2013/06/07 by Meir Shimon, Shimon, Meir
Earth and Planetary Sciences · Physics and Astronomy · #Cosmology and Gravitation Theories #Earth Systems and Cosmic Evolution #FOS: Physical sciences #General Physics (physics.gen-ph) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1306.1616
openalex publication_date 2013/06/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Our conventional system of physical units is based on local or microscopic \it dimensional quantities which are \it defined, for convenience or otherwise aesthetic reasons, to be spacetime-independent. A more general choice of units may entail variation of fundamental physical quantities (`constants') in spacetime. The theory of gravitation generally does not satisfy conformal symmetry, i.e. it is not invariant to local changes of the unit of length. Consequently, the \it dimensionless action associated with the Einstein-Hilbert action (SEH) of gravitation, ϕEH=SEH/ℏ, is not invariant to local changes of the length unit; clearly an unsatisfactory feature for a dimensionless quantity. Here we amend the phase by adding extra terms that account for spacetime variation of the physical `constants' in arbitrary unit systems. In such a unit system, all dimensional quantities are implicitly spacetime-dependent; this is achieved by a conformal transformation of the metric augmented by appropriate metric-dependent rescalings of the dimensional quantities. The resulting modified dimensionless action is scale-invariant, i.e. independent of the unit system, as desired. The deep connection between gravitation, dimensionless physical quantities, and quantum mechanics, is elucidated and the implicit ambiguity in interpretations of dimensional quantities is underlined.