A brief History of Time: From Big Bang to Black Holes

partition, but a small amount will go through the slits. Now suppose one
places a screen on the far side of the partition from the light. 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

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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!
The phenomenon of interference between particles has been crucial to our
understanding of the structure of atoms, the basic units of chemistry and
biology and the building blocks out of which we, and everything around us,
are made. At the beginning of this century it was thought that atoms were
rather like the planets orbiting the sun, with electrons (particles of negative
electricity) orbiting around a central nucleus, which carried positive
electricity. The attraction between the positive and negative electricity was
supposed to keep the electrons in their orbits in the same way that the
gravitational attraction between the sun and the planets keeps the planets in
their orbits. The trouble with this was that the laws of mechanics and
electricity, before quantum mechanics, predicted that the electrons would
lose energy and so spiral inward until they collided with the nucleus. This
would mean that the atom, and indeed all matter, should rapidly collapse to a
state of very high density. A partial solution to this problem was found by
the Danish scientist Niels Bohr in 1913. He suggested that maybe the
electrons were not able to orbit at just any distance from the central nucleus
but only at certain specified distances. If one also supposed that only one or
two electrons could orbit at any one of these distances, this would solve the
problem of the collapse of the atom, because the electrons could not spiral in
any farther than to fill up the orbits with the least distances and energies.
This model explained quite well the structure of the simplest atom,
hydrogen, which has only one electron orbiting around the nucleus. But it
was not clear how one ought to extend it to more complicated atoms.
Moreover, the idea of a limited set of allowed orbits seemed very arbitrary.
The new theory of quantum mechanics resolved this difficulty. It revealed
that an electron orbiting around the nucleus could be thought of as a wave,
with a wavelength that depended on its velocity. For certain orbits, the length
of the orbit would correspond to a whole number (as opposed to a fractional

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number) of wavelengths of the electron. For these orbits the wave crest
would be in the same position each time round, so the waves would add up:
these orbits would correspond to Bohr’s allowed orbits. However, for orbits
whose lengths were not a whole number of wavelengths, each wave crest
would eventually be canceled out by a trough as the electrons went round;
these orbits would not be allowed.
A nice way of visualizing the wave/particle duality is the so-called sum
over histories introduced by the American scientist Richard Feynman. In this
approach the particle is not supposed to have a single history or path in
space-time, as it would in a classical, nonquantum theory. Instead it is
supposed to go from A to B by every possible path. With each path there are
associated a couple of numbers: one represents the size of a wave and the
other represents the position in the cycle (i.e., whether it is at a crest or a
trough). The probability of going from A to B is found by adding up the
waves for all the paths. In general, if one compares a set of neighboring
paths, the phases or positions in the cycle will differ greatly. This means that
the waves associated with these paths will almost exactly cancel each other
out. However, for some sets of neighboring paths the phase will not vary
much between paths. The waves for these paths will not cancel out. Such
paths correspond to Bohr’s allowed orbits.
With these ideas, in concrete mathematical form, it was relatively
straightforward to calculate the allowed orbits in more complicated atoms
and even in molecules, which are made up of a number of atoms held
together by electrons in orbits that go round more than one nucleus. Since
the structure of molecules and their reactions with each other underlie all of
chemistry and biology, quantum mechanics allows us in principle to predict
nearly everything we see around us, within the limits set by the uncertainty
principle. (In practice, however, the calculations required for systems
containing more than a few electrons are so complicated that we cannot do
them.)
Einstein’s general theory of relativity seems to govern the large-scale
structure of the universe. It is what is called a classical theory; that is, it does
not take account of the uncertainty principle of quantum mechanics, as it
should for consistency with other theories. The reason that this does not lead
to any discrepancy with observation is that all the gravitational fields that we
normally experience are very weak. However, the singularity theorems
discussed earlier indicate that the gravitational field should get very strong in

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at least two situations, black holes and the big bang. In such strong fields the
effects of quantum mechanics should be important. Thus, in a sense,
classical general relativity, by predicting points of infinite density, predicts
its own downfall, just as classical (that is, nonquantum) mechanics predicted
its downfall by suggesting that atoms should collapse to infinite density. We
do not yet have a complete consistent theory that unifies general relativity
and quantum mechanics, but we do know a number of the features it should
have. The consequences that these would have for black holes and the big
bang will be described in later chapters. For the moment, however, we shall
turn to the recent attempts to bring together our understanding of the other
forces of nature into a single, unified quantum theory.

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5
ELEMENTARY PARTICLES AND THE FORCES OF NATURE
ARISTOTLE BELIEVED THAT
all the matter in the universe was made up of four
basic elements – earth, air, fire, and water. These elements were acted on by
two forces: gravity, the tendency for earth and water to sink, and levity, the
tendency for air and fire to rise. This division of the contents of the universe
into matter and forces is still used today.
Aristotle believed that matter was continuous, that is, one could divide a
piece of matter into smaller and smaller bits without any limit: one never
came up against a grain of matter that could not be divided further. A few
Greeks, however, such as Democritus, held that matter was inherently
grainy and that everything was made up of large numbers of various
different kinds of atoms. (The word atom means ‘indivisible’ in Greek.) For
centuries the argument continued without any real evidence on either side,
but in 1803 the British chemist and physicist John Dalton pointed out that
the fact that chemical compounds always combined in certain proportions
could be explained by the grouping together of atoms to form units called
molecules. However, the argument between the two schools of thought was
not finally settled in favor of the atomists until the early years of this
century. One of the important pieces of physical evidence was provided by
Einstein. In a paper written in 1905, a few weeks before the famous paper
on special relativity, Einstein pointed out that what was called Brownian
motion – the irregular, random motion of small particles of dust suspended
in a liquid – could be explained as the effect of atoms of the liquid colliding
with the dust particles.
By this time there were already suspicions that these atoms were not,
after all, indivisible. Several years previously a fellow of Trinity College,
Cambridge, J. J. Thomson, had demonstrated the existence of a particle of

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matter, called the electron, that had a mass less than one thousandth of that
of the lightest atom. He used a set-up rather like a modern TV picture tube:
a red-hot metal filament gave off the electrons, and because these have a
negative electric charge, an electric field could be used to accelerate them
toward a phosphor-coated screen. When they hit the screen, flashes of light
were generated. Soon it was realized that these electrons must be coming
from within the atoms themselves, and in 1911 the British physicist Ernest
Rutherford finally showed that the atoms of matter do have internal
structure: they are made up of an extremely tiny, positively charged
nucleus, around which a number of electrons orbit. He deduced this by
analyzing the way in which alpha-particles, which are positively charged