![]() ![]() I distinguish three options for the relationalist in the face of the success of Galilean invariant physics and trace how these generalise to relativistic physics. The bulk of the paper is therefore an investigation of various concrete relationalist proposals. However, for this to be successful there must be genuine relationalist theories that share the theoretical virtues of their substantivalist rivals but without the additional ontological commitment. ![]() The interim conclusion is that the best argument for relationalism is an appeal to Ockham's razor. I move on to consider and reject two recent antisubstantivalist lines of thought. The resulting position has many affinities with what are arguably the most natural interpretations of (. I then review the obvious substantivalist response to the problem, which is to ditch substantival space for substantival spacetime. I begin by describing how the Galilean symmetries of Newtonian physics tell against both Newton's brand of substantivalism and the most obvious relationalist alternative. Relationalists deny this, claiming that spacetime enjoys only a derivative existence. Substantivalists believe that spacetime and its parts are fundamental constituents of reality. 37 1.7 Derivative Operators and Geodesics. 21 1.5 The Action of Smooth Maps on Tensor Fields. 15 1.4 Tensors and Tensor Fields on Manifolds. 7 1.3 Vector Fields, Integral Curves, and Flows. These features are highlighted here, along with an explanation of why Curie's Principle, though valid in quantum field theory, is nearly vacuous in that context. The features of spontaneous symmetry that are peculiar to quantum field theory have received scant attention in the philosophical literature. The present paper aims to advance the discussion of both of these twin topics by tracing their interaction in classical physics, ordinary quantum mechanics and quantum field theory. ) mysteries of spontaneous symmetry breaking. Only comparatively recently have they begun to delve into the (. Philosophers have long been interested in the meaning and status of Curie's Principle. In the same publication Curie discussed a key feature of what later came to be known as spontaneous symmetry breaking: the phenomena generally do not exhibit the symmetries of the laws that govern them. ![]() In 1894 Pierre Curie announced what has come to be known as Curie's Principle: the asymmetry of effects must be found in their causes. Disappointingly, in their interpretation of general relativity, the logical empiricists unwittingly replicated some epistemological remarks Kretschmann had written before General Relativity even existed. While Einstein had taken nothing from Kretschmann but the expression “point-coincidences”, the logical empiricists, however, instinctively dragged along with it the entire apparatus of Kretschmann’s conventionalism. Kretschmann himself realized this and turned the point-coincidence argument against Einstein in his second (. Whereas Kretschmann was inspired by the work of Mach and Poincaré, Einstein inserted Kretschmann’s point-coincidence parlance into the context of Ricci and Levi-Civita’s absolute differential calculus. The present paper attempts to show that a 1915 article by Erich Kretschmann must be credited not only for being the source of Einstein’s point-coincidence remark, but also for having anticipated the main lines of the logical-empiricist interpretation of general relativity. Moreover, the motivation for the program-that isomorphic substantival models should be regarded as representing the same physical situation-is misguided. In fact, for the category of topological spaces of interest in spacetime physics, the program is equivalent to the original spacetime approach. I argue that the program of Leibniz algebras is subject to radical local indeterminism to the same extent as substantivalism. ) prey to radical local indeterminism, the Leibniz algebras do not. An alleged virtue of this is that, while a substantival interpretation of spacetime theories falls (. The idea is that the structure common to the members of an equivalence class of substantival models is captured by a Leibniz algebra which can then be taken to directly characterize the intrinsic reality only indirectly represented by the substantival models. In a number of publications, John Earman has advocated a tertium quid to the usual dichotomy between substantivalism and relationism concerning the nature of spacetime. ![]()
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