Reply to Comment on "Global positioning system test of the local position invariance of Planck's constant"

TL;DR

This paper defends the validity of testing Planck's constant variation using GPS data against criticisms about the physical meaning of its dimensions, emphasizing a unique model based on general relativity.

Contribution

It provides a rebuttal to critiques on measuring dimensional constants and introduces a distinct theoretical framework for such tests.

Findings

Rebuttal to criticism about the dimensionality of $h$

Introduction of a model based on general relativity

Clarification of the relevance of constant variation measurements

Abstract

We reply to a Comment [Berengut and Flambaum, Phys. Rev. Lett. 109, 068901 (2012), arXiv:1203.5592] on our recent Letter [Kentosh and Mohageg, Phys. Rev. Lett. 108, 110801 (2012), arXiv:1203.0102]. The Comment objects to our work partly because $h$ has dimensions and therefore measuring any variation of it is meaningless. We reply that the relevance of dimensions in the study of fundamental constants has been the subject of some debate. We also note that our model differs from the one normally used to compare hydrogen masers and cryogenic optical resonators. Ours is based on a different treatment of proper length and energy to conform to general relativity. We also enclose in an Appendix our transmittal to the editors of Physical Review Letters.