Caspar Jacobs (Oxford): Earman’s Symmetry Principles for Internal Symmetries

Quine (1951) famously distinguished between the ontology and the ideology of a theory: what the theory says that exists, and what we can say about it. This distinction is similar to the one in modern physics between internal and external degrees of freedom. The latter correspond to the theory’s dependent variables, and so represent quantities that are predicated of the theory’s independent variables, which represent the bearers of those quantities. In what Earman and Norton (1987) call local spacetime theories, the external DOFs coincide with the spatiotemporal variables. The idea that spacetime has a certain structure is well-known in the philosophy of physics. Earman’s (1989) famous ‘symmetry principles’ entail that the theory’s dynamical symmetries tell us something about this structure. By contrast, the idea that internal DOFs such as mass or charge also possess a certain non-trivial structure, and that symmetries can tell us something about this structure, are less common in the literature (but not entirely absent: see especially recent work by Dewar (2019); Martens (2019); Wolff (2020)). It is this second set of claims that I will defend in this talk. In a slogan: symmetries are a guide towards the structure of physical quantities. In order to do so, I extend Earman’s symmetry principles to internal symmetries (including gauge symmetries). This leads to a set of more general principles: every kinematical symmetry is a dynamical symmetry and vice versa. As I will argue, the parallel between external and internal symmetries that results puts pressure on Quine’s distinction between ontology and ideology as applied to local spacetime theories. In particular, it follows that the distinction between what is predicated and what it is predicated of is not a difference in kind, but the result of an asymmetry in the relation between two classes of objects. In this way, symmetry principles play a decisive role in the interpretation of modern theories of physics.

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_{Philosophy of Physics Graduate Lunch Seminar Convenor: Caspar Jacobs}