Same-diff? Part I: Conceptual similarities (and one difference) between gauge transformations and diffeomorphisms

Abstract

The following questions are germane to our understanding of gauge-(in)variant quantities and physical possibility: in which ways are gauge transformations and spacetime diffeomorphisms similar, and in which are they different? To what extent are we justified in endorsing different attitudes-sophistication, quidditism/haecceitism, or full elimination-towards each? In a companion paper, I assess new and old contrasts between the two types of symmetries. In this one, I propose a new contrast: whether the symmetry changes pointwise the dynamical properties of a given field. This contrast distinguishes states that are related by a gauge-symmetry from states related by generic spacetime diffeomorphisms, as being 'pointwise dynamically indiscernible'. Only the rigid isometries of homogeneous spacetimes fall in the same category, but they are neither local nor modally robust, in the way that gauge transformations are. In spite of this difference, I argue that for both gauge transformations and spacetime diffeomorphisms, symmetry-related models are best understood through the doctrine of 'sophistication'.

The metaphysics of fibre bundles

“…4). Gomes (2021) calls this object the Atiyah-Lie manifold. §7 Locality, Separability, Holism second redundancy.…”

How to Choose a Gauge? The Case of Hamiltonian Electromagnetism

“…So this is analogous to saying, about general relativity, that diffeomorphism-related models of the metric correspond to the same physical possibility: an interpretation that we argue(Gomes & Butterfield, 2022a) is recommended, though not mandated, by the mathematics. As argued at length inGomes (2021cGomes ( , 2021d there is thus no major interpretative difference between the gauge transformations of Yang-Mills theories and the diffeomorphisms of general relativity.…”

“…4, we conclude; and sketch how this work can be set against the background, not just of Maudlin's discussion, but of other similar enterprises, viz. those pursued in Gomes (2019bGomes ( , 2021aGomes ( , 2021bGomes ( , 2021cGomes ( , 2021d and .…”