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. (shrink)

Brown and Pooley’s ‘dynamical approach’ to physical theories asserts, in opposition to the orthodox position on physical geometry, that facts about physical geometry are grounded in, or explained by, facts about dynamical fields, not the other way round. John Norton has claimed that the proponent of the dynamical approach is illicitly committed to spatiotemporal presumptions in ‘constructing’ space-time from facts about dynamical symmetries. In this article, I present an abstract, algebraic formulation of field theories and demonstrate that the proponent of (...) the dynamical approach is not committed, in special relativity, to the illicit presumptions to which Norton refers. (shrink)

Supersymmetry (SUSY) is a proposed symmetry between bosons and fermions. The structure of the space of SUSY generators is such that the distinction between internal and spacetime symmetries is blurred. As a result, there are two viable candidates for the correct spacetime setting for a flat supersymmetric field theory---Minkowski spacetime and superspace. an extension of four- dimensional Minkowski spacetime to include (at least) four new dimensions, coordinatised by mathematical objects known as supernumbers. These objects are, in one significant way, quite (...) different from real or complex number---some of them have the property that their order of multiplication makes a difference; in mathematical terms, they are said to have nontrivial commutation properties. This paper argues for two theses: first, that one standard set of arguments, related to universality of symmetry behaviour, that motivate a particular choice of spacetime structure in familiar spacetime theories motivates the choice of superspace as the appropriate spacetime for SUSY field theories. And second, that the metaphysical utility of the concept of spacetime requires more than just the satisfaction of this universality condition; in supersymmetric theories, the spacetime concept is not as useful as in special relativity. (shrink)

Recent work in the physics literature demonstrates that, in particular classes of rotating spacetimes, physical light rays in general do not traverse null geodesics. Having presented this result, we discuss its philosophical significance, both for the clock hypothesis (and, in particular, a recent purported proof thereof for light clocks), and for the operational meaning of the metric field. 1Introduction 2Fletcher's Theorem 2.1Maudlin on the clock hypothesis in special relativity 2.2Fletcher’s result in special relativity 2.3Fletcher’s theorem in general relativity 3Electromagnetism and (...) the Geometrical-Optical Limit 3.1Maxwell’s equations in curved spacetime 3.2The geometrical-optical limit 3.3Rotating spacetimes 3.4Aren’t Gödel spacetimes unphysical? 4The Clock Hypothesis and Chronogeometry 4.1Natural and mathematical observations 4.2Clock registry discord 4.3Chronogeometry 5Conclusion. (shrink)

If we cannot directly empirically test the claims of particular scientific theory, then it would be nice to have some other criteria with which to assess its viability. In his 2013 book, String Theory and the Scientific Method, Richard Dawid aims to develop such criteria, with an eye to vindicating research programs in disciplines where direct empirical data is scant or non-existent. In an accompanying paper, Dawid, Hartmann and Sprenger formalise Dawid’s so-called ‘No Alternatives Argument’ using a generalised Bayesian framework, (...) as a first step towards formalising Dawid’s entire re- search programme. In this paper, I argue that the formalisation of the NAA cannot play the central role in Dawid’s programme as intended. This is based on the observation that not all confirmation is non-negligible confirmation. For Dawid’s programme to be useful, it must demonstrate the viability not just of non-empirical theory confirmation, but of non-negligible non-empirical theory confirmation. I argue that Dawid et al.’s appeal to Bayesian confirmation theory to formalise his NAA cannot guarantee non-negligible confirmation. As a result, I conclude that if Dawid’s overall project is to succeed, it must do so without the NAA formalised in this way. (shrink)

Noncommutative geometries generalize standard smooth geometries, parametrizing the noncommutativity of dimensions with a fundamental quantity with the dimensions of area. The question arises then of whether the concept of a region smaller than the scale—and ultimately the concept of a point—makes sense in such a theory. We argue that it does not, in two interrelated ways. In the context of Connes’ spectral triple approach, we show that arbitrarily small regions are not definable in the formal sense. While in the scalar (...) field Moyal–Weyl approach, we show that they cannot be given an operational definition. We conclude that points do not exist in such geometries. We therefore investigate (a) the metaphysics of such a geometry, and (b) how the appearance of smooth manifold might be recovered as an approximation to a fundamental noncommutative geometry. (shrink)

In a recent article, Halvorson and Manchak (Br J Philos Sci, Forthcoming) claim that there is no basis for the Hole Argument, because (in a certain sense) hole isometries are unique. This raises two important questions: (a) does their argument succeed?; (b) how does this formalist response to the Hole Argument relate to other recent responses to the Hole Argument in the same tradition—in particular, that of Weatherall (Br J Philos Sci 69(2):329–350, 2018)? In this article, _ad_ (a), we argue (...) that Halvorson and Manchak’s claim does not go through; _ad_ (b), we argue that although one _prima facie_ plausible reading would see Halvorson and Manchak as filling an important hole (no pun intended) in Weatherall’s argument, in fact this reading is implausible; there is no need to supplement Weatherall’s work with Halvorson and Manchak’s results. (shrink)

Recent work in the physics literature demonstrates that, in particular classes of rotating spacetimes, physical light rays in general do not traverse null geodesics. Having presented this result, we discuss its philosophical significance, both for the clock hypothesis (and, in particular, a recent purported proof thereof for light clocks), and for the operational meaning of the metric field. 1Introduction 2Fletcher's Theorem 2.1Maudlin on the clock hypothesis in special relativity 2.2Fletcher’s result in special relativity 2.3Fletcher’s theorem in general relativity 3Electromagnetism and (...) the Geometrical-Optical Limit 3.1Maxwell’s equations in curved spacetime 3.2The geometrical-optical limit 3.3Rotating spacetimes 3.4Aren’t Gödel spacetimes unphysical? 4The Clock Hypothesis and Chronogeometry 4.1Natural and mathematical observations 4.2Clock registry discord 4.3Chronogeometry 5Conclusion. (shrink)

In his paper, ‘Regarding the ‘Hole Argument”, Weatherall suggests that models of general relativity related by a hole diffeomorphism must be regarded as being physically equivalent. At a later stage in the paper, however, he also argues that there is a sense in which two such models may be regarded as being empirically distinct—a fortiori physically distinct. We attempt to delineate the logic behind these two prima facie contradictory claims. We argue that the latter sense rests upon a misunderstanding of (...) the import of shift arguments in the foundations of spacetime theories. (shrink)