All the known particles in the universe can be divided into two groups: particles of spin
½, which make up the matter in the universe, and particles of spin 0, 1, and 2, which, as
we shall see, give rise to forces between the matter particles. The matter particles obey
what is called Pauli’s exclusion principle. This was discovered in 1925 by an Austrian
physicist, Wolfgang Pauli– for which he received the Nobel Prize in 1945. He was the
archetypal theoretical physicist: it was said of him that even his presence in the same
town would make experiments go wrong! Pauli’s exclusion principle says that two
similar particles cannot exist in the same state; that is, they cannot have both the same
position and the same velocity, within the limits given by the uncertainty principle. The
exclusion principle is crucial because it explains why matter particles do not collapse to a
state of very high density under the influence of the forces produced by the particles of
spin 0, 1, and 2: if the matter particles have very nearly the same positions, they must
have different velocities, which means that they will not stay in the same position for
long. If the world had been created without the exclusion principle, quarks would not
form separate, welldefined protons and neutrons. Nor would these, together with
electrons, form separate, welldefined atoms. They would all collapse to form a roughly
uniform, dense “soup.”
A proper understanding of the electron and other spin½ particles did not come until
1928, when a theory was proposed by Paul Dirac, who later was elected to the Lucasian
Professorship of Mathematics at Cambridge (the same professorship that Newton had
once held and that I now hold). Dirac’s theory was the first of its kind that was consistent
with both quantum mechanics and the special theory of relativity. It explained
mathematically why the electron had spin½; that is, why it didn’t look the same if you
turned it through only one complete revolution, but did if you turned it through two
revolutions. It also predicted that the electron should have a partner: an antielectron, 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 the case of the forcecarrying particles,
the antiparticles are the same as the particles themselves.) There could be whole
antiworlds and antipeople made out of antiparticles. However, if you meet your antiself,
don’t shake hands! You would both vanish in a great flash of light. The question of why
there seem to be so many more particles than antiparticles around us is extremely
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– 0, 1, or 2. What happens is that a
matter particle, such as an electron or a quark, emits a forcecarrying particle. The recoil
from this emission changes the velocity of the matter particle. The forcecarrying particle
then collides with another matter particle and is absorbed. This collision changes the
velocity of the second particle, just as if there had been a force between the two matter
particles. It is an important property of ' the forcecarrying particles that they do not obey
the exclusion principle. This means that there is no limit to the number that can be
exchanged, and so they can give rise to a strong force. However, if the forcecarrying
particles have a high mass, it will be difficult to produce and exchange them over a large
distance. So the forces that they carry will have only a short range. On the other hand, if
the forcecarrying particles have no mass of their own, the forces will be long range. The
forcecarrying particles exchanged between matter particles are said to be virtual particles
because, unlike “real” particles, theycannot be directly detected by a particle detector.
We know they exist, however, because they do have a measurable effect: they give rise to
forces between matter particles. Particles of spin 0, 1, or 2 do also exist in some
circumstances as real particles, when they can be directly detected. They then appear to
us as what a classical physicist would call waves, such as waves of light or gravitational
waves. They may sometimes be emitted when matter particles interact with each other by
exchanging virtualforcecarrying particles. (For example, the electric repulsive force
between two electrons is due to the exchange of virtual photons, which can never be
directly detected; but if one electron moves past another, real photons may be given off,
which we detect as light waves.)
Forcecarrying particles can be grouped into four categories according to the strength of
the force that they carry and the particles with which they interact. It should be
emphasized that this division into four classes is manmade; it is convenient for the
construction of partial theories, but it may not correspond to anything deeper. Ultimately,
most physicists hope to find a unified theory that will explain all four forces as different
aspects of a single force. Indeed, many would say this is the prime goal of physics today.
Recently, successful attempts have been made to unify three of the four categories of
force – and I shall describe these in this chapter. The question of the unification of the
remaining category, gravity, we shall leave till later.
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. This means that the very weak gravitational forces between the individual
particles in two large bodies, such as the earth and the sun, can all add up to produce a
significant force. The other three forces are either short range, or are sometimes attractive
and sometimes repulsive, so they tend to cancel out. 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. This has no mass of its own, so
the force that it carries is long range. The gravitational force between the sun and the
earth is ascribed to the exchange of gravitons between the particles that make up these
two bodies. Although the exchanged particles are virtual, they certainly do produce a
measurable effect –they make the earth orbit the sun! Real gravitons make up what
classical physicists would call gravitational waves, which are very weak – and so difficult
to detect that they have not yet been observed.
