The hole argument has become one of the main issues in the philosophy of space-time after the article by Earman and Norton (1987), according to which a certain version of substantivalism (manifold substantivalism) cannot be defended because it brings about to a radical indeterminism. In this article, we try to show that, first, the naming of manifold substantivalism is not appropriate since as some philosophers have said, manifold points cannot be considered to have an independent identity. Second, with a commitment (...) to ontic structural realism, it is possible to offer a proper understanding of manifold substantivalism, which according to the hole argument, does not lead to the radical indeterminism. As a result, the hole argument does not arise, simply. Thus, the last point is that the fact that structural realism is able to solve the problem of the hole argument can itself be seen as considerable evidence in favor of this philosophical position, and thus, the degree of its confirmation goes up. (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)

This paper will serve as the editorial note on Einstein's 1916 review article on general relativity in a planned volume with all of Einstein's papers in Annalen der Physik. It summarizes much of my other work on history of general relativity and draws heavily on the annotation of Einstein's writings and correspondence on general relativity for Vols. 4, 7, and 8 of the Einstein edition.

In 1915 not being able to find field equations for a generally covariant theory of gravitation Einstein came up with a fundamental argument against general covariance – the hole argument. This essay discusses the hole argument and focusses on its consequences for substantivalism and determinism. Two different definitions of determinism are introduced and their compatibility with general covariance from a substantivalist's point of view is discussed.

This article develops an analogy proposed by Stachel between general relativity (GR) and quantum mechanics (QM) as regards permutation invariance. Our main idea is to overcome Pooley's criticism of the analogy by appeal to paraparticles. In GR, the equations are (the solution space is) invariant under diffeomorphisms permuting spacetime points. Similarly, in QM the equations are invariant under particle permutations. Stachel argued that this feature—a theory's ‘not caring which point, or particle, is which’—supported a structuralist ontology. Pooley criticizes this analogy: (...) in QM the (anti-)symmetrization of fermions and bosons implies that each individual state (solution) is fixed by each permutation, while in GR a diffeomorphism yields in general a distinct, albeit isomorphic, solution. We define various versions of structuralism, and go on to formulate Stachel's and Pooley's positions, admittedly in our own terms. We then reply to Pooley. Though he is right about fermions and bosons, QM equally allows more general types of particle symmetry, in which states (vectors, rays, or density operators) are not fixed by all permutations (called ‘paraparticle states’). Thus Stachel's analogy is revived. (shrink)

In this paper Modern Essentialism is used to solve a problem of individuation of spacetime points in General Relativity that has been raised by a New Leibnizian Argument against spacetime substantivalism, elaborated by Earman and Norton. An earlier essentialistic solution, proposed by Maudlin, is criticized as being against both the spirit of metrical essentialism and the fundamental principles of General Relativity. I argue for a modified essentialistic account of spacetime points that avoids those obstacles.

”The last remnant of physical objectivity of space-time” is disclosed in the case of a continuous family of spatially non-compact models of general relativity. The physical individuation of point-events is furnished by the autonomous degrees of freedom of the gravitational field, which represent -as it were -the ontic part of the metric field. The physical role of the epistemic part is likewise clarified as embodying the unavoidable non-inertial aspects of GR. At the end the philosophical import of the Hole Argument (...) is substantially weakened and in fact the Argument itself dis-solved, while a specific four-dimensional holistic and structuralist view of space-time emerges, including elements common to the tradition of both substantivalism and relationism. The observables of our models undergo real temporal change: this gives new evidence to the fact that statements like the frozen-time character of evolution, as other ontological claims about GR, are model dependent. (shrink)

The determination of inertia by matter is looked at in general relativity, where inertia can be represented by affine or projective structure. The matter tensor T seems to underdetermine affine structure by ten degrees of freedom, eight of which can be eliminated by gauge choices, leaving two. Their physical meaning---which is bound up with that of gravitational waves and the pseudotensor t, and with the conservation of energy-momentum---is considered, along with the dependence of reality on invariance and of causal explanation (...) on conservation. (shrink)