A Puzzle Concerning Local Symmetries and Their Empirical Significance

In the last five years, the controversy about whether or not gauge transformations can be empirically significant has intensified. On the one hand, Greaves and Wallace(2014) developed a framework according to which, under some circumstances, gauge transformations can be empirically significant, and Teh (2015) further supported this result by using the Constrained Hamiltonian formalism. On the other hand, Friederich (2015, 2016) claims to have proved that gauge transformation can never be empirically significant. In this paper, I accomplish two tasks: first, I show that Friederich’s proof is not valid, and that once it is corrected, it entails a result that is compatible with the treatments by Greaves and Wallace, and Teh. Second, I show that, despite criticism byBrading and Brown (2004) and Friederich (2015), t'Hooft's Beam-Splitter experimentis indeed a concrete realization of a case where a local gauge symmetry has empiri-cal significance. By shedding light on these two points, this paper shows that recent arguments that claim gauge transformations cannot be empirically significant are not satisfactory.