Empirical Consequences of Symmetries

It is widely recognized that ‘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, conventional wisdom 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 conventional wisdom. We develop a framework for analysing the relationship between Galileo-ship empirical phenomena on the one hand, and physical theories that model such phenomena on the other, 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 an analogue of Galileo’s ship for the local gauge invariance of electromagnetism. 1 Introduction 2 Analogues of Galileo’s Ship? Faraday’s Cage and t’Hooft’s Beam-Splitter 2.1 Faraday’s cage 2.2 t’Hooft’s beam-splitter 3 A Framework for Symmetries I: Systems and Subsystems 4 An Example: Coulombic Electrostatics 5 A Framework for Symmetries II: The Relationship between Theoretical and Empirical Symmetries 6 Newtonian Gravity 7 Local Symmetries that Are Not Boundary-Preserving: Classical Electromagnetism and Faraday’s Cage 8 Local Boundary-Preserving Symmetries: Klein-Gordon-Maxwell Gauge Theory and t’Hooft’s Beam-Splitter 9 Summary 10 Conclusions