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Philosophy of Symmetry

Fields as Bodies: a unified presentation of spacetime and internal gauge symmetry (February 2015)

In submission.

Using the parametrised representation of field theory (in which the location in spacetime of a part of a field is itself represented by a map from the base manifold to Minkowski spacetime) I demonstrate that in both local and global cases, internal (Yang-Mills-type) and spacetime (Poincare) symmetries can be treated precisely on a par, so that gravitational theories may be regarded as gauge theories in a completely standard sense.

Deflating the Aharonov-Bohm Effect (July 2014)

In submission.

I argue that the metaphysical import of the Aharonov-Bohm effect has been overstated: correctly understood, it does not require either rejection of gauge invariance or any novel form of nonlocality. The conclusion that it does require one or the other follows from a failure to keep track, in the analysis, of the complex scalar field to which the magnetic vector potential is coupled. Once this is recognised, the way is clear to a local account of the ontology of electrodynamics (or at least, to an account no more nonlocal than quantum theory in general requires); I sketch a possible such account.

Empirical Consequences of Symmetries (November 2011)

(Hilary Greaves and DW)

British Journal for the Philosophy of Science 65 (2014), pp. 59-89

`Global' symmetries, such as the boost invariance of classical mechanics and special relativity, can give rise to direct empirical counterparts such as the Galileo-ship phenomenon. However, a widely accepted line of thought holds that `local' symmetries, such as the diffeomorphism invariance of general relativity and the gauge invariance of classical electromagnetism, have no such direct empirical counterparts. We argue against this line of thought. We develop a framework for analysing the relationship between Galileo-ship empirical phenomena and physical theories that model such phenomena that renders the relationship between theoretical and empirical symmetries transparent, and from which it follows that both global and local symmetries can give rise to Galileo-ship phenomena. In particular, we use this framework to exhibit analogs of Galileo's ship for both the diffeomorphism invariance of general relativity and the gauge invariance of electromagnetism.

The Relativity and Equivalence Principles for Self-Gravitating Systems (March 2009)

Forthcoming in "Towards a Theory of Spacetime Theories", edited by Dennis Lehmkuhl, in the Einstein Studies series, to appear in 2016.

I criticise the view that the relativity and equivalence principles are consequences of the small-scale structure of the metric in general relativity, by arguing that these principles also apply to systems with non-trivial self-gravitation and hence non-trivial spacetime curvature (such as black holes). I provide an alternative account, incorporating aspects of the criticised view, which allows both principles to apply to systems with self-gravity.

QFT, Antimatter, and Symmetry (March 2009)

Studies in the History and Philosophy of Modern Physics 40 (2009) pp. 209-222.

A systematic analysis is made of the relations between the symmetries of a classical field and the symmetries of the one-particle quantum system that results from quantizing that field in regimes where interactions are weak. The results are applied to gain a greater insight into the phenomenon of antimatter.

Time-dependent symmetries: the link between gauge symmetries and indeterminism (2003)

In Symmetries in physics: philosophical reflections, edited by Katherine Brading and Elena Castellani (CUP, 2003).

Mathematically, gauge theories are extraordinarily rich --- so rich, in fact, that it can become all too easy to lose track of the connections between results, and become lost in a mass of beautiful theorems and properties: indeterminism, constraints, Noether identities, local and global symmetries, and so on.

One purpose of this short article is to provide some sort of a guide through the mathematics, to the conceptual core of what is actually going on. Its focus is on the Lagrangian, variational-problem description of classical mechanics, from which the link between gauge symmetry and the apparent violation of determinism is easy to understand; only towards the end will the Hamiltonian description be considered.

The other purpose is to warn against adopting too unified a perspective on gauge theories. It will be argued that the meaning of the gauge freedom in a theory like general relativity is (at least from the Lagrangian viewpoint) significantly different from its meaning in theories like electromagnetism. The Hamiltonian framework blurs this distinction, and orthodox methods of quantization obliterate it; this may, in fact, be genuine progress, but it is dangerous to be guided by mathematics into conflating two conceptually distinct notions without appreciating the physical consequences.