Indeed, the police make use of the Doppler effect to measure the speed of cars by measuring the wavelength
of pulses of radio waves reflected off them.
ln the years following his proof of the existence of other galaxies, Rubble spent his time cataloging their
distances and observing their spectra. At that time most people expected the galaxies to be moving around
quite randomly, and so expected to find as many blue-shifted spectra as red-shifted ones. It was quite a
surprise, therefore, to find that most galaxies appeared red-shifted: nearly all were moving away from us! 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 was one of the great intellectual revolutions of the twentieth
century. With hindsight, it is easy wonder why no one had thought of it before. Newton, and others should have
realized that a static universe would soon start to contract under the influence of gravity. But suppose instead
that the universe is expanding. If it was expanding fairly slowly, the force of gravity would cause it eventually to
stop expanding and then to start contracting. However, if it was expanding at more than a certain critical rate,
gravity would never be strong enough to stop it, and the universe would continue to expand forever. This is a bit
like what happens when one fires a rocket upward from the surface of the earth. If it has a fairly low speed,
gravity will eventually stop the rocket and it will start falling back. On the other hand, 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, so it will
keep going away from the earth forever. This behavior of the universe could have been predicted from
Newton’s theory of gravity at any time in the nineteenth, the eighteenth, or even the late seventeenth century.
Yet so strong was the belief in a static universe that it persisted into the early twentieth century. Even Einstein,
when he formulated the general theory of relativity in 1915, was so sure that the universe had to be static that
he modified his theory to make this possible, introducing a so-called cosmological constant into his equations.
Einstein introduced a new “antigravity” force, which, unlike other forces, did not come from any particular
source but was built into the very fabric of space-time. He claimed that space-time had an inbuilt tendency to
expand, and this could be made to balance exactly the attraction of all the matter in the universe, so that a
static universe would result. Only one man, it seems, was willing to take general relativity at face value, and
while Einstein and other physicists were looking for ways of avoiding general relativity’s prediction of a
nonstatic universe, the Russian physicist and mathematician Alexander Friedmann instead set about explaining
it.
Friedmann made two very simple assumptions about the universe: that the universe looks identical in
whichever direction we look, and that this would also be true if we were observing the universe from anywhere
else. From these two ideas alone, Friedmann showed that we should not expect the universe to be static. In
fact, in 1922, several years before Edwin Hubble’s discovery, Friedmann predicted exactly what Hubble found!
The assumption that the universe looks the same in every direction is clearly not true in reality. For example, as
we have seen, the other stars in our galaxy form a distinct band of light across the night sky, called the Milky
Way. But if we look at distant galaxies, there seems to be more or less the same number of them. So the
universe does seem to be roughly the same in every direction, provided one views it on a large scale compared
to the distance between galaxies, and ignores the differences on small scales. For a long time, this was
sufficient justification for Friedmann’s assumption – as a rough approximation to the real universe. But more
recently a lucky accident uncovered the fact that Friedmann’s assumption is in fact a remarkably accurate
description of our universe.
In 1965 two American physicists at the Bell Telephone Laboratories in New Jersey, Arno Penzias and Robert
Wilson, were testing a very sensitive microwave detector. (Microwaves are just like light waves, but with a
wavelength of around a centimeter.) Penzias and Wilson were worried when they found that their detector was
picking up more noise than it ought to. The noise did not appear to be coming from any particular direction.
First they discovered bird droppings in their detector and checked for other possible malfunctions, but soon
ruled these out. They knew that any noise from within the atmosphere would be stronger when the detector
was not pointing straight up than when it was, because light rays travel through much more atmosphere when
received from near the horizon than when received from directly overhead. The extra noise was the same
whichever direction the detector was pointed, so it must come from outside the atmosphere. It was also the
same day and night and throughout the year, even though the earth was rotating on its axis and orbiting around
the sun. This showed that the radiation must come from beyond the Solar System, and even from beyond the
galaxy, as otherwise it would vary as the movement of earth pointed the detector in different directions.
In fact, we know that the radiation must have traveled to us across most of the observable universe, and since
it appears to be the same in different directions, the universe must also be the same in every direction, if only
on a large scale. We now know that whichever direction we look, this noise never varies by more than a tiny
fraction: so Penzias and Wilson had unwittingly stumbled across a remarkably accurate confirmation of
Friedmann’s first assumption. However, because the universe is not exactly the same in every direction, but
only on average on a large scale, the microwaves cannot be exactly the same in every direction either. There
have to be slight variations between different directions. These were first detected in 1992 by the Cosmic
Background Explorer satellite, or COBE, at a level of about one part in a hundred thousand. Small though these
variations are, they are very important, as will be explained in Chapter 8.
At roughly the same time as Penzias and Wilson were investigating noise in their detector, two American
physicists at nearby Princeton University, Bob Dicke and Jim Peebles, were also taking an interest in
microwaves. They were working on a suggestion, made by George Gamow (once a student of Alexander
Friedmann), that the early universe should have been very hot and dense, glowing white hot. Dicke and
Peebles argued that we should still be able to see the glow of the early universe, because light from very
distant parts of it would only just be reaching us now. However, the expansion of the universe meant that this
light should be so greatly red-shifted that it would appear to us now as microwave radiation. Dicke and Peebles
were preparing to look for this radiation when Penzias and Wilson heard about their work and realized that they
had already found it. For this, Penzias and Wilson were awarded the Nobel Prize in 1978 (which seems a bit
hard on Dicke and Peebles, not to mention Gamow!).
