Physical basis for GR’s optical-cavity length scaling in a gravitational potential

Establish a concrete physical mechanism that justifies the General Relativity postulate that the geometric length of an optical cavity varies proportionally with c1 = c0(1 + Φ/c0^2) as the gravitational potential Φ changes, thereby ensuring that the cavity resonance frequency fopt = c2/l shares the same gravitational dependence as atomic clock frequencies that scale with c1. Clarify how this length scaling reconciles the factor-of-two difference between the gravitational dependence of the speed of light (c2 = c0(1 + 2Φ/c0^2)) and that of atomic frequencies, so that optical cavity resonances and atomic clocks remain equal under changes in Φ.

Background

The paper reviews Einstein’s predictions that atomic clock frequencies scale with c1 = c0(1 + Φ/c0^2) while, in General Relativity, the speed of light scales with c2 = c0(1 + 2Φ/c0^2). To keep optical cavity resonances equal to atomic clock frequencies as gravitational potential changes, the cavity frequency fopt = c2/l would require the cavity length l to scale with c1.

The authors note that General Relativity effectively assumes l ∝ c1 but emphasize that no physical basis for this assumption is known and that, to their knowledge, it has not been experimentally tested. They propose that comparing an optical cavity’s resonance with an atomic clock in varying gravitational potential could test this claim, but the underlying physical explanation remains unresolved.