Note on the absence of the second clock effect in Weyl gauge theories of gravity

Abstract

We reconsider the status of the so-called second clock effect in Weyl gauge theories of gravity, which are invariant both under local Poincaré transformations and local changes of scale. In particular, we revisit and extend our previous demonstration that the second clock effect does not occur in such theories, in order both to clarify our argument and confirm our original findings in response to recent counterclaims in the literature.

arXiv comment5 pages, no figures, accepted for publication as a Letter in PRD. Minor edits to match published version. arXiv admin note: text overlap with arXiv:2009.06407

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• The Non-Relativistic Geometric Trinity of Gravity
• Weyl covariance, second clock effect and proper time in theories of symmetric teleparallel gravity
• A novel approach to autoparallels for the theories of symmetric teleparallel gravity
• Conformally-rescaled Schwarzschild metrics do not predict flat galaxy rotation curves
• Phenomenological signatures of gauge invariant theories of gravity with vectorial nonmetricity
• Revisiting local-scale invariant gravitational theory