Equivalence-principle Analog of the Gravitational Redshift

TL;DR

This paper explores a special relativity analog of gravitational redshift by examining clock synchronization loss under identical acceleration profiles, proposing an experiment to test the equivalence principle with potential applications in navigation.

Contribution

It introduces a novel experimental setup to measure the equivalence principle analog in special relativity, which has not been directly tested before.

Findings

Synchronization loss observed in identical acceleration profiles

Conditions identified that simplify experimental observation

Potential implications for ultra-precise navigation systems

Abstract

What happens when two synchronized clocks on a rigid beam are both given the exact same acceleration profile? Will they remain synchronized? What if we use a rigid-rod Rindler acceleration profile? The special relativity prediction surprises many people. This experimental setup is the special-relativity analog of the gravitational redshift. Just like two clocks higher and lower in a gravitational field lose synchronization, one sees a loss of synchronization in these clocks with `identical' acceleration profiles. To the best of our knowledge this equivalence principle analog has never been directly measured, and current experimental techniques are sensitive enough to measure it. We discuss the origin of the essential physics behind this synchronization loss, and some special conditions which simplify its experimental observation. We discuss the origin of the essential physics behind this synchronization loss, and some special conditions which simplify its experimental observation. If validated this effect will not only test the equivalence principle from a new vantage, but it may one day aid in understanding and enhancing future ultra-precise navigation systems.