Gravitational redshift revisited: inertia, geometry, and charge

TL;DR

The paper reevaluates gravitational redshift experiments, arguing that first-order effects can be explained using uniformly accelerated frames in special relativity, while higher-order results may be accounted for by curvature, torsion, or non-metricity within the geometric trinity. It emphasizes that curvature is not strictly necessary to explain redshift phenomena and that the absence of redshift does not imply Minkowski spacetime, since charge in Reissner-Nordström spacetimes can shield or invert redshift effects. The authors also critique claims that redshift experiments directly prove spacetime torsion, clarifying the role of torsion and non-metricity as alternative, dynamically equivalent descriptions. They support a nuanced view: gravitational redshift experiments constrain local physics and spacetime structure but do not uniquely determine the underlying geometry, especially in the presence of charge. The work thereby refines the interpretation of redshift data and highlights the operational relevance of the geometric trinity for understanding gravity.

Abstract

Gravitational redshift effects undoubtedly exist; moreover, the experimental setups which confirm the existence of these effects-the most famous of which being the Pound-Rebka experiment-are well-known. Nonetheless-and perhaps surprisingly-there remains a great deal of confusion in the literature regarding what these experiments establish. Our goal in the present article is to clarify these issues, in three concrete ways. First, although (i) Brown and Read (2016) are correct to point out that, given their sensitivity, the outcomes of experimental setups such as the original Pound-Rebka configuration can be accounted for using solely the machinery of accelerating frames in special relativity (barring some subtleties due to the Rindler spacetime necessary to model the effects rigorously), nevertheless (ii) an explanation of the results of more sensitive gravitational redshift outcomes does in fact require more. Second, although typically this 'more' is understood as the invocation of spacetime curvature within the framework of general relativity, in light of the so-called 'geometric trinity' of gravitational theories, in fact curvature is not necessary to explain even these results. Thus (a) one can often explain the results of these experiments using only the resources of special relativity, and (b) even when one cannot, one need not invoke spacetime curvature. And third: while one might think that the absence of gravitational redshift effects would imply that spacetime is flat, this can be called into question given the possibility of the cancelling of gravitational redshift effects by charge in the context of the Reissner-Nordström metric. This argument is shown to be valid and both attractive forces as well as redshift effects can be effectively shielded in the charged setting. Thus, it is not the case that the absence of gravitational effects implies a Minkowskian spacetime setting.

Figures (5)

• Figure 1: Two observers at different heights experience a time dilation effect in Earth's gravitational field. Emitter $O_1$ on the surface of the Earth sends a train of electromagnetic pulses from point $P_1$ with energy momentum 4-vector $k^a$ to a receiver $O_2$, placed at point $P_2$, at height $h$ above $P_1$. We assume $O_1$ and $O_2$ are stationary, i.e. their 4-velocities $u_1^a$ and $u_2^a$ are tangential to the Killing field $\xi^a=\left(\frac{\partial}{\partial t}\right)^a$.
• Figure 2: The gravitational redshift experiment in a uniformly accelerated spaceship. The redshift effect can be explained by the equivalence principle---to first order.
• Figure 3: The world-lines of emitter $E$ and receiver $R$ are Rindler hyperbolae when experiencing constant proper acceleration.
• Figure 4: The Pound-Rebka experiment. Receiver $R$ measures a lower frequency of the photon than what it was when emitted at $E$.
• Figure 5: Gravitational redshift as a consequence of energy conservation. A test body of mass $m_0$ at rest at a height $h$ is dropped. When it reaches the ground the total energy $\gamma m_0c^2$ is obtained. The mass subsequently is transformed into a photon of energy $\hbar \omega_1$, which is then sent from the ground back to height $h$. There, the photon is transformed back into a mass $m$. By energy conservation, $m$ must equal the mass $m_0$, from which it follows that the photon's frequency must have decreased at its ascent.