Some philosophers respond to Leibniz’s “shift” argument against absolute space by appealing to antihaecceitism about possible worlds, using David Lewis’s counterpart theory. But separated from Lewis’s distinctive system, it is difficult to understand what this doctrine amounts to or how it bears on the Leibnizian argument. In fact, the best way of making sense of the relevant kind of antihaecceitism concedes the main point of the Leibnizian argument, pressing us to consider alternative spatiotemporal metaphysics.

This article deals with empty spacetime and the question of its physical reality. By “empty spacetime” we mean a collection of bare spacetime points, the remains of ridding spacetime of all matter and fields. We ask whether these geometric objects—themselves intrinsic to the concept of field—might be observable through some physical test. By taking quantum-mechanical notions into account, we challenge the negative conclusion drawn from the diffeomorphism invariance postulate of general relativity, and we propose new foundational ideas regarding the possible (...) observation—as well as conceptual overthrow—of this geometric ether. (shrink)

Is there anything more to temperature than the ordering of things from colder to hotter? Are there also facts, for example, about how much hotter (twice as hot, three times as hot...) one thing is than another? There certainly are---but the only strong justification for this claim comes from statistical mechanics. What we knew about temperature before the advent of statistical mechanics (what we knew about it from thermodynamics) provided only weak reasons to believe it.

We analyze the geometric foundations of classical Yang-Mills theory by studying the relationships between internal relativity, locality, global/local invariance, and background independence. We argue that internal relativity and background independence are the two independent defining principles of Yang-Mills theory. We show that local gauge invariance -heuristically implemented by means of the gauge argument- is a direct consequence of internal relativity. Finally, we analyze the conceptual meaning of BRST symmetry in terms of the invariance of the gauge fixed theory under general (...) local gauge transformations. (shrink)

This essay explores the possibility of constructing a structural realist interpretation of spacetime theories that can resolve the ontological debate between substantivalists and relationists. Drawing on various structuralist approaches in the philosophy of mathematics, as well as on the theoretical complexities of general relativity, our investigation will reveal that a structuralist approach can be beneficial to the spacetime theorist as a means of deflating some of the ontological disputes regarding similarly structured spacetimes.

While many take Newton's argument for absolute space to be an inference to the best explanation, some argue that Newton is primarily concerned with the proper definition of true motion, rather than with independent existence of spatial points. To an extent the latter interpretation is correct. However, all prior interpretations are mistaken in thinking that 'absolute motion' is defined as motion with respect to absolute space. Newton is also using this notion to refer to the quantity of motion (momentum). This (...) reading reveals a misunderstood argument for absolute space, according to which absolute space is necessary for a workable definition of momentum. (shrink)

I argue against theories that attempt to reduce scientific representation to similarity or isomorphism. These reductive theories aim to radically naturalize the notion of representation, since they treat scientist's purposes and intentions as non-essential to representation. I distinguish between the means and the constituents of representation, and I argue that similarity and isomorphism are common but not universal means of representation. I then present four other arguments to show that similarity and isomorphism are not the constituents of scientific representation. I (...) finish by looking at the prospects for weakened versions of these theories, and I argue that only those that abandon the aim to radically naturalize scientific representation are likely to be successful. (shrink)

The aim of this article is to argue that a temporal asymmetry may be established within the framework of quantum field theory, independently of any violation of CP, and thereby T, in weak interactions, and independently of the property of time reversal invariance that its dynamical equations instantiate. Particularly, I shall argue that the temporal asymmetry can be stemmed from assessing the links between the proper group of symmetries of the theory and the ontology of the theory: arguments applied to (...) establish which elements and magnitudes remain invariants under group transformations can also be used to establish a temporal asymmetry. (shrink)

The aim of this paper is to place the considerations provided by a philosophical family of positions called “spacetime structuralism” in the context of the debate between classical views: substantivalism and relationism in the philosophy of spacetime. Altough this task was somehow tackled in the past by other researchers, they never stated most generally, what exactly the problem with spacetime structuralism as a standpoint was. I view that problem as the problem of its autonomy and potential reducibility to both of (...) the classical views. I modestly suggest a general viewpoint on spacetime structuralism: as a purely interpretative endeavour. (shrink)

The paper considers the "GR-desideratum", that is, the way general relativity implements general covariance, diffeomorphism invariance, and background independence. Two cases are discussed where 5-dimensional generalizations of general relativity run into interpretational troubles when the GR-desideratum is forced upon them. It is shown how the conceptual problems dissolve when such a desideratum is relaxed. In the end, it is suggested that a similar strategy might mitigate some major issues such as the problem of time or the embedding of quantum non-locality (...) into relativistic spacetimes. (shrink)

