Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws (the role of determining local inertial structure). I raise two complications for this approach. First, our spacetime concept seems to have the structure of a cluster concept, which means that Knox's inertial criteria for spacetime cannot succeed with complete generality. Second, the notion of metaphysical fundamentality may feature in the spacetime concept, in which case spacetime functionalism may be uninformative (...) in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

Constructivists, such as Harvey Brown, urge that the geometries of Newtonian and special relativistic spacetimes result from the properties of matter. Whatever this may mean, it commits constructivists to the claim that these spacetime geometries can be inferred from the properties of matter without recourse to spatiotemporal presumptions or with few of them. I argue that the construction project only succeeds if constructivists antecedently presume the essential commitments of a realist conception of spacetime. These commitments can be avoided only by (...) adopting an extreme form of operationalism. (shrink)

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 theoperationalrole 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)

Eleanor Knox has argued that our concept of spacetime applies to whichever structure plays a certain functional role in the laws. I raise two objections to this inertial functionalism. First, it depends on a prior assumption about which coordinate systems defined in a theory are reference frames, and hence on assumptions about which geometric structures are spatiotemporal. This makes Knox’s account circular. Second, her account is vulnerable to several counterexamples, giving the wrong result when applied to topological quantum field theories (...) and parity- and time-asymmetric theories. I advance an alternative account on which our spacetime concept is a cluster concept. On this view, the notion of metaphysical fundamentality may feature in the cluster, in which case spacetime functionalism may be uninformative in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

Supersymmetry in quantum physics is a mathematically simple phenomenon that raises deep foundational questions. To motivate these questions, I present a toy model, the supersymmetric harmonic oscillator, and its superspace representation, which adds extra anticommuting dimensions to spacetime. I then explain and comment on three foundational questions about this superspace formalism: whether superspace is a substance, whether it should count as spatiotemporal, and whether it is a necessary postulate if one wants to use the theory to unify bosons and fermions.

I examine the debate between Michel Janssen and Harvey Brown over the arrow of explanation in special relativity. Brown argues that the symmetries of the dynamical laws explain the symmetries of space-time, whereas Janssen argues for the converse. Janssen has recently argued against Brown's position on the grounds that it recommends trying to infer information from the relativistic effects, e.g., length contraction, in a way wasteful of time and resources. I show how Brown can respond to Janssen and trace the (...) dispute not to a methodological difference, but to opposing positions on the meaning of spatio-temporal symmetries. According to Janssen, the symmetries of space-time are constraints on dynamical laws. According to Brown, symmetries of space-time arise jointly from matter distributions and the laws governing matter. Finally, I provide some considerations in favor of Brown's position. (shrink)