Light is attracted by gravity

Light deflection by gravity

Information on one of the fundamental predictions of general relativity: the deflection of light in the gravitational field

An article by Steven S. Shapiro and Irwin I. Shapiro

Theories about the deflection of light by mass have been around since the end of the 18th century at the latest. At the time, John Michell, an English clergyman and natural philosopher, argued that even light would not be able to escape from the surface of the sun if the sun were of sufficient mass. Isaac Newton, to whom we owe the mathematical description of the force of gravity, seems to have devoted only a brief comment to the question of the influence of mass on the course of light rays at the end of his treatise "Opticks", published in 1704, with the statement , Light particles would probably be influenced by gravity in the same way as conventional matter.

The first calculations of how light is deflected by a mass were published in 1801 by the German astronomer Johann Georg von Soldner. Soldner had come to the conclusion that rays of light from a distant star that sweep past the edge of the sun should be deflected by an angle of 0.9 arc seconds - around a quarter of a thousandth of an angular degree. This is the same angle at which a CD appears when viewed from around 30 kilometers away. Soldner's calculations were based on Newton's laws of classical mechanics and gravity, as well as the assumption that light behaves like fast moving particles. As far as we know, neither Soldner nor his colleagues attempted to verify this prediction, and with good reason: Such an attempt would have been far beyond the capabilities of the astronomical instruments of the 19th century.

Light deflection in general relativity

Over a century later, at the beginning of the 20th century, Einstein developed his general theory of relativity. Einstein calculated that his theory also predicted a deflection of light at the edge of the sun, namely by twice the Newtonian value.

The following figure shows the deflection of light rays that travel in the immediate vicinity of a mass sphere. So that the effect can even be seen in the figure, the sphere has the same mass as the sun, but a diameter that is five thousand times smaller (and therefore a density of 125 billion).

According to the general theory of relativity, a light beam coming from the left would be bent inwards in such a way that the direction from which the light reaches the observer on the right deviates by a certain angle (the deflection angle α, see the figure below) from the original direction of the light would. The size of the deflection angle is proportional to the reciprocal of the smallest distance (d) from the light beam to the center of the mass sphere:

The following figure shows how α changes as a function of d:

The yellow area in the middle shows the spatial extent of the mass sphere. The curves to the left and right show the dependence of the deflection angle α on the distance d. The angle of deflection is greatest where the light comes closest to the mass and decreases with increasing distance. There is a similar curve for the sun; however, the predicted value α for light rays that run directly along the edge of the sun is five thousand times smaller than for the mass sphere shown here.

When stars shift

An observer on earth can detect the deflection of light from a (naturally distant) star by the sun by looking at how the position of the star in question changes in the course of a year. The following animation shows a star on the left, an observer on the right, as well as the change in the direction of incidence of light when light is deflected by an intermediate mass:

The image section at the bottom right shows in detail how the light rays reach the observer's eye. Without the mass, the light travels along a straight line from the star to the observer. In the presence of the mass, the light beam is bent, the light now reaches the observer from a slightly different direction, and so the star now appears to be at a slightly different point on the celestial sphere for the observer.

Such changes in position due to the deflection of starlight in the vicinity of the sun should be able to detect an observer equipped with appropriate optical devices - although the shift is much smaller than in the animation above. However, under normal conditions, sunlight brightens the Earth's philosophies to such an extent that it is impossible to observe stars near the Sun with an optical telescope from Earth. For the first observations that could be used to check Einstein's predictions, the astronomers involved waited for a solar eclipse, in which the moon is by definition pushed between the earth and the sun in such a way that certain regions of the earth can no longer be reached by sunlight (and thus can there is also no lightening of the earth's atmosphere).

Light deflection measurements

The first successful attempt to measure the deflection of light caused by gravity fell in 1919. The Royal Astronomical Society and the Royal Society in Great Britain had organized and financed two expeditions for this purpose. Each of the two groups took photographs of the sun's surroundings during the solar eclipse in May 1919 and compared the positions of the stars visible on them with photographs of the same section of sky that were taken in July 1919, when the sun had moved further and moved away from the region in question . The evaluation showed that the starlight had actually been deflected to an extent that was compatible with the predictions of general relativity, but not with the calculations based on Newtonian physics. This result caused a sensation, made Einstein world famous overnight and made him the only scientist to date for whom a confetti parade ("ticker-tape parade") was held on New York's Broadway.

When such solar eclipse observations were repeated over the course of the next half century, the astronomers did not succeed in increasing the accuracy by more than a factor of two. The predictions of the general theory of relativity could thus be confirmed with an accuracy of around ten percent. A breakthrough came in 1967 with the realization that simultaneous observations with several radio telescopes (especially in the context of the so-called “Very Long Baseline Interferometry”) make it possible to measure the light deflection much more precisely.

The fact that light is deflected by mass not only enables highly precise tests of the general theory of relativity, but has also proven to be extremely beneficial for astronomical research. Masses, which act as gravitational lenses, are now standard tools in astronomy. They help astronomers determine the masses of cosmic objects and the structure and extent of the universe as a whole. With their magnification effect, the gravitational lenses can also be used to determine the properties of distant galaxies and quasars and to detect planets of distant stars.

additional Information


is Professor of Physics at Guilford College in Greensboro, North Carolina. His research interests are in the dynamics of the upper regions of the earth's mantle, seismology, and, more recently, precision testing of the predictions of the general theory of relativity for light deflection by the sun. For Einstein Online he wrote (together with I. Shapiro) the specialization topic Light deflection by gravity.

is Timken Professor at Harvard University and Senior Scientist at the Smithsonian Institution. He works at the Harvard-Smithsonian Center for Astrophysics in Cambridge, Massachusetts. His research interests are in the applications of radio and radar measurements in geophysics, the physics of planets and astrophysics. He has also designed and carried out general relativity precision tests based on measurements within our solar system. His contribution to Einstein Online is the advanced topic of light deflection by gravity (together with S. Shapiro).


To be quoted as:
Steven S. Shapiro and Irwin I. Shapiro, “Light deflection through gravitation” in: Einstein OnlineVolume 04 (2010), 03-1105