Pound-Rebka experiment and torsion in the Schwarzschild spacetime

TL;DR

This paper explores the idea that gravitational acceleration may be due to spacetime torsion rather than curvature, and analyzes the Pound-Rebka experiment in Schwarzschild spacetime to reveal torsion effects.

Contribution

It demonstrates that gravitational acceleration can be attributed to spacetime torsion and explicitly derives the torsion tensor from the Pound-Rebka experiment in Schwarzschild spacetime.

Findings

Spacetime torsion explains nonclosure of parallelograms in the Pound-Rebka experiment.

Geodesic acceleration can vary independently of spacetime curvature.

Explicit form of the torsion tensor related to the experiment's spacetime events.

Abstract

We develop some ideas discussed by E. Schucking [arXiv:0803.4128] concerning the geometry of the gravitational field. First, we address the concept according to which the gravitational acceleration is a manifestation of the spacetime torsion, not of the curvature tensor. It is possible to show that there are situations in which the geodesic acceleration of a particle may acquire arbitrary values, whereas the curvature tensor approaches zero. We conclude that the spacetime curvature does not affect the geodesic acceleration. Then we consider the the Pound-Rebka experiment, which relates the time interval $\Delta \tau_1$ of two light signals emitted at a position $r_1$, to the time interval $\Delta \tau_2$ of the signals received at a position $r_2$, in a Schwarzschild type gravitational field. The experiment is determined by four spacetime events. The infinitesimal vectors formed by these events do not form a parallelogram in the (t,r) plane. The failure in the closure of the parallelogram implies that the spacetime has torsion. We find the explicit form of the torsion tensor that explains the nonclosure of the parallelogram.