This book discusses the notion that quantum gravity may represent the "breakdown" of spacetime at extremely high energy scales. If spacetime does not exist at the fundamental level, then it has to be considered "emergent", in other words an effective structure, valid at low energy scales. The author develops a conception of emergence appropriate to effective theories in physics, and shows how it applies (or could apply) in various approaches to quantum gravity, including condensed matter approaches, discrete approaches, (...) and loop quantum gravity. (shrink)

The interpretation and justification of Earman’s symmetry principles (stating that any spacetime symmetry should be a dynamical symmetry and vice-versa) are controversial. This is directly connected to the question of how certain structures in physical theories acquire a spatiotemporal character. In this paper I address these issues from a perspective (arguably functionalist) that relates the classical discussion about the measurement and geometrical determination of space with a characterization of the notion of dynamical symmetry in which its application to subsystems (...) that act as measuring devices plays an essential role. I argue that in order to reformulate and justify Earman’s principles, and to provide a general account of the chronogeometrical character of some structures, the existence of a coordination between two notions of congruence, one mathematical and one dynamical, must be assumed for the interpretation of physical theories. This coordination provides the basis on which we can understand space-time in physical theories as the codification (representation) of certain features of the access ideal observers have to experience. (shrink)

Collaboration on the First Edition of Spacetime Physics began in the mid-1960s when Edwin Taylor took a junior faculty sabbatical at Princeton University where John Wheeler was a professor. The resulting text emphasized the unity of spacetime and those quantities (such as proper time, proper distance, mass) that are invariant, the same for all observers, rather than those quantities (such as space and time separations) that are relative, different for different observers. The book has become a standard introduction (...) to relativity. The Second Edition of Spacetime Physics embodies what the authors have learned during an additional quarter century of teaching and research. They have updated the text to reflect the immense strides in physics during the same period and modernized and increased the number of exercises, for which the First Edition was famous. Enrichment boxes provide expanded coverage of intriguing topics. An enlarged final chapter on general relativity includes new material on gravity waves, black holes, and cosmology. The Second Edition of Spacetime Physics provides a new generation of readers with a deep and simple overview of the principles of relativity. (shrink)

What is the relation between material objects and spacetime regions? Supposing that spacetime regions are one sort of substance, there remains the question of whether or not material objects are a second sort of substance. This is the question of dualistic versus monistic substantivalism. I will defend the monistic view. In particular, I will maintain that material objects should be identified with spacetime regions. There is the spacetime manifold, and the fundamental properties are pinned directly to (...) it. (shrink)

Michel Janssen and Harvey Brown have driven a prominent recent debate concerning the direction of an alleged arrow of explanation between Minkowski spacetime and Lorentz invariance of dynamical laws in special relativity. In this article, I critically assess this controversy with the aim of clarifying the explanatory foundations of the theory. First, I show that two assumptions shared by the parties—that the dispute is independent of issues concerning spacetime ontology, and that there is an urgent need for a (...) constructive interpretation of special relativity—are problematic and negatively affect the debate. Second, I argue that the whole discussion relies on a misleading conception of the link between Minkowski spacetime structure and Lorentz invari-ance, a misconception that in turn sheds more shadows than light on our understand-ing of the explanatory nature and power of Einstein’s theory. I state that the arrow connecting Lorentz invariance and Minkowski spacetime is not explanatory and uni-directional, but analytic and bidirectional, and that this analytic arrow grounds the chronogeometric explanations of physical phenomena that special relativity offers. (shrink)

In this essay, I consider the ontological status of spacetime from the points of view of the standard tensor formalism and three alternatives: twistor theory, Einstein algebras, and geometric algebra. I briefly review how classical field theories can be formulated in each of these formalisms, and indicate how this suggests a structural realist interpretation of spacetime.

