Universal constants and natural systems of units in a spacetime of arbitrary dimension
arXiv:2005.08196 · doi:10.3390/universe6100166
Abstract
We study the properties of fundamental physical constants using the threefold classification of dimensional constants proposed by J.-M. L{é}vy-Leblond: constants of objects (masses, etc.), constants of phenomena (coupling constants), and "universal constants" (such as and ). We show that all of the known "natural" systems of units contain at least one non-universal constant. We discuss the possible consequences of such non-universality, e.g., the dependence of some of these systems on the number of spatial dimensions. In the search for a "fully universal" system of units, we propose a set of constants that consists of , , and a length parameter and discuss its origins and the connection to the possible kinematic groups discovered by L{é}vy-Leblond and Bacry. Finally, we give some comments about the interpretation of these constants.
arXiv comment18 pages, pedagogical article. v3: small corrections and extensions, some references added. This version matches the published one
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