The document titled “Gravitational Redshift, Inertia, and the Role of Charge” by Johannes Fankhauser and James Read explores several nuanced aspects of gravitational redshift and related phenomena. Here is a summary of the key points discussed in the paper:

  1. Gravitational Redshift:
    • The authors revisit the concept of gravitational redshift, emphasizing its experimental verification through setups like the Pound-Rebka experiment.
    • They discuss the explanations of gravitational redshift outcomes using accelerating frames in special relativity versus spacetime curvature in general relativity.
  2. Equivalence Principle:
    • The equivalence principle, which states that locally (in a small region of spacetime) the effects of gravity are indistinguishable from those of acceleration, is central to their discussion.
    • The authors delve into the limitations of the equivalence principle, particularly noting that it holds only in a small neighborhood around a point-like observer.
  3. Gravitational Redshift without Spacetime Curvature:
    • They argue that gravitational redshift can often be explained using only special relativity, without invoking spacetime curvature. This is in light of the “geometric trinity” of gravitational theories that replace curvature with torsion or non-metricity.
    • They specifically refute claims that gravitational redshift experiments provide direct evidence for spacetime torsion.
  4. Role of Charge in Gravitational Redshift:
    • The document explores how charge can influence gravitational effects, particularly through the Reissner-Nordström metric, which describes the spacetime around a charged, non-rotating, spherically symmetric body.
    • They introduce the concept of “shielding” gravitational effects using charge, where attractive gravitational forces and redshift effects can be shielded, potentially resulting in repulsive forces or blueshifted effects.
  5. Thought Experiments and Derivations:
    • Various thought experiments and mathematical derivations are used to illustrate the points, including the derivation of gravitational redshift from the Schwarzschild metric and considerations of uniformly accelerated frames.
  6. Conclusion:
    • The authors conclude that gravitational redshift experiments do not necessarily imply spacetime curvature and that charge can play a significant role in modifying gravitational effects.
    • They also stress that the absence of gravitational effects does not imply a flat (Minkowskian) spacetime, especially in the presence of charge.

The document aims to clarify misconceptions about the nature of gravitational redshift and its implications for our understanding of spacetime and gravity.