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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 (...) 

As Harvey Brown emphasizes in his book Physical Relativity, inertial motion in general relativity is best understood as a theorem, and not a postulate. Here I discuss the status of the "conservation condition", which states that the energymomentum tensor associated with noninteracting matter is covariantly divergencefree, in connection with such theorems. I argue that the conservation condition is best understood as a consequence of the differential equations governing the evolution of matter in general relativity and many other theories. I conclude (...) 

This article gives an explicit presentation of Newtonian gravitation on the backdrop of Maxwell spacetime, giving a sense in which acceleration is relative in gravitational theory. However, caution is needed: assessing whether this is a robust or interesting sense of the relativity of acceleration depends on some subtle technical issues and on substantive philosophical questions over how to identify the spacetime structure of a theory. 

Using as a starting point recent and apparently incompatible conclusions by Saunders and Knox, I revisit the question of the correct spacetime setting for Newtonian physics. I argue that understood correctly, these two versions of Newtonian physics make the same claims both about the background geometry required to define the theory, and about the inertial structure of the theory. In doing so I illustrate and explore in detail the view—espoused by Knox, and also by Brown —that inertial structure is defined (...) 

I provide an alternative characterization of a "standard of rotation" in the context of classical spacetime structure that does not refer to any covariant derivative operator. 

I argue that a criterion of theoretical equivalence due to Glymour :227–251, 1977) does not capture an important sense in which two theories may be equivalent. I then motivate and state an alternative criterion that does capture the sense of equivalence I have in mind. The principal claim of the paper is that relative to this second criterion, the answer to the question posed in the title is “yes”, at least on one natural understanding of Newtonian gravitation. 

Harvey Brown’s Physical Relativity defends a view, the dynamical perspective, on the nature of spacetime that goes beyond the familiar dichotomy of substantivalist/relationist views. A full defense of this view requires attention to the way that our use of spacetime concepts connect with the physical world. Reflection on such matters, I argue, reveals that the dynamical perspective affords the only possible view about the ontological status of spacetime, in that putative rivals fail to express anything, either true or false. I (...) 

Coordinatebased approaches to physical theories remain standard in mainstream physics but are largely eschewed in foundational discussion in favour of coordinatefree differentialgeometric approaches. I defend the conceptual and mathematical legitimacy of the coordinatebased approach for foundational work. In doing so, I provide an account of the Kleinian conception of geometry as a theory of invariance under symmetry groups; I argue that this conception continues to play a very substantial role in contemporary mathematical physics and indeed that supposedly ``coordinatefree'' differential geometry (...) 

I review some recent work on applications of category theory to questions concerning theoretical structure and theoretical equivalence of classical field theories, including Newtonian gravitation, general relativity, and YangMills theories. 

It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct spacetime structure underlying Newton’s methods in Principia is neoNewtonian or Galilean spacetime. I argue to the contrary that inertial frames are not needed in Newton’s theory of motion, and that the right spacetime structure for Newton’s Principia requires the notion of parallelism of spatial directions at different times and nothing more. Only relative motions are definable in this framework, never absolute (...) 

I discuss several issues related to "classical" spacetime structure. I review Galilean, Newtonian, and Leibnizian spacetimes, and briefly describe more recent developments. The target audience is undergraduates and early graduate students in philosophy; the presentation avoids mathematical formalism as much as possible. 

ABSTRACT I explore the viability of a Galilean relational theory of spacetime—a theory that includes a threeplace collinearity relation among its stock of basic relations. Two formal results are established. First, I prove the existence of a class of dynamically possible models of Newtonian mechanics in which collinearity is uninstantiated. Second, I prove that the dynamical properties of Newtonian systems fail to supervene on their Galilean relations. On the basis of these two results, I argue that Galilean relational spacetime is (...) 

The paper investigates the status of gravitational energy in Newtonian Gravity, developing upon recent work by Dewar and Weatherall. The latter suggest that gravitational energy is a gauge quantity. This is potentially misleading: its gauge status crucially depends on the spacetime setting one adopts. In line with MøllerNielsen’s plea for a motivational approach to symmetries, we supplement Dewar and Weatherall’s work by discussing gravitational energy–stress in Newtonian spacetime, Galilean spacetime, MaxwellHuygens spacetime, and Newton–Cartan Theory. Although we ultimately concur with Dewar (...) 

This article uncovers a foundational relationship between the ‘gauge symmetry’ of a NewtonCartan theory and the celebrated Trautman Recovery Theorem and explores its implications for recent philosophical work on NewtonCartan gravitation. 

I point out a radical indeterminism in potentialbased formulations of Newtonian gravity once we drop the condition that the potential vanishes at infinity. This indeterminism, which is well known in theoretical cosmology but has received little attention in foundational discussions, can be removed only by specifying boundary conditions at all instants of time, which undermines the theory's claim to be fully cosmological, i.e., to apply to the Universe as a whole. A recent alternative formulation of Newtonian gravity due to Saunders (...) 