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Type: Journal article
Title: Hilbert's forgotten equation, the equivalence principle and velocity dependence of free fall
Author: Berkahn, D.
Chappell, J.M.
Abbott, D.
Citation: European Journal of Physics, 2020; 41(3):035604-1-035604-17
Publisher: IOP Publishing
Issue Date: 2020
ISSN: 0143-0807
Statement of
David L Berkahn, James M Chappell and Derek Abbott
Abstract: Referring to the behavior of accelerating objects in special relativity, and applying the principle of equivalence, one expects that the coordinate acceleration of point masses under gravity will be velocity dependent. Also, using the Schwarzschild solution, we analyze the similar case of masses moving on timelike geodesics, which reproduces a little-known result by Hilbert from 1917, describing this dependence. We find that the relativistic correction term for the acceleration based on general relativity differs by a factor of two from the simpler acceleration arguments in flat space. As we might expect from the general theory, the velocity dependence can be removed by a suitable coordinate transformation, such as the Painlevé–Gullstrand coordinate system. The validity of this approach is supported by previous authors who have demonstrated vacuum solutions to general relativity producing true flat space metrics for uniform gravitational fields. We suggest explicit experiments could be undertaken to test the property of velocity dependence.
Keywords: General relativity; special relativity; equivalence principle; geodesics; velocity dependence
Rights: © 2020 European Physical Society
DOI: 10.1088/1361-6404/ab782f
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