Natural units and the vector space of physical values

TL;DR

This paper develops a mathematical framework for the vector space of physical values, extending the concept of physical dimensions, to facilitate the use of natural units and unit system transformations.

Contribution

It introduces a formalism for the vector space of physical values, building upon previous work on physical dimensions, enabling systematic unit transformations.

Findings

Formalism for the vector space of physical values

Extension of the dimension vector space to values

Potential applications in natural units and unit conversions

Abstract

We explore the mathematical foundations of the vector space of physical dimensions introduced in A. Maksymowicz, Am. J. Phys. 44, 1976, and extend this formalism to the vector space of physical values. As different unit systems correspond to different bases of this vector space, our formalism may find use for introducing the concept of natural units and transforming physical values between unit systems.