Abstract
Ever since Eddington’s analysis of the gravitational redshift a century ago, and the arguments in the relativity community that it produced, fine details of the roles of proper time and coordinate time in the redshift remain somewhat obscure. We shed light on these roles by appealing to the physics of the uniformly accelerated frame, in which coordinate time and proper time are well defined and easy to understand; and because that frame exists in flat spacetime, special relativity is sufficient to analyse it. We conclude that Eddington’s analysis was indeed correct—as was the 1980 analysis of his detractors, Earman and Glymour, who (it turns out) were following a different route. We also use the uniformly accelerated frame to pronounce invalid Schild’s old argument for spacetime curvature, which has been reproduced by many authors as a pedagogical introduction to curved spacetime. More generally, because the uniformly accelerated frame simulates a gravitational field, it can play a strong role in discussions of proper and coordinate times in advanced relativity.
Highlights
The prediction and subsequent confirmation of gravitational redshift is a standard topic of courses on general relativity
The purpose of this paper is to show how the roles and correct use of proper and coordinate times arise naturally in a flat spacetime context, when we analyse the pseudogravitational redshift that appears in the uniformly accelerated frame in flat spacetime (UAF)
Because the UAF mimics a gravitational field over small differences in “height”, the equivalence principle guarantees that it forms a good test-bed for discussing the redshift in curved spacetime
Summary
The prediction and subsequent confirmation of gravitational redshift is a standard topic of courses on general relativity. The natural question arises: what are the correct roles of proper and coordinate times in the gravitational redshift, and why did these apparently contrasting analyses both yield the correct result?. The purpose of this paper is to show how the roles and correct use of proper and coordinate times arise naturally in a flat spacetime context, when we analyse the pseudogravitational redshift that appears in the uniformly accelerated frame in flat spacetime (UAF). Because the UAF mimics a gravitational field over small differences in “height”, the equivalence principle guarantees that it forms a good test-bed for discussing the redshift in curved spacetime.. Because the UAF mimics a gravitational field over small differences in “height”, the equivalence principle guarantees that it forms a good test-bed for discussing the redshift in curved spacetime.1 Despite this utility, the UAF is almost absent from textbooks on relativity; even.
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