While there is a longstanding discussion about the interpretation of the extended, general principle of relativity, there seems to be a consensus that the special principle of relativity is absolutely clear and unproblematic. However, a closer look at the literature on relativistic physics reveals a more confusing picture. There is a huge variety of, sometimes metaphoric, formulations of the relativity principle, and there are different, sometimes controversial, views on its actual content. The aim of this paper is to develop a (...) precise language in order to provide a precise formulation of the principle. In view of the fact that the special relativity principle is considered as a universal meta-law, which must be valid for all physical laws in all situations, we try to keep the formalism as general as possible. The benefit of the formal reconstruction is that it makes explicit all the necessary conceptual components of the principle; it brings out many subtle details and the related conceptual problems. (shrink)

In the aftermath of the rediscovery of Einstein’s hole argument by Earman and Norton (1987), we hear that the ontological relational/substantival debate over the status of spacetime seems to have reached stable grounds. Despite Einstein’s early intention to cast GR’s spacetime as a relational entity à la Leibniz-Mach, most philosophers of science feel comfortable with the now standard sophisticated substantivalist (SS) account of spacetime. Furthermore, most philosophers share the impression that although relational accounts of certain highly restricted models of GR (...) are viable, at a deep down level, they require substantival spacetime structures. SS claims that although manifold spacetime points do not enjoy the sort of robust existence provided by primitive identity, it is still natural to be realistic about the existence of spacetime as an independent entity in its own right. It is argued that since the bare manifold lacks the basic spacetime structures –such as geometry and inertia- one should count as an independent spacetime the couple manifold +metric (M, g). The metric tensor field of GR encodes inertial and metrical structure so, in a way, it plays the explanatory role that Newtonian absolute space played in classical dynamics. In a nutshell, according to the SS account of spacetime, one should view the metric field of GR as the modern version of a realistically constructed spacetime since it has the properties –or contains the structures- that Newtonian space had. I will try to dismantle the widespread impression that a relational account of full GR is implausible. To do so, I will start by highlighting that when turning back to the original Leibniz-Newton dispute one sees that substantivalism turns out prima facie triumphant since Newton was able to successfully formulate dynamics. However, to give relationalism a fair chance, one can also put forward the following hypothetical questions: What if Leibniz –or some leibnizian- had had a good relational theory? What role would geometry play in this type of theory? Would it be natural to view geometry and inertia as intrinsic properties of substantival space –if not spacetime? Would it still seem natural to interpret the metric field of GR along substantival lines regardless of the fact that it also encodes important material properties such as energy-momentum? After bringing these questions out into the light I will cast some important doubts on the substantival (SS) interpretation of the metric field. Perhaps the metric turns out to be viewed as a relational matter field. Finally, to strengthen the relational account of spacetime I expect to remove the possible remaining interpretative tension by briefly discussing the relevance of two important facts: i) Dynamical variables are usually linked to material objects in physical theories. The metric field of GR is a dynamical object so, I claim, it should be viewed as a matter field. ii) Barbour and Bertotti (BB2, 1982) have provided and alternative formulation of classical dynamics. They provide a “genuinely relational interpretation of dynamics” (Pooley & Brown 2001). Geometry and inertia become –contra SS- relational structures in BB2. (shrink)

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. (shrink)

In this article I subject to criticism Field's argument, according to which field theory takes space-time to be substance since it ascribes field properties to space-time points. There is petitio principii error made in this reasoning because Field does not give any justification for his controversial assumption that fields are properties of space-time points. What is more, I suggest, Field's interpretation of field theory is incompatible with the way this theory is understood and utilized by its users, namely scientists. My (...) criticism is based on the assumption that one cannot propose an ontology of a given scientific theory, at the same time imposing on it an interpretation which clashes with the interpretation current among its users. I also suggest that in order to establish the ontology of a scientific theory one should also take into account the way it has been constructed. According to this criterion, field theory does indeed take space-time to be a substance. (shrink)

The implications for the substantivalist–relationalist controversy of Barbour and Bertotti's successful implementation of a Machian approach to dynamics are investigated. It is argued that in the context of Newtonian mechanics, the Machian framework provides a genuinely relational interpretation of dynamics and that it is more explanatory than the conventional, substantival interpretation. In a companion paper (Pooley [2002a]), the viability of the Machian framework as an interpretation of relativistic physics is explored. 1 Introduction 2 Newton versus Leibniz 3 Absolute space versus (...) an affine connection 4 Anti-relationalist arguments 5 Rehabilitating relationalism 6 Dynamics on the relative configuration space 7 Intrinsic particle dynamics 8 Conclusion. (shrink)

