Gravitational redshift contradicts the curved-spacetime interpretation of general relativity

It is shown that the measurement of a change in a photon frequency in the gravitational redshift experiment is in fact an indirect measurement of a change in the photon local velocity since both frequency and velocity change in this experiment. This means that the local velocity of a photon depends upon its pre-history (whether it has been emitted at the observation point or at a point of different gravitational potential) a result that contradicts the standard curved-spacetime interpretation of general relativity according to which the local velocity of light is c. This result, however, does not contradict general relativity itself. PACS numbers: 04.20.Cv, 04.20.-q As shown by Schild [1] the existence of the gravitational redshift demonstrates that gravitational phenomena cannot be described in the framework of Minkowski geometry. It has been thought that Schild’s result provides further evidence in support of the standard curved-spacetime interpretation of general relativity in which spacetime is curved and described by Riemannian geometry [2, p. 187]. In this interpretation the Minkowski geometry being tangent to each spacetime event of the global Riemannian geometry is valid only locally which means that special and general relativity are locally indistinguishable [2, Ch. 16]. An important consequence from here is that the local velocity of light is c due to the local validity of special relativity [2, p. 385]. Stated another way, all light signals passing through a given point have the same local velocities (equal to c) since their worldlines, laying in the neighborhood of this point where the Riemannian spacetime coincides with the tangent Minkowski spacetime at that point, are locally straight lines [2, pp. 313, 385]. The very existence of the gravitational redshift, however, shows that since the frequencies of two light signals one emitted at the observation point (where both frequencies are measured) and another at a point of different gravitational potential differ, their local velocities at the observation point also differ. One possible reason why this has not been noticed up to now is that the existing derivations of the redshift effect obtained either through energy considerations [2, p. 187] or by using the proper times (periods) at the source and observation points to calculate the frequencies at those points [4], [5] do not address the question of whether a change in the frequency of a photon implies a change in its velocity as well. The meaning of ”local” here is precisely what is meant by this concept in [2]; see also [3]. These derivations are carried out in a non-inertial reference frame N supported in a gravitational field. The only derivation of the gravitational redshift that implicitly involves the velocity of light [6], [7] cannot provide any insight into the question of whether or not the local velocity of light measured in N is independent of light pre-history. The reason is that this derivation is based on a description of how the redshift effect being measured in N looks from the viewpoint of an inertial frame I falling in the gravitational field and therefore involves not the velocity of light in N but the constant light velocity in I. From the standpoint of I the frequency shift measured in N (a measurement in I gives no frequency shift [7]) is not a gravitational effect since there is no gravitational field in I which can cause the redshift; as viewed from I the photon frequency experiences a Doppler shift and therefore it is the wavelength λ of the photon that changes along with its frequency whereas its velocity (being constant in the inertial frame I) is not affected. For a non-inertial observer at rest in frame N , however, the photon frequency changes not