Principle of equivalence and the deflection of light by the sun

Abstract

We review the usual principle-of-equivalence calculation for the deflection of light by the sun, which fails to give the general relativistic answer. We show that the discrepancy arises because, by construction, this calculation can in fact only yield the deflection relative to the trajectories of infinitely fast particles (purely spatial geodesics). The total deflection is thus the sum of the deflection given by the principle of equivalence and the deflection of infinitely fast particles. We verify this result, which we extend from the case of photons to fast particles in general, by direct calculation.

Kinetic energy and the equivalence principle

“…This argument does not seem to be widely published; instead, many texts rely on a simple "Einstein elevator" analysis that actually gives only half the correct deflection. 23 But it is not uncommon among students, and appears frequently in Internet discussions. In such a simple form, the argument is easily addressed: it is attempting to impose Newtonian categories on general relativity, ignoring in particular the curvature of space.…”

“…It seems safe to assume that there should be no perverse cancellation between the gravitational couplings of, say, electron kinetic energy in beryllium and nuclear binding energy in platinum. Equation (23) can thus be combined with our earlier analysis to remove any "virial theorem ambiguities" in the limits ( 9) and ( 11) for kinetic energy. We can thus tell our students with confidence that kinetic energy has weight, not just as a theoretical expectation, but as an experimental fact.…”

The rate of deflection of light in an accelerated frame and a gravitational field

“…[6][7][8][9][10][11][12][13][14][15][16][17] Although it might seem that after so much attention this subject would be exhausted, we feel that there is still further insight to be gained by concentrating on a purely local quantity, namely the rate of deflection per unit central angle in a sequence of stationary frames along the light path in the sun's gravitational field and in an ''equivalent'' ͑except for spacetime curvature͒ set of accelerated frames in flat spacetime. 18 As Weinberg has pointed out in his book, 19 the equivalence principle is necessarily a local concept in the context of a metric theory of gravity.…”

Traveling towards fame: Albert Einstein and the Eddington eclipse expedition to Príncipe and Sobral in 1919

“…According to the equivalence principle, light must 'fall' in a gravity field as if it were made of massive particles. However, the 1911 prediction by Einstein of the amount of light bending due to the Sun was wrong because it did not take into account the fact that the geometry of space is not flat (Comer and Lathrop 1978;Ehlers and Rindler 1997), resulting in the prediction of a smaller effect (actually, one half of the correct value: 0.875 arc seconds). Being entirely based on the equivalence principle, the 1911 prediction was equivalent to assuming that light moves in a gravitational field as if it were made of material particles following the Newton's laws of motion: therefore, it is commonly referred to as the 'Newtonian prediction'.…”