Reciprocity principle and relative accelerations in the theory of relativity

Abstract

It is proved that in the theory of relativity, the magnitudes of the relative accelerations of two observers with respect to each other can be unequal. The breaking of a reciprocal relationship between the accelerations is a property of special relativity, which seems not to have been mentioned previously, even though it is in contrast with the prediction of Newtonian physics. As an application of this result, we determine the acceleration of a freely falling particle with respect to a locally static observer in the Schwarzschild space-time and show that this acceleration, unlike the prediction of Newtonian physics, depends on the initial value of the velocity of the freely falling particle. It is worthwhile to emphasize that this result is not a consequence of the well-known behavior of special relativity, which makes the measured acceleration of an object differ from one inertial frame to another.