Electromagnetic Waves in a Uniform Gravitational Field and Planck's Postulate

Abstract

The gravitational redshift forms the central part of the majority of the classical tests for the general theory of relativity. It could be successfully checked even in laboratory experiments on the earth's surface. The standard derivation of this effect is based on the distortion of the local structure of spacetime induced by large masses. The resulting gravitational time-dilation near these masses gives rise to a frequency change of any periodic process, including electromagnetic oscillations as the wave propagates across the gravitational field. This phenomenon can be tackled with classical electrodynamics assuming a curved spacetime background and Maxwell's equations in a generally covariant form. In the present paper, we show that in a classical field-theoretical context the gravitational redshift can be interpreted as the propagation of electromagnetic waves in a medium with corresponding conductivity $\sigma=g/(\mu_0 c^3)$, where $g$ is the gravitational acceleration and $\mu_0$ is the vacuum magnetic permeability. Moreover, the energy density of the wave remains proportional to its frequency in agreement with Planck's postulate.