three-dimensional space. (This is rather like watching an airplane flying over hilly ground. Although it follows a
straight line in three-dimensional space, its shadow follows a curved path on the two-dimensional ground.)
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.
Fact, the orbits of the planets predicted by general relativity are almost exactly the same as those predicted by
the Newtonian theory of gravity. However, in the case of Mercury, which, being the nearest planet to the sun,
feels the strongest gravitational effects, and has a rather elongated orbit, general relativity predicts that the long
axis of the ellipse should rotate about the sun at a rate of about one degree in ten thousand years. Small
though this effect is, it had been noticed before 1915 and served as one of the first confirmations of Einstein’s
theory. In recent years the even smaller deviations of the orbits of the other planets from the Newtonian
predictions have been measured by radar and found to agree with the predictions of general relativity.
Light rays too must follow geodesics in space-time. Again, the fact that space is curved means that light no
longer appears to travel in straight lines in space. So general relativity predicts that light should be bent by
gravitational fields. For example, 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. This means that light from a distant star that happened to pass
near the sun would be deflected through a small angle, causing the star to appear in a different position to an
observer on the earth (Fig. 2.9). Of course, if the light from the star always passed close to the sun, we would
not be able to tell whether the light was being deflected or if instead the star was really where we see it.
However, as the earth orbits around the sun, different stars appear to pass behind the sun and have their light
deflected. They therefore change their apparent position relative to other stars. It is normally very difficult to see
this effect, because the light from the sun makes it impossible to observe stars that appear near to the sun the
sky. However, it is possible to do so during an eclipse of the sun, when the sun’s light is blocked out by the
moon. Einstein’s prediction of light deflection could not be tested immediately in 1915, because the First World
War was in progress, and it was 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. This proof of a German
theory by British scientists was hailed as a great act of reconciliation between the two countries after the war. It
is ionic, therefore, that later examination of the photographs taken on that expedition showed the errors were as
great as the effect they were trying to measure. Their measurement had been sheer luck, or a case of knowing
the result they wanted to get, not an uncommon occurrence in science. The light deflection has, however, been
accurately confirmed by a number of later observations.
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. The difference in the speed of clocks at different heights
above the earth is now of considerable practical importance, with the advent of very accurate navigation
systems based on signals from satellites. If one ignored the predictions of general relativity, the position that
one calculated would be wrong by several miles!
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. Thus, if they met again, one would be
older than the other. In this case, the difference in ages would be very small, but it would be much larger if one
of the twins went for a long trip in a spaceship at nearly the speed of light. When he returned, he would be
much younger than the one who stayed on earth. This is known as the twins paradox, but it is a paradox only if
one has the idea of absolute time at the back of one’s mind. In the theory of relativity there is no unique
absolute time, but instead each individual has his own personal measure of time that depends on where he is
and how he is moving.
Before 1915, space and time were thought of as a fixed arena in which events took place, but which was not
affected by what happened in it. This was true even of the special theory of relativity. Bodies moved, forces
attracted and repelled, but time and space simply continued, unaffected. It was natural to think that space and
time went on forever.
The situation, however, is quite different in the general theory of relativity. Space and time are now dynamic
quantities: when a body moves, or a force acts, it affects the curvature of space and time – and in turn the
structure of space-time affects the way in which bodies move and forces act. Space and time not only affect but
also are affected by everything that happens in the universe. Just as one cannot talk about events in the
universe without the notions of space and time, so in general relativity it became meaningless to talk about
space and time outside the limits of the universe.
In the following decades this new understanding of space and time was to revolutionize our view of the
universe. The old idea of an essentially unchanging universe that could have existed, and could continue to
exist, forever was replaced by the notion of a dynamic, expanding universe that seemed to have begun a finite
time ago, and that might end at a finite time in the future. That revolution forms the subject of the next chapter.
And years later, it was also to be the starting point for my work in theoretical physics. Roger Penrose and I
showed that Einstein’s general theory of relativity implied that the universe must have a beginning and,
possibly, an end.
