Theoretical equivalence and duality are two closely related notions: but their interconnection has so far not been well understood. In this paper I explicate the contribution of a recent schema for duality to discussions of theoretical equivalence. I argue that duality suggests a construal of theoretical equivalence in the physical sciences. The construal is in terms of the isomorphism of models, as defined by the schema. This construal gives interpretative constraints that should be useful for discussions of theoretical equivalence more (...) generally. I illustrate the construal in various formulations of Maxwell’s electromagnetic theory. (shrink)

One of Julian Barbour’s main aims is to solve the problem of time that appears in quantum geometrodynamics (QG). QG involves the application of canonical quantization procedure to the Hamiltonian formulation of General Relativity. The problem of time arises because the quantization of the Hamiltonian constraint results in an equation that has no explicit time parameter. Thus, it appears that the resulting equation, as apparently timeless, cannot describe evolution of quantum states. Barbour attempts to resolve the problem by allegedly eliminating (...) time from his interpretation of QG. In order to evaluate the efficacy of his solution, it is necessary to ascertain in what sense time has been eliminated from his theory. I proceed to do so by developing a form of conceptual analysis that is applicable to the concept of time in physical theories and applying this analysis to Barbour’s account. (shrink)

For the past two decades, Einstein's Hole Argument (which deals with the apparent indeterminateness of general relativity due to the general covariance of the field equations) and its resolution in terms of "Leibniz equivalence" (the statement that pseudo-Riemannian geometries related by active diffeomorphisms represent the same physical solution) have been the starting point for a lively philosophical debate on the objectivity of the point-events of space-time. It seems that Leibniz equivalence makes it impossible to consider the points of the space-time (...) manifold as physically individuated without recourse to dynamical individuating fields. Various authors have posited that the metric field itself can be used in this way , but nobody so far has considered the problem of explicitly distilling the "metrical fingerprint" of point-events from the gauge-dependent elements of the metric field. Working in the Hamiltonian formulation of general relativity, and building on the results of Lusanna and Pauri (2002), we show how Bergmann and Komar's "intrinsic pseudo-coordinates" (based on the value of curvature invariants) can be used to provide a physical individuation of point-events in terms of the true degrees of freedom (the "Dirac observables") of the gravitational field, and we suggest how this conceptual individuation could in principle be implemented with a well-defined empirical procedure. We argue from these results that point-events retain a significant kind of physical objectivity. (shrink)