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Einstein's chance to predict an effect that had not been seen came in the bending of light passing by the edge of the Sun. He said that the warping of space-time alters the path of light as it passes near the source of a strong gravitational field. According to general relativity, photons follow geodesies. The light will then appear to be coming from a slightly different direction. If the light is coming from a star, the position of the star will appear to be slightly different than if the bending had not taken place, as indicated in Fig. 8.8.

According to Einstein, the angle q (in radians) through which the light passing a distance b from an object of mass M is given by

If we set b equal to the radius of the Sun (6.96 x 1010 cm) we get an angle of 8.47 x 10-6 rad, which is equal to 1.74 arc seconds. This is a very small angle and is hard to measure.

The measurement is made even more difficult by the fact that we cannot see stars close to the Sun on the sky. Therefore, the test must be made during a total eclipse of the Sun, when the sky is photographed, and then the same part of sky is photographed approximately six months later.

The positions of the stars on the two photographs are then compared. The first attempt to carry this out was by a German team trying to get to a Russian viewing site for a 1914 eclipse. They were thwarted by the state of war between the two countries. The next try was in 1919, in an effort headed by Sir Arthur Eddington. In the intervening years, Einstein had found an error in his calculations, so it is probably just as well that the observations weren't done until the theoretical prediction was finalized. The result was a confirmation of Einstein's prediction. The recognition of the magnitude of Einstein's contribution was immediate, both among physicists and the general public.

The solar eclipse experiment is a hard one, and the original one had a 10% uncertainty associated with it. More recent tries have reduced the uncertainty to about 5%. Different types of experiments are needed for greater accuracy. A major improvement can be made by using radio waves. The bending applies equally to electromagnetic radiation of all wavelengths. The advantage of radio waves is that the Earth's atmosphere does not scatter them. We can observe any radio source as the Sun passes in front of it and watch the position of the source change. These tests have confirmed Einstein's predictions to greater accuracy than the eclipse experiments.

There is another effect related to the bending of light. The longer path that results from the curvature of space-time around the Sun causes a delay in the time for a signal to pass by the Sun. Two types of observations have been done to test this. One involves the reflection of radio waves from Mercury and Venus as they pass behind the Sun. We know the positions of the planets very accurately, so we know how long it should take for the signal to make a round trip. The other type of experiment involves spacecraft that have been sent to various parts of the Solar System, especially Mariners 6, 7 and 9, and Viking orbiters and landers on Mars. We simply follow the signals from the spacecraft. Since we know where the spacecraft should be, we can determine the time delay as the spacecraft pass behind the Sun. Using this technique, Einstein's predictions have been confirmed to an accuracy of 0.1%..

There is another interesting result related to the bending of the paths of electromagnetic waves. A massive object can bend rays so well that it can act as a gravitational lens. Physicists have speculated on this possibility for some time. Recent observations of quasars, to be discussed in Chapter 19, have revealed a number of sources in which double images are seen as a result of this gravitational lens effect.