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

TL;DR

This paper interprets gravitational redshift as electromagnetic wave propagation in a medium with effective conductivity, linking classical electrodynamics with Planck's postulate in a curved spacetime context.

Contribution

It introduces a classical field-theoretical interpretation of gravitational redshift as electromagnetic wave propagation in a medium with specific conductivity, connecting it to Planck's postulate.

Findings

Gravitational redshift can be modeled as wave propagation in a medium with conductivity σ=g/(_0 c^3)

Wave energy density remains proportional to frequency, consistent with Planck's postulate

Classical electrodynamics can describe gravitational effects on electromagnetic waves

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.