Realism about general relativity (GR) seems to imply realism about spacetime curvature. The existence of the teleparallel equivalent of general relativity (TEGR) calls this into question, for (a) TEGR is set in a torsionful but flat spacetime, and (b) TEGR is empirically equivalent to GR. Knox (Stud Hist Philos Sci Part B Stud Hist Philos Mod Phys 42(4):264–275, 2011) claims that there is no genuine underdetermination between GR and TEGR; we call this verdict into question by isolating and (...) addressing her individual arguments. In addition, we anticipate and evaluate two further worries for realism about the torsionful spacetimes of TEGR, which we call the ‘problem of operationalisability’ and the ‘problem of visualisability’. (shrink)

Discussions of the metaphysical status of spacetime assume that a spacetime theory offers a causal explanation of phenomena of relative motion, and that the fundamental philosophical question is whether the inference to that explanation is warranted. I argue that those assumptions are mistaken, because they ignore the essential character of spacetime theory as a kind of physical geometry. As such, a spacetime theory does notcausally explain phenomena of motion, but uses them to construct physicaldefinitions of basic (...) geometrical structures by coordinating them with dynamical laws. I suggest that this view of spacetime theories leads to a clearer view of the philosophical foundations of general relativity and its place in the historical evolution of spacetime theory. I also argue that this view provides a much clearer and more defensible account of what is entailed by realism concerning spacetime. (shrink)

That space and time should be integrated into a single entity, spacetime, is the great insight of Einstein's special theory of relativity, and leads us to regard spacetime as a fundamental context in which to make sense of the world around us. But it is not the only one. Causality is equally important and at least as far as the special theory goes, it cannot be subsumed under a fundamentally geometrical form of explanation. In fact, the agent of (...) propagation of causal influence is electromagnetic radiation. In this examination, the authors find support for a rationalist approach to physics, never neglecting experimentation, but rejecting a simple empiricist or positivist view of science. (shrink)

This paper explains why spacetime singularities do not constitute a breakdown of physical laws, and points out that the difference between the metrics at singularities and those outside of singularities is factual, rather than nomological.

Spacetime functionalism is the view that spacetime is a functional structure implemented by a more fundamental ontology. Lam and Wüthrich have recently argued that spacetime functionalism helps to solve the epistemological problem of empirical coherence in quantum gravity and suggested that it also (dis)solves the hard problem of spacetime, namely the problem of offering a picture consistent with the emergence of spacetime from a non-spatio-temporal structure. First, I will deny that spacetime functionalism solves the (...) hard problem by showing that it comes in various species, each entailing a different attitude towards, or answer to, the hard problem. Second, I will argue that the existence of an explanatory gap, which grounds the hard problem, has not been correctly taken into account in the literature. (shrink)

Theories of quantum gravity generically presuppose or predict that the reality underlying relativistic spacetimes they are describing is significantly non-spatiotemporal. On pain of empirical incoherence, approaches to quantum gravity must establish how relativistic spacetime emerges from their non-spatiotemporal structures. We argue that in order to secure this emergence, it is sufficient to establish that only those features of relativistic spacetimes functionally relevant in producing empirical evidence must be recovered. In order to complete this task, an account must be given (...) of how the more fundamental structures instantiate these functional roles. We illustrate the general idea in the context of causal set theory and loop quantum gravity, two prominent approaches to quantum gravity. (shrink)

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.

We explore the significance of physical theories set in Euclidean spacetimes. In particular, we explore the use of these theories in contemporary physics at large, and the sense in which there can be a notion of temporal evolution in these theories. Having achieved these tasks, we proceed to reflect on the lessons that one can take from such theories for Knox’s ‘inertial frame’ version of spacetime functionalism, which seems to issue incorrect verdicts in the case of theories with Euclidean (...) metrical structure. (shrink)

Here, we examine hole-freeness - a condition sometimes imposed to rule out seemingly artificial spacetimes. We show that under existing definitions (and contrary to claims made in the literature) there exist inextendible, globally hyperbolic spacetimes which fail to be hole-free. We then propose an updated formulation of the condition which enables us to show the intended result. We conclude with a few general remarks on the strength of the definition and then formulate a precise question which may be interpreted as: (...) Are all physically reasonable spacetimes hole-free? (shrink)

According to a number of approaches in theoretical physics, spacetime does not exist fundamentally. Rather, spacetime exists by depending on another, more fundamental, non-spatiotemporal structure. A prevalent opinion in the literature is that this dependence should not be analyzed in terms of composition. We should not say, that is, that spacetime depends on an ontology of non-spatiotemporal entities in virtue of having them as parts. But is that really right? On the contrary, we argue that a mereological (...) approach to dependent spacetime is not only viable, but promises to enhance our understanding of the physical situation. (shrink)

