Empirical consequences of symmetries

TL;DR

This paper challenges the view that only global symmetries have empirical counterparts by developing a framework showing local symmetries can also produce observable phenomena, exemplified through analogs of Galileo's ship.

Contribution

It introduces a new framework linking symmetries to empirical phenomena, demonstrating that local symmetries like gauge invariance can have observable consequences.

Findings

Both global and local symmetries can produce Galileo-ship phenomena

Framework clarifies the relationship between symmetries and empirical effects

Analogues of Galileo's ship are identified for both general relativity and electromagnetism

Abstract

`Global' symmetries, such as the boost invariance of classical mechanics and special relativity, can give rise to direct empirical counterparts such as the Galileo-ship phenomenon. However, a widely accepted line of thought holds that `local' symmetries, such as the diffeomorphism invariance of general relativity and the gauge invariance of classical electromagnetism, have no such direct empirical counterparts. We argue against this line of thought. We develop a framework for analysing the relationship between Galileo-ship empirical phenomena and physical theories that model such phenomena that renders the relationship between theoretical and empirical symmetries transparent, and from which it follows that both global and local symmetries can give rise to Galileo-ship phenomena. In particular, we use this framework to exhibit analogs of Galileo's ship for both the diffeomorphism invariance of general relativity and the gauge invariance of electromagnetism.