The role of unit systems in expressing and testing the laws of nature

TL;DR

This paper discusses the importance of unit systems in physics, emphasizing complete equations for invariance, clarifying atomic quantities, and exploring how unit choices affect measurements of fundamental constants.

Contribution

It introduces the concept of complete equations for invariant physical laws and clarifies the dual nature of the reduced Planck constant, proposing distinct symbols for different quantities.

Findings

Complete equations reduce ambiguity in physical laws.

The reduced Planck constant represents two distinct quantities.

Unit choices influence measurements of fundamental constants.

Abstract

The paper firstly argues from conservation principles that, when dealing with physics aside from elementary particle interactions, the number of naturally independent quantities, and hence the minimum number of base quantities within a unit system, is five. These can be, for example, mass, charge, length, time, and angle. It also highlights the benefits of expressing the laws of physics using equations that are invariant when the size of the chosen unit for any of these base quantities is changed. Following the pioneering work in this area by Buckingham, these are termed complete equations, in contrast with equations that require a specific unit to be used. Using complete equations is shown to remove much ambiguity and confusion, especially where angles are involved. As an example, some quantities relating to atomic frequencies are clarified. Also, the reduced Planck constant h-bar, as commonly used, is shown to represent two distinct quantities, one an action (energy x time), and the other an angular momentum (action divided by angle). There would be benefits in giving these two quantities different symbols. Lastly, the freedom to choose how base units are defined is shown to allow, in principle, measurements of changes over time to dimensional fundamental constants like c.