On the gravitational redshift

The purpose of this paper is twofold to demonstrate that in the gravitational redshift it is the frequency a photon that is constant, and to describe the mechanism responsible for the change of its wavelength. PACS: 04.20.Cv, 04.20.-q It is usually assumed that both frequency and wavelength of a photon in the gravitational redshift change whereas its velocity remains constant. In this note we shall show that it is the frequency of a photon that does not change whereas its velocity and wavelength change. It will be also shown that it is the change of the coordinate velocity of the photon along its path that leads to a change in its wavelength. Three things should be kept in mind when dealing with the gravitational redshift: 1. If two observers at different points A and B in a gravitational field determine the characteristics of a photon emitted from identical atoms placed at A and B, each observer will find that the photon characteristics frequency, wavelength and local velocity will have the same numerical values. 2. In a parallel gravitational field coordinate and proper distances coincide dx = dxA = dxB [1] and therefore the wavelength of a photon at a point is the same for all observers λA = λB = λ. 3. The local velocity of a photon at a point is different for different observers (it is c only for an observer at that point). Consider a non-inertial frame N at rest in a parallel gravitational field of strength g. If the z-axis is anti-parallel to the acceleration g the spacetime metric in N has the form [2] ds = (