The Dynamical Approach as Practical Geometry

Stevens, Syman

doi:10.1086/683447

Cited by 10 publications

(5 citation statements)

References 28 publications

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“…While the dynamical approach's seeking to reduce spacetime structure to dynamical symmetries is compelling and intriguing, it (a) does not undercut this metaphysical plurality, and (b) itself needs to be undergirded by a preciselyarticulated metaphysical strategy (see e.g. the liberalised Humean approach of [32,33,59,69,70,71]).…”

Section: The Dynamical Approach and Perspectivalismmentioning

confidence: 99%

Geometric Objects and Perspectivalism

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2022

The Philosophy and Physics of Noether's Theorems

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The purpose of this article is to consider the metaphysics of geometric and non-geometric objects as they appear in physical theories such as general relativity, and the interactions between these considerations and the contemporary doctrines of perspectivalism and fragmentalism in the philosophy of science. I argue for the following: (i) Taking (following Quine) a kind's being associated with a projectable predicate as a necessary condition for its being natural, there is a sense in which geometric objects can be assimilated to natural kinds, but non-geometric objects cannot; this affords a rational reconstruction of philosophers' and physicists' suspicion of the latter (although this verdict can also be questioned). (ii) Even granting this, nongeometric objects can nevertheless represent real quantities in a perspectival sense-this is one way in which the doctrine of perspectival realism can be endorsed. (iii) More than this: the recognition that non-geometric objects can represent real quantities in a perspectival sense affords support for fragmentalism: the view (at least in part) that frame-dependent effects are physically real. That being said, there are arguments to be made that perspectivalism is superior to this fragmentalism. (iv) There is a certain sense in which perspectivalism should be congenial to proponents of the 'dynamical approach' to spacetime theories-however, the pairing is, in fact, imperfect. (v) Endorsing perspectivalism/fragmentalism in this sense does not commit one to endorsing related-but arguably more opaque-'structuralist' views.

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Section: The Dynamical Approach and Perspectivalismmentioning

confidence: 99%

Geometric Objects and Perspectivalism

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2022

The Philosophy and Physics of Noether's Theorems

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“…The question of whether the dynamical approach to SR is viable has been widely discussed-see e.g. [1,6,26,29,44,48,56,57]. In this paper, I focus on a different issue: whether advocates of the dynamical approach have been fair to the geometrical approach, and whether 'geometricians' can, in fact, offer a coherent answer to the question of why metric and dynamical symmetries coincide, in SR. Before doing so, however, I consider how the nature of the dynamical/geometrical debate shifts on moving to GR.…”

Section: The Dynamical Approachmentioning

confidence: 99%

“…[10, §3.1]. 56 Even in this case, however, one might take Weatherall's anticipated assessment that this theory is 'theoretically equivalent' (in a technical, category-theoretic sense-cf. [65,67,71]) to NGT set in a Galilean structure, combined with an implicit commitment to such theoretical equivalence being sufficient for physical equivalence, to indicate that he does not consider such to be the case-meaning that perhaps he should be regarded as siding with advocates of the dynamical approach after all.…”

Section: Two Miracles Reprisementioning

confidence: 99%

Explanation, Geometry, and Conspiracy in Relativity Theory

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2020

Einstein Studies

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I discuss the debate between dynamical versus geometrical approaches to spacetime theories, in the context of both special and general relativity, arguing that (a) the debate takes a substantially different form in the two cases; (b) different versions of the geometrical approach-only some of which are viable-should be distinguished; (c) in general relativity, there is no difference between the most viable version of the geometrical approach and the dynamical approach. In addition, I demonstrate that what have previously been dubbed two 'miracles' of general relativity admit of no resolution from within general relativity, on either the dynamical or 'qualified' geometrical approaches, modulo some possible hints that the second 'miracle' may be resolved by appeal to recent results regarding the 'geodesic principle' in GR.

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“…For example, if the dynamical equations governing matter fields are invariant under Poincaré transformations, then one just has a Minkowski metric in one's theory. In Stevens (2015), it is argued that the dynamical approach should, therefore, be understood as a means of identifying spacetime structure with what Einstein dubbed in 1921 practical geometry (Einstein 1921)-that is, that geometrical structure which is actually surveyed by physical measurement apparatuses. In light of our distinction between theoretical and operational spacetime, however, we can see that this claim is in general too fast-while it might be true for theories such as special relativity, it is not in general correct to state that what we have called in this paper 'operational spacetime'-Einstein's 'practical geometry'-is the same as that structure which codifies the symmetries of the dynamical equations governing matter fields.…”

Section: Dynamical and Geometrical Approachesmentioning

confidence: 99%

The limitations of inertial frame spacetime functionalism

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Menon

2019

Synthese

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For Knox, 'spacetime' is to be defined functionally, as that which picks out a structure of local inertial frames. Assuming that Knox is motivated to construct this functional definition of spacetime on the grounds that it appears to identify that structure which plays the operational role of spacetime-i.e., that structure which is actually surveyed by physical rods and clocks built from matter fields-we identify in this paper important limitations of her approach: these limitations are based upon the fact that there is a gap between inertial frame structure and that which is operationally significant in the above sense. We present five concrete cases in which these two notions come apart, before considering various ways in which Knox's spacetime functionalism might be amended in light of these issues.

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The Dynamical Approach as Practical Geometry

Cited by 10 publications

References 28 publications

Geometric Objects and Perspectivalism

Geometric Objects and Perspectivalism

Explanation, Geometry, and Conspiracy in Relativity Theory

The limitations of inertial frame spacetime functionalism

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