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# Bending of Light in a Gravitational Field by Shana Priwer & Cynthia Phillips, Ph.D.

After his 1907 paper on the principle of equivalence, Einstein's next contribution to the study of general relativity did not come until 1911. As part of his principle of equivalence, Einstein had realized that light itself should be bent by a gravitational field. However, when considering only terrestrial measurements, Einstein thought that there was little chance of any kind of experimental verification of this claim.

In his 1911 paper, though, Einstein realized that the bending of light could be seen by way of astronomical observations. The masses of stars and galaxies, Einstein surmised, would be large enough to bend light to a sufficient extent that it could be observed.

## Why Should Light Bend?

The bending of light is, in fact, a direct consequence of the principle of equivalence. Think about an elevator in free fall here on Earth. If a laser shines a beam of light from one side of the elevator, it will make a dot on the wall of the opposite side. Since the inside of the elevator is an inertial reference frame, the laser will make a dot of light directly across the elevator from the position of the laser. This is the same behavior that we would expect from a laser located in a nonmoving laboratory.

However, now imagine that there is a window in the elevator and an observer outside the elevator observes the laser beam. The external observer sees that the elevator is accelerating downward, toward the surface of the Earth, due to the Earth's gravity. In order for the beam of light to reach the directly opposite wall of the elevator, then, the beam of light itself must also be accelerating down toward the Earth at the same rate.

If the external observer plotted the path of the beam of light with respect to his nonmoving reference frame, the path would look like a curve. Therefore, even light can be affected by gravity, and a gravitational force will bend the path of light. Since the speed of light is very fast, the bending is very small; however, it is detectable if the mass is large enough and the distance long enough.

## Observational Confirmation!

Einstein's bold prediction that light would be bent by a gravitational field was stunningly confirmed by observations made on May 29, 1919, during a total solar eclipse. Astronomers made very careful measurements of the positions of stars near the sun during the eclipse. They saw that their apparent positions were deflected by a distance of 1.7 seconds of arc, a very small distance, but the amount Einstein had predicted. This measurement pushed the boundaries of scientific accuracy at the time, but it was precise enough to confirm Einstein's theory.

Einstein proved that even light could be affected by gravity.

The confirmation of Einstein's theory in 1919 made Einstein an overnight celebrity, and the myth of Einstein the genius began to build up. It was only six months after the end of World War I, and the world embraced the idea that this forty-year-old scientist had made such an amazing revelation in the realm of pure science, untouched by political or social conflict.

The 1919 observations certainly launched Einstein and general relativity into the limelight, but questions still remained about whether his theory was in fact correct. The eclipse observations could include up to a 20 percent error, not precise enough to rule out some competing theories of gravity that conflicted with Einstein's. It was not until the Hipparcos satellite charted stellar positions with unprecedented accuracy, from 1989 to 1993, that scientists finally had enough proof to show that Einstein's predictions were correct to an accuracy of

of a percent–one part in a thousand. That was enough to convince even the most skeptical scientists.

The elegant bending of light by stars can be seen in astronomical features called “gravitational lenses,” in which the light of a faraway star or galaxy is pulled into shapes such as arcs or rings by an intervening mass. Many of such features have been observed by the Hubble Space Telescope and other telescopes, and their configuration can be used to extract information about the masses of the objects.

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By Shana Priwer & Cynthia Phillips, Ph.D.

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