanced by a flow of negative energy particles into the black hole. By Einstein’s equation E = mc2 (where E is energy, m is mass, and c is the speed of light), energy is proportional to mass. A flow of negative energy into the black hole therefore reduces its mass.

So as the black hole loses mass, its temperature and rate of emission increase, so it loses mass more quickly

These X rays and gamma rays are like waves of light, but with a much shorter wavelength. Such holes
hardly deserve the epithet black: they really are white hot and are emitting energy at a rate of about ten thousand megawatts.

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 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.

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?


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.

About one hundred seconds after the big bang, the temperature would have fallen to one thousand million degrees, the temperature inside the hottest stars. At this temperature protons and neutrons would no longer have sufficient energy to escape the attraction of the strong nuclear force, and would have started to combine together to produce the nuclei of atoms of deuterium (heavy hydrogen), which contain one proton and one neutron.

Within only a few hours of the big bang, the production of helium and other elements would have stopped. And after that, for the next million years or so, the universe would have just continued expanding, without anything much happening. Eventually, once the temperature had dropped to a few thousand degrees, and electrons and nuclei no longer had enough energy to overcome the electromagnetic attraction between them, they would have started combining to form atoms. The universe as a whole would have continued expanding and cooling, but in regions that were slightly denser than average, the expansion would have been slowed down by the extra gravitational attraction. This would eventually stop expansion in some regions and cause them to start to recollapse. As they were collapsing, the gravitational pull of matter outside these regions might start them rotating slightly. As the collapsing region got smaller, it would spin faster – just as skaters spinning on ice spin faster as they draw in their arms. Eventually, when the region got small enough, it would be spinning fast enough to balance the attraction of gravity, and in this way disklike rotating galaxies were born.

As time went on, the hydrogen and helium gas in the galaxies would break up into smaller clouds that would collapse under their own gravity. As these contracted, and the atoms within them collided with one another, the temperature of the gas would increase, until eventually it became hot enough to start nuclear fusion reactions. These would convert the hydrogen into more helium, and the heat given off would raise the pressure, and so stop the clouds from contracting any further. They would remain stable in this state for a long time as stars like our sun, burning hydrogen into helium and radiating the resulting energy as heat and light

contract slightly, and as they heated up further, would start to convert helium into heavier elements like carbon or oxygen. This, however, would not release much more energy, so a crisis would occur, as was described in the chapter on black holes. What happens next is not completely clear, but it seems likely that the central regions of the star would collapse to a very dense state, such as a neutron star or black hole. The outer regions of the star may sometimes get blown off in a tremendous explosion called a supernova

Our own sun contains about 2 percent of these heavier elements, because it is a second- or third-generation star, formed some five thousand million years ago out of a cloud of rotating gas containing the debris of earlier supernovas. Most of the gas in that cloud went to form the sun or got blown away, but a small amount of the heavier elements collected together to form the bodies that now orbit the sun as planets like the earth.
The earth was initially very hot and without an atmosphere. In the course of time it cooled and acquired an

atmosphere from the emission of gases from the rocks. This early atmosphere was not one in which we could have survived. It contained no oxygen, but a lot of other gases that are poisonous to us, such as hydrogen sulfide (the gas that gives rotten eggs their smell). There are, however, other primitive forms of life that can flourish under such conditions. It is thought that they developed in the oceans, possibly as a result of chance combinations of atoms into large structures, called macromolecules, which were capable of assembling other atoms in the ocean into similar structures. They would thus have reproduced themselves and multiplied. In some cases there would be errors in the reproduction.

process of evolution was started

Space-time would have a boundary – a beginning at the big bang.

The first one or two thousand million years of the earth’s existence were too hot for the development of anything complicated. The remaining three thousand million years or so have been taken up by the slow process of biological evolution, which has led from the simplest organisms to beings who are capable of measuring time back to the big bang

“Why is the universe the way we see it?” The answer is then simple: if it had been different, we would not be here

The new inflationary model was a good attempt to explain why the universe is the way it is. However, I and several other people showed that, at least in its original form, it predicted much greater variations in the temperature of the microwave background radiation than are observed.

