On the gravitational redshift

TL;DR

This paper revisits the gravitational redshift, emphasizing the small ratio of gravitational to electrostatic forces in atoms, and proposes a two-step process explanation based on energy and momentum conservation, challenging geometric interpretations.

Contribution

It introduces a novel two-step process model for gravitational redshift that does not rely on geometric descriptions and highlights the importance of force ratios.

Findings

The gravitational to electrostatic force ratio in atoms is extremely small (~10^{-21}).

A two-step process explains the redshift consistent with energy and momentum conservation.

The gravitational field influences photon emission, not atomic transitions.

Abstract

The study of the gravitational redshift\,---\,a relative wavelength increase of $\approx 2 \times 10^{-6}$ was predicted for solar radiation by Einstein in 1908\,---\,is still an important subject in modern physics. In a dispute whether or not atom interferometry experiments can be employed for gravitational redshift measurements, two research teams have recently disagreed on the physical cause of the shift. Regardless of any discussion on the interferometer aspect\,---\,we find that both groups of authors miss the important point that the ratio of gravitational to the electrostatic forces is generally very small. For instance, the gravitational force acting on an electron in a hydrogen atom situated in the Sun's photosphere to the electrostatic force between the proton and the electron is approximately $3 \times 10^{-21}$. A comparison of this ratio with the predicted and observed solar redshift indicates a discrepancy of many orders of magnitude. Here we show, with Einstein's early assumption of the frequency of spectral lines depending only on the generating ion itself as starting point, that a solution can be formulated based on a two-step process in analogy with Fermi's treatment of the Doppler effect. It provides a sequence of physical processes in line with the conservation of energy and momentum resulting in the observed shift and does not employ a geometric description. The gravitational field affects the release of the photon and not the atomic transition. The control parameter is the speed of light. The atomic emission is then contrasted with the gravitational redshift of matter-antimatter annihilation events.