Cartan’s spacetime reformulation of the Newtonian theory of gravity is a generallycovariant Galilean-relativistic limit-form of Einstein’s theory of gravity known as the Newton-Cartan theory. According to this theory, space is flat, time is absolute with instantaneous causal influences, and the degenerate ‘metric ’ structure of spacetime remains fixed with two mutually orthogonal non-dynamical metrics, one spatial and the other temporal. The spacetime according to this theory is, nevertheless, curved, duly respecting the principle of equivalence, and the non-metric gravitational connection-field is dynamical in the sense that it is determined by matter distributions. Here, this generallycovariant but Galilean-relativistic theory of gravity with a possible non-zero cosmological constant, viewed as a parameterized gauge theory of a gravitational vector-potential minimally coupled to a complex Schrödinger-field (bosonic or fermionic), is successfully cast — for the first time — into a manifestly covariant Lagrangian form. Then, exploiting the fact that Newton-Cartan spacetime is intrinsically globally-hyperbolic with a fixed causal structure, the theory is recast both into a constraint-free Hamiltonian form in 3+1dimensions

this paper we present an alternative account, based primarily on the basic network of formal ontological relations---specifically, mereological and topological relations---that a domain of events must arguably satisfy. The motivations for this approach are quite general and lie beyond the specific issue of temporal constructions. Among other things, we also believe it may shed light on the first question above. In the following, however, we shall not go much beyond the main issue that we just outlined; our only concern will be to show how mereological and topological reasoning---which we take to be among the basic tools for ontological analysis---provides adequate grounds for the construction of temporal relations.

I will discuss only one of the several entwined strands of the philosophy of

The CPT theorem of quantum field theory states that any relativistic (Lorentz-invariant) quantum field theory must also be invariant under CPT, the composition of charge conjugation, parity reversal and time reversal. This paper sketches a puzzle that seems to arise when one puts the existence of this sort of theorem alongside a standard way of thinking about symmetries, according to which spacetime symmetries (at any rate) are associated with features of the spacetime structure. The puzzle is, roughly, that the existence of a CPT theorem seems to show that it is not possible for a well-formulated theory that does not make use of a preferred frame or foliation to make use of a temporal orientation. Since a manifold with only a Lorentzian metric can be temporally orientable — capable of admitting a temporal orientation — this seems to be an odd sort of necessary connection between distinct existences. The paper then suggests a solution to the puzzle: it is suggested that the CPT theorem arises because temporal orientation is unlike other pieces of spacetime structure, in that one cannot represent it by a tensor field. To avoid irrelevant technical details, the discussion is carried out in the setting of classical field theory, using a little-known classical analog of the CPT theorem. 1

We discuss several ways of making precise the informal concept of physical determinism, drawing on ideas from mathematical logic and computability theory. We outline a programme of investigating these notions of determinism in detail for specific, precisely articulated physical theories. We make a start on our programme by proposing a general logical framework for describing physical theories, and analysing several possible formulations of a simple Newtonian theory from the point of view of determinism. Our emphasis throughout is on clarifying the precise physical and metaphysical assumptions that typically underlie a claim that some physical theory is ‘deterministic’. A sequel paper is planned, in which we shall apply similar methods to the analysis of other physical theories. Along the way, we discuss some possible repercussions of this kind of investigation for both physics and logic. 1

The main aim of our paper is to show that interpretative issues belonging to classical General Relativity (GR) might be preliminary to a deeper understanding of conceptual problems stemming from ongoing attempts at constructing a quantum theory of gravity. Among such interpretative issues, we focus on the meaning of general covariance and the related question of the identity of points, by basing our investigation on the Hamiltonian formulation of GR. In particular, we argue that the adoption of a peculiar gauge-fixing within the canonical reduction of ADM metric gravity may yield a new solution to the debate between substantivalists and relationists, by suggesting a tertium quid between these two age-old positions. Such a third position enables us to evaluate the controversial relationship between entity realism and structural realism in a well-defined case study. After having indicated the possible developments of this approach in Quantum

Newton-Cartan theory presents a four-dimensional covariant geometrical formulation of Newton's gravity. This report, reviews the history and structure of Newton-Cartan space-time and its applications to dynamical theories like Newton's Gravity, Lagrangian mechanics or even Quantum Mechanics. Ideas of classical physics, combined with Einstein's equivalence principle, mesh with quantum mechanics, as we present a way to describe a quantum test particle moving in a gravitational Newto-Cartan space-time.

Some recent philosophical debate about persistence has focussed on an argument against perdurantism that discusses rotating perfectly homogeneous discs (the ‘rotating discs argument’; RDA). The argument has been mostly discussed by metaphysicians, though it appeals to ideas from classical mechanics, especially about rotation. In contrast, I assess the RDA from the perspective of the philosophy of physics. After introducing the argument and emphasizing the relevance of physics (Sections 1 to 3), I review some metaphysicians ’ replies to the argument, especially those by Callender, Lewis, Robinson and Sider (Section 4). Thereafter, I argue for three main conclusions. They all arise from the fact, emphasized in Section 2, that classical mechanics (non-relativistic as well as relativistic) is both more subtle, and more problematic, than philosophers generally realize. The first conclusion is that the RDA can be formulated more strongly than is usually recognized: it is not necessary to “imagine away ” the dynamical effects