Abstract
It is well-known that any scalar can be promoted to a Jordan-Brans-Dicke type scalar coupling to the Einstein-Hilbert term through a field dependent Weyl transformation of the metric. The Weyl rescaling also transforms mass terms into coupling constants between matter and the scalar. It is pointed out that there exists a distinguished metric where all scalars decouple from an arbitrary fiducial fermion, e.g. the nucleon. If bound states of this fermion are used to define distances and to probe the interior of the forward light cone, it seems reasonable to say that the metric in that particular frame defines the local geometry of space-time at low energies, as probed by experimental gravity and cosmology.
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Dick, R. Inequivalence of Jordan and Einstein Frame: What Is the Low Energy Gravity in String Theory?. General Relativity and Gravitation 30, 435–444 (1998). https://doi.org/10.1023/A:1018810926163
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DOI: https://doi.org/10.1023/A:1018810926163