Page 20 - A Brief History of Time - Stephen Hawking

A Brief History of Time - Stephen Hawking... Chapter 2
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. A
geodesic is the shortest (or longest) path between two nearby points. For example, the surface of the earth is a
two-dimensional curved space. A geodesic on the earth is called a great circle, and is the shortest route
between two points (Fig. 2.8). As the geodesic is the shortest path between any two airports, this is the route
an airline navigator will tell the pilot to fly along. In general relativity, bodies always follow straight lines in
four-dimensional space-time, but they nevertheless appear to us to move along curved paths in our
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

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