Empirical consequences of symmetries

`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.