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PREVIOUS NEXT
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CHAPTER 3
THE EXPANDING UNIVERSE
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If one looks at the sky on a clear, moonless night, the brightest objects one sees are likely to be the planets
Venus, Mars, Jupiter, and Saturn. There will also be a very large number of stars, which are just like our own
sun but much farther from us. Some of these fixed stars do, in fact, appear to change very slightly their
positions relative to each other as earth orbits around the sun: they are not really fixed at all! This is because
they are comparatively near to us. As the earth goes round the sun, we see them from different positions
against the background of more distant stars. This is fortunate, because it enables us to measure directly the
distance of these stars from us: the nearer they are, the more they appear to move. The nearest star, called
Proxima Centauri, is found to be about four light-years away (the light from it takes about four years to reach
earth), or about twenty-three million million miles. Most of the other stars that are visible to the naked eye lie
within a few hundred light-years of us. Our sun, for comparison, is a mere light-minutes away! The visible stars
appear spread all over the night sky, but are particularly concentrated in one band, which we call the Milky
Way. As long ago as 1750, some astronomers were suggesting that the appearance of the Milky Way could be
explained if most of the visible stars lie in a single disklike configuration, one example of what we now call a
spiral galaxy. Only a few decades later, the astronomer Sir William Herschel confirmed this idea by
painstakingly cataloging the positions and distances of vast numbers of stars. Even so, the idea gained
complete acceptance only early this century.
Our modern picture of the universe dates back to only 1924, when the American astronomer Edwin Hubble
demonstrated that ours was not the only galaxy. There were in fact many others, with vast tracts of empty
space between them. In order to prove this, he needed to determine the distances to these other galaxies,
which are so far away that, unlike nearby stars, they really do appear fixed. Hubble was forced, therefore, to
use indirect methods to measure the distances. Now, the apparent brightness of a star depends on two factors:
how much light it radiates (its luminosity), and how far it is from us. For nearby stars, we can measure their
apparent brightness and their distance, and so we can work out their luminosity. Conversely, if we knew the
luminosity of stars in other galaxies, we could work out their distance by measuring their apparent brightness.
Hubble noted that certain types of stars always have the same luminosity when they are near enough for us to
measure; therefore, he argued, if we found such stars in another galaxy, we could assume that they had the
same luminosity – and so calculate the distance to that galaxy. If we could do this for a number of stars in the
same galaxy, and our calculations always gave the same distance, we could be fairly confident of our estimate.
In this way, Edwin Hubble worked out the distances to nine different galaxies. We now know that our galaxy is
only one of some hundred thousand million that can be seen using modern telescopes, each galaxy itself
containing some hundred thousand million stars. Figure 3:1 shows a picture of one spiral galaxy that is similar
to what we think ours must look like to someone living in another galaxy.
Figure 3:1
We live in a galaxy that is about one hundred thousand light-years across and is slowly rotating; the stars in its
spiral arms orbit around its center about once every several hundred million years. Our sun is just an ordinary,
average-sized, yellow star, near the inner edge of one of the spiral arms. We have certainly come a long way
since Aristotle and Ptolemy, when thought that the earth was the center of the universe!
Stars are so far away that they appear to us to be just pinpoints of light. We cannot see their size or shape. So
how can we tell different types of stars apart? 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. By focusing a telescope on an individual star or galaxy, one can similarly observe the spectrum
of the light from that star or galaxy. Different stars have different spectra, but the relative brightness of the
different colors is always exactly what one would expect to find in the light emitted by an object that is glowing
red hot. (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, we can determine exactly which elements are present in the star’s atmosphere.
In the 1920s, when astronomers began to look at the spectra of stars in other galaxies, they found something
most peculiar: there were the same characteristic sets of missing colors as for stars in our own galaxy, but they
were all shifted by the same relative amount toward the red end of the spectrum. To understand the
implications of this, we must first understand the Doppler effect. As we have seen, visible light consists of
fluctuations, or waves, in the electromagnetic field. The wavelength (or distance from one wave crest to the
next) of light is extremely small, ranging from four to seven ten-millionths of a meter. The different wavelengths
of light are what the human eye sees as different colors, with the longest wavelengths appearing at the red end
of the spectrum and the shortest wavelengths at the blue end. Now imagine a source of light at a constant
distance from us, such as a star, emitting waves of light at a constant wavelength. Obviously the wavelength of
the waves we receive will be the same as the wavelength at which they are emitted (the gravitational field of the
galaxy will not be large enough to have a significant effect). Suppose now that the source starts moving toward
us. When the source emits the next wave crest it will be nearer to us, so the distance between wave crests will
be smaller than when the star was stationary. This means that the wavelength of the waves we receive is
shorter than when the star was stationary. Correspondingly, if the source is moving away from us, the
wavelength of the waves we receive will be longer. In the case of light, therefore, means that stars moving
away from us will have their spectra shifted toward the red end of the spectrum (red-shifted) and those moving
toward us will have their spectra blue-shifted. This relationship between wavelength and speed, which is called
the Doppler effect, is an everyday experience. Listen to a car passing on the road: as the car is approaching, its
engine sounds at a higher pitch (corresponding to a shorter wavelength and higher frequency of sound waves),
and when it passes and goes away, it sounds at a lower pitch. The behavior of light or radio waves is similar.
