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

TL;DR

This paper analyzes fundamental physical constants within various systems of units across different spatial dimensions, proposing a set of universal constants and discussing their implications for natural units and physical theories.

Contribution

It introduces a classification of constants, identifies non-universality in known systems, and proposes a new set of universal constants for natural units applicable in arbitrary dimensions.

Findings

All known natural units contain at least one non-universal constant.

A proposed set of universal constants includes c, ℏ, and a length parameter.

Discussion of the implications of non-universality and the connection to kinematic groups.

Abstract

We study the properties of fundamental physical constants using the threefold classification of dimensional constants proposed by J.-M. L{\'e}vy-Leblond: constants of objects (masses, etc.), constants of phenomena (coupling constants), and "universal constants" (such as $c$ and $\hbar$). 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 $c$, $\hbar$, and a length parameter and discuss its origins and the connection to the possible kinematic groups discovered by L{\'e}vy-Leblond and Bacry. Finally, we give some comments about the interpretation of these constants.