John Earman and John Norton have argued that substantivalism leads to a radical form of indeterminism within local spacetime theories. I compare their argument to more traditional arguments typical in the Relationist/Substantivalist dispute and show that they all fail for the same reason. All these arguments ascribe to the substantivalist a particular way of talking about possibility. I argue that the substantivalist is not committed to the modal claims required for the arguments to have any force, and show that (...) this naturally leads to an alteration in the way determinism is characterized for local spacetime theories. (shrink)

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 (...) class='Hi'>spacetime functionalism may be uninformative in the absence of answers to fundamental metaphysical questions like the substantivalist/relationist debate. (shrink)

This exploration of the global structure of spacetime within the context of general relativity examines the causal and singular structures of spacetime, revealing some of the curious possibilities that are compatible with the theory, such as `time travel' and `holes' of various types. Investigations into the epistemic and modal structures of spacetime highlight the difficulties in ruling out such possibilities, unlikely as they may seem at first. The upshot seems to be that what counts as a `physically (...) reasonable' spacetime structure in modern physics is far from clear. (shrink)

In this paper I take a sceptical view of the standard cosmological model and its variants, mainly on the following grounds: (i) The method of mathematical modelling that characterises modern natural philosophy-as opposed to Aristotle's-goes well with the analytic, piecemeal approach to physical phenomena adopted by Galileo, Newton and their followers, but it is hardly suited for application to the whole world. (ii) Einstein's first cosmological model (1917) was not prompted by the intimations of experience but by a desire to (...) satisfy Mach's Principle. (iii) The standard cosmological model-a Friedmann-Lematre-Robertson-Walker spacetime expanding with or without end from an initial singularity-is supported by the phenomena of redshifted light from distant sources and very nearly isotropic thermal background radiation provided that two mutually inconsistent physical theories are jointly brought to bear on these phenomena, viz the quantum theory of elementary particles and Einstein's theory of gravity. (iv) While the former is certainly corroborated by high-energy experiments conducted under conditions allegedly similar to those prevailing in the early world, precise tests of the latter involve applications of the Schwarzschild solution or the PPN formalism for which there is no room in a Friedmann-Lematre-Robertson-Walker spacetime. (shrink)

Could spacetime be derived rather than fundamental? The question is pressing because attempts to quantize gravity have led to theories in which (arguably) there are either no, or only extremely thin, spacetime structures. Moreover, recent proposals for the interpretation of quantum mechanics have suggested that 3-dimensional space may be an ‘appearance’ derived from the 3N-dimensional space in which an N-particle wavefunction lives (cross- reference). In fact, I will largely assume a positive answer, and investigate how it could be; (...) in particular, I want to explicate the role of philosophy in producing a satisfactory explanation of spacetime, providing a roadmap for philosophical engagement with quantum gravity. (shrink)

This paper argues that spacetime visualisability is not a necessary condition for the intelligibility of theories in physics. Visualisation can be an important tool for rendering a theory intelligible, but it is by no means a sine qua non. The paper examines the historical transition from classical to quantum physics, and analyses the role of visualisability and its relation to intelligibility. On the basis of this historical analysis, an alternative conception of the intelligibility of scientific theories is proposed, based (...) on Heisenberg 's reinterpretation of the notion of Anschaulichkeit. (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)

In his paper Bare Particulars, T. Sider claims that one of the most plausible candidates for bare particulars are spacetime points. The aim of this paper is to shed light on Sider’s reasoning and its consequences. There are three concepts of spacetime points that allow their identification with bare particulars. One of them, Moderate structural realism, is considered to be the most adequate due its appropriate approach to spacetime metric and moderate view of mereological simples. However, it (...) pushes the Substratum theory to dismiss primitive thisness as the only identity condition for bare particulars, but the paper argues that such elimination is a legitimate step. (shrink)

Numerous approaches to a quantum theory of gravity posit fundamental ontologies that exclude spacetime, either partially or wholly. This situation raises deep questions about how such theories could relate to the empirical realm, since arguably only entities localized in spacetime can ever be observed. Are such entities even possible in a theory without fundamental spacetime? How might they be derived, formally speaking? Moreover, since by assumption the fundamental entities cannot be smaller than the derived and so cannot (...) ‘compose’ them in any ordinary sense, would a formal derivation actually show the physical reality of localized entities? We address these questions via a survey of a range of theories of quantum gravity, and generally sketch how they may be answered positively. (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.

