Menon, Tushar
(2018)
Algebraic fields and the dynamical approach to physical geometry.
[Preprint]
Abstract
Brown and Pooley's `dynamical approach’ to physical theories zeroes-in on an unexplained correlation between facts about geometry and facts about the behaviour of dynamical fields (such as those constitutive of rods and clocks). The position asserts, among other things, that facts about physical geometry are grounded in, or explained by, facts about dynamical fields, not the other way round. The converse position---that geometry is explanatory of matter field behaviour---is ubiquitous, and is the orthodox position on physical geometry and spacetime structure. John Norton is taken to have articulated a robust objection to the view. Briefly, his claim is that the proponent of the dynamical approach is illicitly committed to spatiotemporal presumptions in `constructing' spacetime from facts about dynamical symmetries. In this paper, I present an abstract, algebraic formulation of field theories. With it, I demonstrate that the proponent of the dynamical approach is not committed, in special relativity, to the illicit presumptions to which Norton refers.
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