Let us consider a ray of light that shines through a window in an elevator at rest, as shown in figure. The ray of light follows a straight line path and hits the opposite wall of the elevator at the point P.
Let us now repeat the experiment, but let the elevator accelerate upward very rapidly, as shown in figure. The ray of light enters the window as before, but before it can cross the room to the opposite wall the elevator is displaced upward because of the acceleration. Instead of the ray of light hitting the wall at the point P, it hits at some lower point Q because of the upward acceleration of the elevator.
To an observer in the elevator, the ray of light follows the parabolic path, as shown in figure. Thus, in the accelerated coordinate system of the elevator, light does not travel in a straight line, but instead follows a curved path. But by the principle of equivalence the accelerated elevator can be replaced by a gravitational field. Therefore light should be bent from a straight line path in the presence of a gravitational field.
The gravitational field of the earth is relatively small and the bending cannot be measured on earth. However, the gravitational field of the sun is much larger and Einstein predicted in 1916 that rays of light that pass close to the sun should be bent by the gravitational field of the sun.
Another way of considering this bending of light is to say that light has energy and energy can be equated to mass, thus the light-mass should be attracted to the sun. Finally, we can think of this bending of light in terms of the curvature of spacetime caused by the mass of the sun. Light follows the shortest path, called a geodesic, and is thus bent by the curvature of spacetime.
Regardless of which conceptual picture we pick, Einstein predicted that a ray of light should be deflected by the sun by the angle of 1.75 seconds of arc. In order to observe this deflection it was necessary to measure the angular deviation between two stars when they are far removed from the sun, and then measure the deflection again when they are close to the sun. Of course when they are close to the sun, there is too much light from the sun to be able to see the stars.
Hence, to test out Einstein’s prediction it was necessary to measure the separation during a total eclipse of the sun. Sir Arthur Eddington led an expedition to the west coast of Africa for the solar eclipse of May 29, 1919, and measured the deflection. On November 6, 1919, the confirmation of Einstein’s prediction of the bending of light was announced to the world.
More modern techniques used today measure radio waves from the two quasars, 3c273 and 3c279 in the constellation of Virgo.
A quasar is a quasi-stellar object, a star that emits very large quantities of radio waves. Because the sun is very dim in the emission of radio waves, radio astronomers do not have to wait for an eclipse to measure the angular separation but can measure it at any time.
On October 8, 1972, when the quasars were close to the sun, radio astronomers measured the angular separation between 3c273 and 3c279 in radio waves and found that the change in the angular separation caused by the bending of the radio waves around the sun was 1.73 seconds of arc, in agreement with the general theory of relativity.