Are Gauge Symmetry Transformations Observable?

Abstract

In a recent paper in the British Journal for the Philosophy of Science, Kosso discussed the observational status of continuous symmetries of physics. While we are in broad agreement with his approach, we disagree with his analysis. In the discussion of the status of gauge symmetry, a set of examples offered by 't Hooft has influenced several philosophers, including Kosso; in all cases the interpretation of the examples is mistaken. In this paper we present our preferred approach to the empirical significance of symmetries, re-analysing the cases of gauge symmetry and general covariance. Direct and Indirect Empirical SignificanceThe notion of symmetry that we are concerned with is defined with respect to the laws of motion. Given the laws, specified in terms of dependent and independent variables, a symmetry transformation is a transformation of these variables that preserves the explicit form of the laws. The issue we are interested in is the empirical status of such symmetry transformations. Galileo's famous ship experiment (Galileo [1967], pp. 186-8) provides an example of where (to an appropriate approximation) a symmetry transformation is both physically implementable and directly observable. The transformation is implemented via two empirically distinct scenarios of the ship at rest and in uniform motion with respect to the shore, and the symmetry is observed by noticing that, relative to the cabin of the ship, the phenomena inside the cabin do not enable us to distinguish between the two scenarios. Following Brown and Sypel ([1995]), 1 we maintain that the direct empirical significance of physical symmetries rests on the possibility of effectively isolated subsystems that may be actively transformed with respect to the rest of the universe. 2 This active transformation need not be physically implementable in practice (try boosting a planet, for example); the point is that we compare two empirically distinct possible scenarios at least theoretically, one containing the untransformed subsystem and one the transformed subsystem.The example of Galileo's ship also illustrates that observing a symmetry involves two observations, as has been discussed by Kosso ([2000] Budden ([1997]). 2 Notice that, since our objective is empirical significance, this goes beyond a purely mathematical active symmetry transformation. We discuss the case symmetries of the universe as a whole in the final paragraph of this section.As long as one can claim to be able to observe that the transformation prescribed by a particular symmetry has taken place, and that the associated invariance held, then one can claim to be able to directly observe the physical symmetry in nature.And he goes on (p. 87):To observe the transformation is to observe both the unchanged reference and the changed system.In other words, we first observe the transformation, which involves transforming a subsystem with respect to some reference that is itself observable, and we then observe that the symmetry holds for the subsystem (p. 86):observation of a...

Symmetry, Empirical Equivalence, and Identity

“…This is in accordance with the "transformation condition" for symmetries having direct empirical significance suggested by Brading and Brown, which says that 'the transformation of a subsystem of the universe with respect to a reference system must yield an empirically distinguishable scenario' (Brading and Brown [2004] p. 646) for the whole universe.…”

“…If one accepts this perspective yet wants to maintain a nontrivial distinction between symmetries with and without direct empirical significance, one will therefore expect this distinction to hold between symmetries operating between the states of subsystems of the universe itself. 5 The idea to focus on subsystem symmetries to elucidate matters of direct empirical significance is suggested already in (Brown and Sypel [1995]), taken up in (Kosso [2000]; Brading and Brown [2004]; Greaves and Wallace [forthcoming]), and adopted in the present paper as well. It goes well with the fact that in examples such as Galileo's ship the symmetries in question are in fact subsystem symmetries: in the case of Galileo's ship it is only the cabin of the ship, not the surrounding ocean, which is represented by a symmetry transformed state in the situation where the ship is moving as compared to where it is at rest.…”

“…If a phase-shifter is inserted in the upper half-beam, however, a physically different situation arises-call it "situation B"-, where the upper half-beam can be described by (e iθ ψ I , A µ,I ), the lower (unchanged) by (ψ II , A µ,II ), and the overlap preserving local gauge transformation which acts only on the state of the upper half-beam] on [sic] cannot be met in such a region.' (Brading and Brown [2004] p. 653. The emphasis is due to Brading and Brown.…”

A partial elucidation of the gauge principle

“…Gauge symmetries in YM theories are peculiar. They do not have direct empirical significance (Brading & Brown, 2004). They imply indeterminism at a classical level (Earman, 2003).…”

Symmetries and the Identity of Physical States

“…Nicholas Teh (2015) has recently argued that according to this criterion there exist interesting analogies to the Galileo ship scenario in the gauge theories that underlie modern elementary particle physics. He takes his analysis to partly vindicates an earlier claim by Greaves and Wallace according to which some of the "local" gauge symmetries in gauge theories have direct empirical significance (Greaves and Wallace 2014), contrary to the claims made by other philosophers (Kosso 2000, Redhead 2002, Brading and Brown 2004, Lyre 2004, Healey 2009). Greaves and Wallace argue that the local gauge symmetries with direct empirical significance are those that do not reduce to the identity transformation on the subsystem boundary.…”