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. It
is much stronger than the gravitational force: the electromagnetic force between two
electrons is about a million million million million million million million (1 with forty
two zeros after it) times bigger than the gravitational force. However, there are two kinds
of electric charge, positive and negative. The force between two positive charges is
repulsive, as is the force between two negative charges, but the force is attractive between
a positive and a negative charge. A large body, such as the earth or the sun, contains
nearly equal numbers of positive and negative charges. Thus the attractive and repulsive
forces between the individual particles nearly cancel each other out, and there is very
little net electromagnetic force. However, on the small scales of atoms and molecules,
electromagnetic forces dominate. The electromagnetic attraction between negatively
charged electrons and positively charged protons in the nucleus causes the electrons to
orbit the nucleus of the atom, just as gravitational attraction causes the earth to orbit the
sun. The electromagnetic attraction is pictured as being caused by the exchange of large
numbers of virtual massless particles of spin 1, called photons. Again, the photons that
are exchanged are virtual particles. However, when an electron changes from one allowed
orbit to another one nearer to the nucleus, energy is released and a real photon is emitted
– which can be observed as visible light by the human eye, ifit has the right wavelength,
or by a photon detector such as photographic film. Equally, if a real photon collides with
an atom, it may move an electron from an orbit nearer the nucleus to one farther away.
This uses up the energy of the photon, so it is absorbed.
The third category is called the weak nuclear force, which is responsible for radioactivity
and which acts on all matter particles of spin½, but not on particles of spin 0, 1, or 2,
such as photons and gravitons. The weak nuclear force was not well understood until
1967, when Abdus Salam at Imperial College, London, and Steven Weinberg at Harvard
both 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 spin1 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 gigaelectronvolt, or one thousand
million electron volts). The WeinbergSalam 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 ona roulette wheel. At high energies
(when the wheel is spun quickly) the ball behaves in essentially only one way– it rolls
round and round. But as the wheel slows, the energy of the ball decreases, and eventually
the ball drops into one of the thirtyseven slots in the wheel. In other words, at low
energies there are thirtyseven different states in which the ball can exist. If, for some
reason, we could only observe the ball at low energies, we would then think that there
were thirtyseven different types of ball!
In the WeinbergSalam theory, at energies much greater than 100 GeV, the three new
particles and the photon would all behave in a similar manner. But at the lower particle
energies that occur in most normal situations, this symmetry between the particles would
be broken. WE, W, and Zº would acquire large masses, making the forces they carry have
a very short range. At the time that Salam and Weinberg proposed their theory, few
people believed them, and particle accelerators were not powerful enough to reach the
+
energies of 100 GeV required to produce real W , W , or Zº particles. However, over the
next ten years or so, the other predictions of the theory at lower energies agreed so well
with experiment that, in 1979, Salam and Weinberg were awardedthe Nobel Prize for
physics, together with Sheldon Glashow, also at Harvard, who had suggested similar
unified theories of the electromagnetic and weak nuclear forces. The Nobel committee
was spared the embarrassment of having made a mistake by 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. Carlo Rubbia, who led the
team of several hundred physicists that made the discovery, received the Nobel Prize in
1984, along with Simon van der Meer, the CERNengineer who developed the antimatter
storage system employed. (It is very difficult to make a mark in experimental physics
these days unless you are already at the top! )
The fourth category is the strong nuclear force, which holds the quarks together in the
proton and neutron, and holds the protons and neutrons together in the nucleus of an
atom. It is believed that this force is carried by another spin1 particle, called the gluon,
which interacts only with itself and with the quarks. The strong nuclear force has a
curious property called confinement: it always binds particles together into combinations
that have no color. One cannot have a single quark on its own because it would have a
color (red, green, or blue). Instead, a red quark has to be joined to a green and a blue
quark by a “string” of gluons (red + green + blue = white). Such a triplet constitutes a
proton or a neutron. Another possibility is a pair consisting of a quark and an antiquark
(red + antired, or green + antigreen, or blue + antiblue = white). Such combinations make
up the particles known as mesons, which are unstable because the quark and antiquark
can annihilate each other, producing electrons and other particles. Similarly, confinement
prevents one having a single gluon on its own, because gluons also have color. Instead,
one has to have a collection of gluons whose colors add up to white. Such a collection
forms an unstable particle called a glueball.
The fact that confinement prevents one from observing an isolated quark or gluon might
seem to make the whole notion of quarks and gluons as particles somewhat metaphysical.