I argued that the frameworks and mechanisms that produce unification do not enable us to explain why the unified phenomena behave as they do. That is, we need to look beyond the unifying process for an explanation of these phenomena. Anya Plutynski ([2005]) has called into question my claim about the relationship between unification and explanation as well as my characterization of it in the context of the early synthesis of Mendelism with Darwinian natural selection. In this paper I argue (...) that her methodological criticisms rest on a misinterpretation of my views on explanation and defend my historical interpretation of the work of Fisher and Wright. A statement of the problem Methodological differences: how to characterize explanation Historical matters: disagreements about details Explanation revisited: the possible versus the ‘merely actual’. (shrink)

Around the turn of the century, Poincare and Hilbert each published an account of geometry that took the discipline to be an implicit definition of its concepts. The terms ‘point’, ‘line’, and ‘plane’ can be applied to any system of objects that satisfies the axioms. Each mathematician found spirited opposition from a different logicist—Russell against Poincare' and Frege against Hilbert— who maintained the dying view that geometry essentially concerns space or spatial intuition. The debates illustrate the emerging idea of mathematics (...) as the science of structure. The article closes with some remarks on structuralist and nonstructuralist themes in Frege's own development of arithmetic. (shrink)

To what extent can constructive mathematics based on intuitionistc logic recover the mathematics needed for spacetime physics? Certain aspects of this important question are examined, both technical and philosophical. On the technical side, order, connectivity, and extremization properties of the continuum are reviewed, and attention is called to certain striking results concerning causal structure in General Relativity Theory, in particular the singularity theorems of Hawking and Penrose. As they stand, these results appear to elude constructivization. On the philosophical side, it (...) is argued that any mentalist-based radical constructivism suffers from a kind of neo-Kantian apriorism. It would be at best a lucky accident if objective spacetime structure mirrored mentalist mathematics. the latter would seem implicitly committed to a Leibnizian relationist view of spacetime, but is it doubtful if implementation of such a view would overcome the objection. As a result, an anti-realist view of physics seems forced on the radical constructivist. (shrink)

I will discuss only one of the several entwined strands of the philosophy of space and time, the question of the relation between the nature of motion and the geometrical structure of the world.1 This topic has many of the virtues of the best philosophy of science. It is of long-standing philosophical interest and has a rich history of connections to problems of physics. It has loomed large in discussions of space and time among contemporary philosophers of science. Furthermore, there (...) is, I think, widespread agreement that recent insights here have lead to a genuine deepening of our understanding. (shrink)

In times of crisis, when current theories are revealed as inadequate to task, and new physics is thought to be required—physics turns to re-evaluate its principles, and to seek new ones. This paper explores the various types, and roles of principles that feature in the problem of quantum gravity as a current crisis in physics. I illustrate the diversity of the principles being appealed to, and show that principles serve in a variety of roles in all stages of the crisis, (...) including in motivating the need for a new theory, and defining what this theory should be like. In particular, I consider: the generalised correspondence principle, UV-completion, background independence, and the holographic principle. I also explore how the current crisis fits with Friedman’s view on the roles of principles in revolutionary theory-change, finding that while many key aspects of this view are not represented in quantum gravity, the view could potentially offer a useful diagnostic, and prescriptive strategy. This paper is intended to be relatively non-technical, and to bring some of the philosophical issues from the search for quantum gravity to a more general philosophical audience interested in the roles of principles in scientific theory-change. (shrink)

Does the gravitational field described in general relativity possess genuine stress-energy? We answer this question in the affirmative, in a weak sense applicable in a certain class of frames of a certain class of models of the theory, and arguably also in a strong sense, applicable in all frames of all models of the theory. In addition, we argue that one can be a realist about gravitational stress-energy in general relativity even if one is a relationist about spacetime ontology. In (...) each case, our reasoning rests upon a functionalist approach to the definition of physical quantities. (shrink)

The aim of the paper is to develop a proper mathematical formalism which can help to clarify the necessary conceptual plugins to the special principle of relativity and leads to a deeper understanding of the principle in its widest generality.

In his general theory of relativity (GR) Einstein sought to generalize the special-relativistic equivalence of inertial frames to a principle according to which all frames of reference are equivalent. He claimed to have achieved this aim through the general covariance of the equations of GR. There is broad consensus among philosophers of relativity that Einstein was mistaken in this. That equations can be made to look the same in different frames certainly does not imply in general that such frames are (...) physically equivalent. We shall argue, however, that Einstein's position is tenable. The equivalence of arbitrary frames in GR should not be equated with relativity of arbitrary motion, though. There certainly are observable differences between reference frames in GR (differences in the way particles move and fields evolve). The core of our defense of Einstein's position will be to argue that such differences should be seen as fact-like rather than law-like in GR. By contrast, in classical mechanics and in special relativity (SR) the differences between inertial systems and accelerated systems have a law-like status. The fact-like character of the differences between frames in GR justifies regarding them as equivalent in the same sense as inertial frames in SR. (shrink)

