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

TL;DR

This paper reaffirms that Weyl gauge theories of gravity do not exhibit the second clock effect, clarifying previous proofs and addressing recent counterclaims to strengthen the theoretical understanding.

Contribution

The authors extend and clarify their previous demonstration that the second clock effect is absent in Weyl gauge theories, countering recent claims to the contrary.

Findings

The second clock effect does not occur in Weyl gauge theories.

The paper confirms the invariance of these theories under local Poincaré and scale transformations.

Counterclaims in recent literature are addressed and refuted.

Abstract

We reconsider the status of the so-called second clock effect in Weyl gauge theories of gravity, which are invariant both under local Poincar\'e 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.