However, there is another property of the strong nuclear force, called asymptotic
freedom, that makes the concept of quarks and gluons well defined. At normal energies,
the strong nuclear force is indeed strong, and it binds the quarks tightly together.
However, experiments with large particle accelerators indicate that at high energies the
strong force becomes much weaker, and the quarks and gluons behave almost like free
particles.
Figure 5:2 shows a photograph of a collision between a highenergy 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 spin½ matter particles, like quarks and electrons,
would also all be essentially the same, thus achieving another unification.
The value of the grand unification energy is not very well known, but it would probably
have to be at least a thousand million million GeV. The present generation of particle
accelerators can collide particles at energies of about one hundred GeV, and machines are
planned that would raise this to a few thousand GeV. But a machine that was powerful
enough to accelerate particles to the grand unification energy would have to be as big as
the Solar System– and would be unlikely to be funded in the present economic climate.
Thus it is impossible to test grand unified theories directly in the laboratory. However,
just as in the case of the electromagnetic and weak unified theory, there are lowenergy
consequences of the theory that can be tested.
The most interesting of these is the predictionthat protons, which make up much of the
mass of ordinary matter, can spontaneously decay into lighter particles such as
antielectrons. The reason this is possible is that at the grand unification energy there is no
essential difference between a quark and an antielectron. The three quarks inside a proton
normally do not have enough energy to change into antielectrons, but very occasionally
one of them may acquire sufficient energy to make the transition because the uncertainty
principle means that the energy of the quarks inside the proton cannot be fixed exactly.
The proton would then decay. The probability of a quark gaining sufficient energy is so
low that one is likely to have to wait at least a million million million million million
years (1 followed by thirty zeros). This is much longer than the time since the big bang,
which is a mere ten thousand million years or so (1 followed by ten zeros). Thus one
might think that the possibility of spontaneous proton decay could not be tested
experimentally. However, one can increase one’s chances of detecting a decay by
observing a large amount of matter containing a very large number of protons. (If, for
example, one observed a number of protons equal to 1 followed by thirtyone 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 thirtyone 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
highenergy 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 antiparticles,
annihilating each other and giving off highenergy radiation.
We have no direct evidence as to whether the matter in other galaxies is made up of
protons and neutrons or antiprotons and antineutrons, 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 righthanded
direction is one spinning in a lefthanded 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, TsungDao 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, ChienShiung 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 Kmesons. Cronin and Fitch eventually received the Nobel Prize for their
work in 1980. (A lot of prizes have been awarded for showing that the universe is not as
simple as we might have thought!)
There is a mathematical theorem that says that any theory that obeys quantum mechanics
and relativity must always obey the combined symmetry CPT. In other words, the
universe would have to behave the same if one replaced particles by antiparticles, took
the mirror image, and also reversed the direction of time. But Cronin and Fitch showed
that if one replaces particles by antiparticles and takes the mirror image, but does not
reverse the direction of time, then the universe does not behave the same. The laws of
physics, therefore, must change if one reverses the direction of time – they do not obey
the symmetry T.
Certainly the early universe does not obey the symmetry T: as time runs forward the
universe expands – if it ran backward, the universe would be contracting. And since there
are forces that do not obey the symmetry T, it follows that as the universe expands, these
forces could cause more antielectrons to turn into quarks than electrons into antiquarks.
Then, as the universe expanded and cooled, the antiquarks would annihilate with the
quarks, but since there would be more quarks than antiquarks, a small excess of quarks
would remain. It is these that make up the matter we see today and out of which we
ourselves are made. Thus our very existence could be regarded as a confirmation of grand
unified theories, though a qualitative one only; the uncertainties are such that one cannot
predict the numbers of quarks that will be left after the annihilation, or even whether it
would be quarks or antiquarks that would remain. (Had it been an excess of antiquarks,
however, we would simply have named antiquarks quarks, and quarks antiquarks.)
Grand unified theories do not include the force of gravity. This does not matter too much,
because gravity is such a weak force that its effects can usually be neglected when we are
dealing with elementary particles or atoms. However, the fact that it is both long range
and always attractive means that its effects all add up. So for a sufficiently large number
of matter particles, gravitational forces can dominate over all other forces. This is why it
is gravity that determines the evolution of the universe. Even for objects the size of stars,
the attractive forceof gravity can win over all the other forces and cause the star to
collapse. My work in the 1970s focused on the black holes that can result from such
stellar collapse and the intense gravitational fields around them. It was this that led to the
first hints of how the theories of quantum mechanics and general relativity might affect
each other – a glimpse of the shape of a quantum theory of gravity yet to come.