This collection of articles on the theme of space and time covers such broad topics as the philosophy of spacetime, spacetime structure, spacetime ontology, the epistemology of geometry, and general relativity.

Quantum gravity is understood as a theory that, in some sense, unifies general relativity (GR) and quantum theory, and is supposed to replace GR at extremely small distances (high-energies). It may be that quantum gravity represents the breakdown of spacetime geometry described by GR. The relationship between quantum gravity and spacetime has been deemed ``emergence'', and the aim of this thesis is to investigate and explicate this relation. After finding traditional philosophical accounts of emergence to be inappropriate, I (...) develop a new conception of emergence by considering physical case studies including condensed matter physics, hydrodynamics, critical phenomena and quantum field theory understood as effective field theory. This new conception of emergence is unconcerned with the ideas of reduction and derivation (i.e. it holds that we may have emergence with reduction or without it). Instead, a low-energy theory (or model) is understood as emergent from a high-energy theory if it is novel and autonomous compared to the high-energy theory, and the low-energy physics is dependent in a particular, minimal sense on the high-energy physics (this dependence is revealed by the techniques of effective field theory and the renormalisation group). While novelty is construed in a broad sense, the autonomy comes essentially from the underdetermination of the high-energy theory by the low-energy theory, which reflects the minimal way in which the emergent, low-energy theory depends on the high-energy one. It results from the scaling behaviour of the theories and the limiting relations between them, and is demonstrated by the renormalisation group and effective field theory techniques, the idea of universality, and the phenomenon of symmetry-breaking. These ideas are important in exploring the relationship between quantum gravity and GR, where GR is understood as an effective, low-energy theory of quantum gravity. Without experimental data or a theory of quantum gravity, we rely on principles and techniques from other areas of physics to guide the way. As well as considering the idea of emergence appropriate to treating GR as an effective field theory, I investigate the emergence of spacetime (and other aspects of GR) in several concrete approaches to quantum gravity, including examples of the condensed matter approaches, the ``discrete approaches'' (causal set theory, causal dynamical triangulations, quantum causal histories and quantum graphity) and loop quantum gravity. (shrink)

An approximate model of a spacetime foam is presented. It is supposed that in the spacetime foam each quantum handle is like to an electric dipole and therefore the spacetime foam is similar to a dielectric. If we neglect of linear sizes of the quantum handle then it can be described with an operator containing a Grassman number and either a scalar or a spinor field. For both fields the Lagrangian is presented. For the scalar field it (...) is the dilaton gravity + electrodynamics and the dilaton field is a dielectric permeability. The spherically symmetric solution in this case give us the screening of a bare electric charge surrounded by a polarized spacetime foam and the energy of the electric field becomes finite one. In the case of the spinor field the spherically symmetric solution give us a ball of the polarized spacetime foam filled with the confined electric field. It is shown that the full energy of the electric field in the ball can be very big. (shrink)

Salmon, following Reichenbach and others, maintained that distant simultaneity was conventional in a special relativistic world in a way in which this was not so in prerelativistic spacetime. This paper surveys and criticizes a number of proposals to unpack this claim. It goes on to argue that if the claim has validity, it rests upon differing facts about epistemic accessibility of temporal relations in the different spacetimes, and not directly upon any facts about differing causal structures in these worlds.