Now at first sight, all this evidence that the universe looks the same whichever direction we look in might seem
to suggest there is something special about our place in the universe. In particular, 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. This, as we have seen, was Friedmann’s second assumption. We have no scientific evidence for, or
against, this assumption. We believe it only on grounds of modesty: it would be most remarkable if the universe
looked the same in every direction around us, but not around other points in the universe! In Friedmann’s
model, all the galaxies are moving directly away from each other. 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. Moreover, the farther
apart the spots are, the faster they will be moving apart. Similarly, in Friedmann’s model the speed at which any
two galaxies are moving apart is proportional to the distance between them. So it predicted that the red shift of
a galaxy should be directly proportional to its distance from us, exactly as Hubble found. Despite the success of
his model and his prediction of Hubble’s observations, Friedmann’s work remained largely unknown in the West
until similar models were discovered in 1935 by the American physicist Howard Robertson and the British
mathematician Arthur Walker, in response to Hubble’s discovery of the uniform expansion of the universe.
Although Friedmann found only one, there are in fact three different kinds of models that obey Friedmann’s two
fundamental assumptions. In the first kind (which Friedmann found) the universe is expanding sufficiently
slowly that the gravitational attraction between the different galaxies causes the expansion to slow down and
eventually to stop. The galaxies then start to move toward each other and the universe contracts.
Figure 3:2
Figure 3:2 shows how the distance between two neighboring galaxies changes as time increases. It starts at
zero, increases to a maximum, and then decreases to zero again. In the second kind of solution, the universe is
expanding so rapidly that the gravitational attraction can never stop it, though it does slow it down a bit.
Figure 3:3
Figure 3:3 Shows the Separation between neighboring galaxies in this model. It starts at zero and eventually
the galaxies are moving apart at a steady speed. Finally, there is a third kind of solution, in which the universe
is expanding only just fast enough to avoid recollapse.
Figure 3:4
In this case the separation, shown in Figure 3:4, also starts at zero and increases forever. However, the speed
at which the galaxies are moving apart gets smaller and smaller, although it never quite reaches zero.
A remarkable feature of the first kind of Friedmann model is that in it the universe is not infinite in space, but
neither does space have any boundary. Gravity is so strong that space is bent round onto itself, making it rather
like the surface of the earth. If one keeps traveling in a certain direction on the surface of the earth, one never
comes up against an impassable barrier or falls over the edge, but eventually comes back to where one
started.
In the first kind of Friedmann model, space is just like this, but with three dimensions instead of two for the
earth’s surface. The fourth dimension, time, is also finite in extent, but it is like a line with two ends or
boundaries, a beginning and an end. We shall see later that when one combines general relativity with the
uncertainty principle of quantum mechanics, it is possible for both space and time to be finite without any edges
or boundaries.
The idea that one could go right round the universe and end up where one started makes good science fiction,
but it doesn’t have much practical significance, because it can be shown that the universe would recollapse to
zero size before one could get round. You would need to travel faster than light in order to end up where you
started before the universe came to an end – and that is not allowed!
In the first kind of Friedmann model, which expands and recollapses, space is bent in on itself, like the surface
of the earth. It is therefore finite in extent. In the second kind of model, which expands forever, space is bent
the other way, like the surface of a saddle. So in this case space is infinite. Finally, in the third kind of
Friedmann model, with just the critical rate of expansion, space is flat (and therefore is also infinite).
But which Friedmann model describes our universe? Will the universe eventually stop expanding and start
contracting, or will it expand forever? To answer this question we need to know the present rate of expansion of
the universe and its present average density. If the density is less than a certain critical value, determined by
the rate of expansion, the gravitational attraction will be too weak to halt the expansion. If the density is greater
than the critical value, gravity will stop the expansion at some time in the future and cause the universe to
recollapse.
We can determine the present rate of expansion by measuring the velocities at which other galaxies are
moving away from us, using the Doppler effect. This can be done very accurately. However, the distances to
the galaxies are not very well known because we can only measure them indirectly. So all we know is that the
universe is expanding by between 5 percent and 10 percent every thousand million years. However, our
uncertainty about the present average density of the universe is even greater. If we add up the masses of all
the stars that we can see in our galaxy and other galaxies, the total is less than one hundredth of the amount
required to halt the expansion of the universe, even for the lowest estimate of the rate of expansion. Our galaxy
and other galaxies, however, must contain a large amount of “dark matter” that we cannot see directly, but
which we know must be there because of the influence of its gravitational attraction on the orbits of stars in the
galaxies. Moreover, most galaxies are found in clusters, and we can similarly infer the presence of yet more
dark matter in between the galaxies in these clusters by its effect on the motion of the galaxies. When we add
up all this dark matter, we still get only about one tenth of the amount required to halt the expansion. However,
