Sun's Gravity Bends Starlight

This article discusses the first confirmation of Einstein's Theory of General Relativity. He had introduced the theory several years earlier (1915); however, since General Relativity reduces to Newtonian Gravity except in cases of extreme speeds (i.e. close to the speed of light) or in strong gravity, the tests of General Relativity were somewhat limited.

The best test accessible to the scientists at the time was to look at starlight passing by a massive object. The closest object with sufficient mass was, of course, the Sun. However, in order to view starlight passing close to the Sun, observations had to take place during a total solar eclipse – otherwise, the light of the Sun drowns out the starlight.

Both Newtonian and Einsteinian gravity predict that the Sun will bend the starlight, but the extent of that bending is different. The test proposed by Eddington would observe how much the gravity of the Sun would cause the starlight to bend.

One possible point of confusion for students is why does Newtonian gravity predict the bending of starlight at all. Light is composed of "photons", and photons are massless. Therefore, since Newtonian gravity depends on the masses of the bodies involved, it is generally assumed that Newtonian gravity would predict that the Sun would not affect light at all.

To help understand this question, here is a brief history of how scientists viewed the possibility of the bending of light:

• Newton suggests the bending of light in his 1704 treatise, Opticks.

• Henry Cavendish calculates the bending of light due to Newtonian gravity in 1784, but does not publish the result. The only evidence of his calculation only surfaced in the 1900s.

• Johann von Soldner calculates the bending of light as it passes by a massive object in 1801, taking 25 pages to do it! The calculation uses Newton's theory of light as a stream of corpuscles (which have mass). However, the mass of the corpuscle (photon) drops out of the calculation, and the angle only depends on the mass of the object and the closest approach to that object.

  The angle of deflection turns out to be:
  a ~ 2m/r,
  where
  m = GM/c²,
  M is the mass of the sun
  r is the closest approach distance of the photon to the sun.

  This solution is an approximation, because it's the first term in a series. All of the other terms in the series are much smaller. Von Soldner's calculation is very close to Cavendish's, and to a first-order approximation, they are the same.

• In early 1800s, Thomas Young's double-slit experiment showed that light must behave as a wave, rather than a particle. At this point, it was realized that light must be massless. Clearly, a massless particle, in Newtonian gravity, would experience no deflection due to gravity.

• Albert Einstein, in 1911, published a paper called "On the Influence of Gravitation on the Propagation of Light" (published in German), which calculated the effect of gravity on light using the equivalence principle, and with did not depend on light having mass. His answer in this paper was identical to von Soldner's approximation. However, this calculation did not include all of the equations of General Relativity.

• In 1915, Einstein finished his theory of general relativity, and found that the prediction for the deflection of starlight due to the Sun would be twice the prediction he published in 1911.

• In 1919, Arthur Eddington led one expedition to observe the total solar eclipse, and found that the light was bent by the amount predicted by General Relativity.

Based on this timeline, prior to the 1919 eclipse, astronomers could have expected one of three results: no deflection at all, assuming a massless photon and Newtonian gravity; some deflection, assuming massless photon that was still accelerated in a Newtonian gravity well; or full deflection, assuming a massless photon in General Relativity.

It's interesting to note that there is some question as to whether or not the equipment and results of the 1919 eclipse expeditions really had the sensitivity to detect the starlight deflections that Eddington claimed. It may be that the researchers injected some of their expectations into the reported results. However, many subsequent (and more robust) observations have been performed, all of which confirm the reported deflection of starlight as that predicted by General Relativity.

Scientists continue, even today, to put General Relativity to the test, and all of those tests have added further evidence in favor of General Relativity.