Structural realist interpretations of generally relativistic spacetimes have recently come to enjoy a remarkable degree of popularity among philosophers. I present a challenge to these structuralist interpretations that arises from considering cosmological models in general relativity. As a consequence of their high degree of spacetime symmetry, these models resist a structuralist interpretation. I then evaluate the various strategies available to the structuralist to react to this challenge. †To contact the author, please write to: Department of Philosophy, 9500 Gilman Drive, (...) 0119, University of California, San Diego, La Jolla, CA 92093‐0119; e‐mail: [email protected]. (shrink)

I discuss candidates for definitions of determinism in the context of general relativistic spacetimes, and argue that a definition which does not make recourse to any particular region of spacetime should be preferred over alternatives; one such notion is discussed in detail in the light of various physical examples. The emerging picture of determinism is a pluralist one: sometimes there is no unique way of making our intuitive concept of determinism precise. Instead, what is crucial for assessment of determinism (...) of the theory are auxiliary conditions under which it counts as deterministic or indeterministic, and justification for using them in a given situation. (shrink)

Space and time, which should properly be taken conjointly, are both communicatively produced and created with certain contextual perspectives—they are not independent physical entities. The standpoint of production makes the relationship between space and time comprehensible. They can either be mental-subjective, physical-objective, or social-intersubjective. Social and intersubjective (or E-series) spacetime might shed new light on biological thinking. For general readers, this paper provides a clue regarding an alternative conceptualization of spacetime based on biology.

In Minkowski spacetime, because of the relativity of simultaneity to the inertial frame chosen, there is no unique world-at-an-instant. Thus the classical view that there is a unique set of events existing now in a three dimensional space cannot be sustained. The two solutions most often advanced are that the four-dimensional structure of events and processes is alone real, and that becoming present is not an objective part of reality; and that present existence is not an absolute notion, but (...) is relative to inertial frame; the world-at-an-instant is a three dimensional, but relative, reality. According to a third view, advanced by Robb, Capek and Stein, what is present at a given spacetime point is, strictly speaking, constituted by that point alone. I argue here against the first of these views that the four-dimensional universe cannot be said to exist now, already, or indeed at any time at all; so that talk of its existence or reality as if that precludes the existence or reality of the present is a non sequitur. The second view assumes that in relativistic physics time lapse is measured by the time co-ordinate function; against this I maintain that it is in fact measured by the proper time, as I argue by reference to the Twin Paradox. The third view, although formally correct, is tarnished by its unrealistic assumption of point-events. This makes it susceptible to paradox, and also sets it at variance with our normal intuitions of the present. I argue that a defensible concept of the present is nonetheless obtainable when account is taken of the non-instantaneity of events, including that of conscious awareness, as that region of spacetime comprised between the forward lightcone of the beginning of a small interval of proper time t and the backward lightcone of the end of that interval. This gives a serviceable notion of what is present to a given event of short duration, as well as saving our intuition of the “reality” or robustness of present events. (shrink)

Several approaches to quantum gravity signal the loss of spacetime at some level. According to spacetime functionalism, spacetime is functionally realised by a more fundamental structure. According to one version of spacetime functionalism, the spacetime role is specified by Ramsifying general relativity. In some approaches to QG, however, there does not appear to be anything that exactly realises the functional role defined by a Ramsey sentence for GR. The spacetime role is approximately realised. It (...) is open to the spacetime functionalist to adopt a ‘near enough is good enough’ attitude to functional realisation, and maintain that spacetime is functionally realised nonetheless. In this paper I present a challenge for such an ‘approximate’ spacetime functionalism. The challenge, in brief, is to provide an account of how ‘close’ is close enough for approximate realisation to occur. I canvass a range of options for spelling out a similarity relation of the relevant kind, and argue that none are successful. In light of the challenge, I recommend giving up on the functional realisation of spacetime. I argue, however, that even if spacetime as a whole is not functionally realised, some of the functions of spacetime may still be performed. (shrink)

A collection of essays discussing the philosophy and foundations of quantum gravity. Written by leading philosophers and physicists in the field, chapters cover the important conceptual questions in the search for a quantum theory of gravity, and the current state of understanding among philosophers and physicists.

I give a new and more general argument against presentism within relativistic spacetimes. This argument is untouched by different recent proposals designed to save presentism in a relativistic setting.

This paper offers an alternative view of spacetime different from both substantivalism and relationism. Using basic ideas underlying the fiber bundle formulation of field theories, it illustrates the function of spacetime in individuating local fields. As the system of numerical identities for entities that we can individually refer to, spacetime is an intrinsic, indispensable, and inalienable structure of the physical world with distinct entities.

