Universal constants and natural systems of units in a spacetime of arbitrary dimension

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 $c$ and $\hslash$). 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 $c$, $\hslash$, 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.

18 pages, pedagogical article. v3: small corrections and extensions, some references added. This version matches the published one

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