We don’t yet have a complete and consistent theory that combines quantum mechanics and gravity. However, we are fairly certain of some features that such a unified theory should have. One is that it should incorporate
Feynman’s proposal to formulate quantum theory in terms of a sum over histories.

A second feature that we believe must be part of any ultimate theory is Einstein’s idea that the gravitational field is represented by curved space-time

In the classical theory of gravity, which is based on real space-time, there are only two possible ways the universe can behave: either it has existed for an infinite time, or else it had a beginning at a singularity at some finite time in the past. In the quantum theory of gravity, on the other hand, a third possibility arises. Because one is using Euclidean space-times, in which the time direction is on the same footing as directions in space, it is possible for space-time to be finite in extent and yet to have no singularities that formed a boundary or edge. Space-time would be like the surface of the earth, only with two more dimensions. The surface of the earth is finite in extent but it doesn’t have a boundary or edge:

With the success of scientific theories in describing events, most people have come to believe that God allows the universe to evolve according to a set of laws and does not intervene in the universe to break these laws. However, the laws do not tell us what the universe should have looked like when it started – it would still be up to God to wind up the clockwork and choose how to start it off. So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no
boundary or edge, it would have neither beginning nor end: it would simply be. What place, then, for a creator?

The explanation that is usually given as to why we don’t see broken cups gathering themselves together off the floor and jumping back onto the table is that it is forbidden by the second law of thermodynamics. This says that in any closed system disorder, or entropy, always increases with time.

First, there is the thermodynamic arrow of time, the direction of time in which disorder or entropy
increases. Then, there is the psychological arrow of time. This is the direction in which we feel time passes, the direction in which we remember the past but not the future. Finally, there is the cosmological arrow of time. This is the direction of time in which the universe is expanding rather than contracting.

But there is a quicker way to find out what will happen: jump into a black hole. The collapse of a star to form a black hole is rather like the later stages of the collapse of the whole universe

At first, I believed that disorder would decrease when the universe recollapsed

the contracting phase would be like the time reverse of the expanding phase. People in the contracting phase
would live their lives backward: they would die before they were born and get younger as the universe contracted.

I was also misled by work I had done on a simple model of the universe in which the collapsing phase looked like the time reverse of the expanding phase.

I realized that I had made a mistake: the no boundary condition implied that disorder would in fact continue to increase during the contraction. The thermodynamic and psychological arrows of time would not reverse when the universe begins to recontract, or inside black holes.

If one believes that the universe will expand and then contract again, as the no boundary proposal seems to imply, this becomes a question of why we should be in the expanding phase rather than the contracting phase. One can answer this on the basis of the weak anthropic principle. Conditions in the contracting phase would not be suitable for the existence of intelligent beings

will not recollapse for a very long time. By then all the stars will have burned out and the protons and neutrons in them will probably have decayed into light particles and radiation. The universe would be in a state of almost complete disorder.

I have shown that the psychological arrow is essentially the same as the thermodynamic arrow, so that the two would always point in the same direction


it seems that the uncertainty principle is a fundamental feature of the universe we live in

The last three may be combined in so-called grand unified theories, or GUTs, which are not very satisfactory because they do not include gravity and because they contain a number of quantities, like the relative masses of different particles, that cannot be predicted from the theory but have to be chosen to fit observations. The main difficulty in finding a theory that unifies gravity with the other forces is that general relativity is a “classical” theory; that is, it does not incorporate the uncertainty principle of quantum mechanics. On the other hand, the other partial theories depend on quantum mechanics in an essential way. A necessary first step, therefore, is to combine general relativity with the uncertainty principle.

The success of these laws led Laplace at the beginning of the nineteenth century to postulate
scientific determinism; that is, he suggested that there would be a set of laws that would determine the
evolution of the universe precisely

The uncertainty principle of quantum mechanics implies that certain pairs of quantities, such as the position and velocity of a particle, cannot both be predicted with complete accuracy. Quantum mechanics deals with this situation via a class of quantum theories in which particles don’t have well-defined positions and velocities but are represented by a wave.

the fact that gravity is always attractive implies that the universe must be either expanding or contracting.