EINSTEIN'S EQUIVALENCE PRINCIPLE AND THE GRAVITATIONAL RED SHIFT

Abstract

Long before the general theory of relativity was finally formulated in 1916, it was claimed that the following argument, based on (the strong) Einstein's equivalence principle (EP for short), predicted the well known and experimentally observed phenomenon of the gravitational red shift; precisely the same argument is being used to this day in almost all books on general relativity to derive the same phenomenon (see, for example, Refs. 1, 2): Consider "Einstein's elevator" at rest on the Earth's surface with an emitter (E) fixed on the floor of the elevator, and a receiver (R) fixed on the ceiling directly above E and distance h from it. Let E send light signals, at frequency νE, to R and let the frequency at which they are received by R be νR. To find the relationship between νE and νR we invoke the EP and consider, instead, E and R as fixed in an elevator which is accelerating relative to an inertial frame S in gravitation-free space with constant acceleration g in the direction [Formula: see text], g being the acceleration due to gravity on the Earth's surface. At time t = 0, when E is assumed to be at rest in S, E emits a light wave towards R. The time it takes the wave to reach R is roughly t = h/c, where c is the speed of light in S. But in this time R has acquired the velocity [Formula: see text] and, therefore, there is a consequent Doppler shift given by [Formula: see text]. By the EP the same result must hold when E and R are fixed near the Earth's surface. In this case gh = △Φ = Φ(R) - Φ(E), so that in the Earth's gravitational field we have [Formula: see text], which is the standard formula for the gravitational red shift. Simple and straight forward as the above argument may seem, we shall show in this lecture that it is, in fact, fundamentally flawed in two important respects. We shall present a new argument, entirely within the framework of classical mechanics (just as the above argument), which is free from these two flaws. Alas!, it leads to zero gravitational red shift for the case dealt with in the above argument. It is argued that this result not only does it not invalidate the general theory of relativity but it strengthens it; for, the full theory of general relativity alone, irrespective of its historical development, can correctly and unambiguously predict the observed gravitational red shift.