The paper presents an inquiry into the question regarding the compatibility of Bohmian mechanics, intended as a non-local theory of moving point-like particles, with background independence. This issue is worth being investigated because, if the Bohmian framework has to be of some help in developing new physics, it has to be compatible with the most well-established traits of modern physics, background independence being one of such traits. The paper highlights the fact that the notion of background independence in the context (...) of spacetime physics is slippery and interpretation-laden. It is then suggested that the best-matching framework developed by Julian Barbour might provide a robust enough meaning of background independence. The structure of Bohmian dynamics is evaluated against this framework, reaching some intermediate results that speak in favor of the fact that Bohmian mechanics can be made background independent. (shrink)

The paper presents a metaphysical characterization of spatiotemporal backgrounds from a realist perspective. The conceptual analysis is based on a heuristic sketch that encompasses the common formal traits of the major spacetime theories, such as Newtonian mechanics and general relativity. It is shown how this framework can be interpreted in a fully realist fashion, and what is the role of background structures in such a picture. In the end it is argued that, although backgrounds are a source of metaphysical discomfort, (...) still they make a spacetime theory easy to interpret. It is also suggested that this conclusion partially explains why the notion of background independence carries a lot of conceptual difficulties. (shrink)

I argue that the best spacetime setting for Newtonian gravitation (NG) is the curved spacetime setting associated with geometrized Newtonian gravitation (GNG). Appreciation of the ‘Newtonian equivalence principle’ leads us to conclude that the gravitational field in NG itself is a gauge quantity, and that the freely falling frames are naturally identified with inertial frames. In this context, the spacetime structure of NG is represented not by the flat neo-Newtonian connection usually made explicit in formulations, but by the sum of (...) the flat connection and the gravitational field. 1 Introduction2 Newtonian Gravity: The Orthodox Approach3 Newtonian Gravity: Additional Symmetries4 Cosmological Considerations5 A Newtonian Equivalence Principle: Inertial Frames in Newtonian Gravitation6 Theory Equivalence?7 Conclusion. (shrink)

Hans Reichenbach's so-called geometrical conventionalism is often taken as an example of a positivistic philosophy of science, based on a verificationist theory of meaning. By contrast, we shall argue that this view rests on a misinterpretation of Reichenbach's major work in this area, the Philosophy of Space and Time (1928). The conception of equivalent descriptions, which lies at the heart of Reichenbach's conventionalism, should be seen as an attempt to refute Poincaré's geometrical relativism. Based upon an examination of the reasons (...) Reichenbach gives for the cognitive equivalence of geometrical descriptions, the paper argues that his conventionalism is a specific form of scientific realism. At the same time we shall argue against those interpretations which lead to a trivialization of Reichenbach's conventionalism or deny it entirely. (shrink)

The desire to minimize the number of individual new entities postulated is often referred to as quantitative parsimony. Its influence on the default hypotheses formulated by scientists seems undeniable. I argue that there is a wide class of cases for which the preference for quantitatively parsimonious hypotheses is demonstrably rational. The justification, in a nutshell, is that such hypotheses have greater explanatory power than less parsimonious alternatives. My analysis is restricted to a class of cases I shall refer to as (...) additive. Such cases involve the postulation of a collection of qualitatively identical individual objects which collectively explain some particular observed phenomenon. Especially clear examples of this sort occur in particle physics. 1 Introduction 2 Particle physics: a case study 3 Three kinds of simplicity 4 Explanatory power 5 Explanation and non-observation 6 Parsimony and scientific methodology 7 Conclusions. (shrink)

ABSTRACT It has recently been argued that Harvey Brown and Oliver Pooley’s ‘dynamical approach’ to special relativity should be understood as what might be called an ontologically and ideologically relationalist approach to Minkowski geometry, according to which Minkowski geometrical structure supervenes upon the symmetries of the best-systems dynamical laws for a material world with primitive topological or differentiable structure. Fleshing out the details of some such primitive structure, and a conception of laws according to which Minkowski geometry could so supervene, (...) has been referred to by some as the ‘constructivist project’. Here, it is explained that Nick Huggett’s work on ‘regularity relationalism’ provides a framework for such an approach, and a relativistic version of Huggett’s regularity relationalism is outlined for that purpose. Finally, by way of examples, it is shown that this approach fails in the simplest cases. Still, reasons are given for which this should not necessarily discourage an advocate of this interpretation of the dynamical approach. 1 Introduction to the Dynamical Approach 2 Huggett’s Regularity Relationalism 3 The Dynamical Approach as a Form of Regularity Relationalism 4 A Simple Way to Set the Stage 5 A First Attempt 5.1 Complex-valued planewave solutions 5.2 Real-valued planewave solutions 6 More General Solutions 7 Summary and Reflections. (shrink)