A Puzzle Concerning Local Symmetries and Their Empirical Significance

Abstract

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, Wallace, and Teh. Second, I show that, despite criticism by Brading and Brown (2004) and Friederich (2015), t'Hooft's Beam-Splitter experiment is indeed a concrete realization of a case where a local gauge symmetry has empirical 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.

Symmetries and Representation

“…47 For technical details, see Wulfman and Wybourne (1976, p. 516). 48 Similar considerations apply to other symmetries that have been discussed in the literature, like those in the Kepler problem that relate the orbits of a planet around a much more massive object like the Sun to other orbits with different eccentricity (see Belot (2013), Murgueitio Ramírez (2021) and Wallace (2022a) for a philosophical discussion, and see Prince and Eliezer (1981) for a physics discussion.) Even if the universe only consisted of a planet around a star, and even if there was no ruler or detector capable of measuring anything, a plausible case can be made for the claim that a perfectly circular orbit, represented with a model m, and an orbit with high eccentricity, represented with a model m 0 , would correspond to empirically distinct situations.…”

“…One can represent the case in which the spring starts to oscillate with a model like x ( t ) = A cos( t ), and the case in which it does not with a model like x ( t ) = 0. Crucially, these two models are related by a symmetry of the equation for an ideal spring (see section 5 in Murgueitio Ramírez, 2024). And so Empirical Indiscernibility seems to fail in such a case.…”

“…8 8 It is worth noting that there could be additional distinctions among models, such as that between the dynamical models that satisfy the boundary conditions or the initial conditions of a problem, and those that do not. See Wolf and Read (2023) and Murgueitio Ramírez (2021, Ch. 4) for recent work exploring the importance of boundary conditions when thinking of the models of a theory. …”

Gauge Symmetries, Symmetry Breaking, and Gauge-Invariant Approaches

“…The question that is in the centre of the debate about direct empirical significance is whether the same holds for local symmetries as in gauge theories. The orthodox view, that local gauge symmetries do not carry empirical significance, has recently been argued to be derivable from three simple assumptions about direct empirical significance and physical identity of subsystem states (Friederich, 2015(Friederich, , 2017, see (Murgueitio Ramirez, 2021) for criticism of the assumptions used there. However, recently, dissonant voices have become more prominent e.g.…”

Why gauge? Conceptual Aspects of Gauge theories

“…Whether gauge symmetries have DES has been discussed in(Brading & Brown, 2004;Chasova, 2019;Friederich, 2014Friederich, , 2017Gomes, 2019aGomes, , 2021aGreaves & Wallace, 2014;Healey, 2009;Kosso, 2000;Ladyman, 2015;S. Ramirez & Teh, 2019;S. M. Ramirez, 2019;Teh, 2016; Wallace, 2019a,b).…”