This paper makes an observation about the ``amount of structure'' that different classical and relativistic spacetimes posit. The observation substantiates a suggestion made by Earman and yields a cautionary remark concerning the scope and applicability of structural parsimony principles.

Spacetime as we know and love it is lost in most approaches to quantum gravity. For many of these approaches, as inchoate and incomplete as they may be, one of the main challenges is to relate what they take to be the fundamental non-spatiotemporal structure of the world back to the classical spacetime of GR. The present essay investigates how spacetime is lost and how it may be regained in one major approach to quantum gravity, loop quantum (...) gravity. (shrink)

In this paper, some conceptual issues are addressed in order to make sense of what string theory is supposed to tell us about spacetime. The dualities in string theory are used as a starting point for our argumentation. We explore the consequences of a standard view towards these dualities, namely that the dual descriptions represent the same physical situation. Given this view, one has to understand string theory in a manner such that what counts as physical spacetime is (...) based only on the shared physical content—or common core—of the dual descriptions. In general such a spatiotemporal picture does not have to agree with, or be similar to, any of the ones suggested by naïve readings of the dual descriptions. However, in certain regimes or limits, one or the other of the initial dual descriptions may give a good effective description of physical spacetime. (shrink)

We propose a stochastic modification of the Schrödinger–Newton equation which takes into account the effect of extrinsic spacetime fluctuations. We use this equation to demonstrate gravitationally induced decoherence of two gaussian wave-packets, and obtain a decoherence criterion similar to those obtained in the earlier literature in the context of effects of gravity on the Schrödinger equation.

I will defend two claims. First, Schaffer's priority monism is in tension with many research programs in quantum gravity. Second, priority monism can be modified into a view more amenable to this physics. The first claim is grounded in the fact that promising approaches to quantum gravity such as loop quantum gravity or string theory deny the fundamental reality of spacetime. Since fundamental spacetime plays an important role in Schaffer's priority monism by being identified with the fundamental structure, (...) namely the cosmos, the disappearance of spacetime in these views might undermine classical priority monism. My second claim is that priority monism can avoid this issue with two moves: first, in dropping one of its core assumptions, namely that the fundamental structure is spatio-temporal, second, by identifying the connection between the non-spatio-temporal structure and the derivative spatio-temporal structure with mereological composition. (shrink)

Unrestricted Composition (UC) is, roughly, the claim that given any objects at all, there is something which those objects compose. (UC) conflicts in an obvious way with common sense. It has as a consequence, for instance, that there is something which has as parts my nose and the moon. One of the more influential arguments for (UC) is Theodore Sider’s version of the Argument from Vagueness. (A version of the Argument from Vagueness was first presented by David Lewis (1986), pp. (...) 212–213). That argument purports to show that some plausible claims concerning the nature of vagueness entail (UC). In this paper I will suggest a response to this argument. I will show that the proponent of Supersubstantivalism (SS)—the view that material objects are identical to regions of spacetime—can reject a premise of Sider’s argument without denying the plausible claims concerning vagueness. Doing so requires only rejecting a certain view concerning the relationship between the proper sub-region relation and the proper parthood relation. So, proponents of (SS) are in a better position than many of us to side with common sense regarding composition. In the first section of the paper, I will present Sider’s argument. In the second section, I will introduce (SS) and briefly discuss some reasons one might have to believe that it is true. In the third section, I will show how the proponent of (SS) can avoid commitment to (UC) and reject a premise of Sider’s argument. Last, I’ll briefly consider and respond to some objections. (shrink)

This paper has two goals. (i) I explore the limits of the mathematical theory of spacetime (more generally, differential geometry) as an analytical tool for interpreting early modern thought. While it dramatically clarifies some issues, it can also lead to misunderstandings of some figures, and is a very poor tool indeed for others - Leibniz in particular. (ii) I will show how to blunt a very influential argument against a relational conception of spacetime - the view that the (...) properties and relations of bodies exhaust the spatiotemporal. (shrink)

This is a proceedings based on the talk that was made in the workshop “Black Holes, Gravitational Waves and Spacetime Singularities” at Vatican Observatory on 9–12 May 2017. Since then we have constructed some corrections, hence this paper includes them. Here we employ the \\)D Kitaev superconductor model and perform the Wilsonian renormalization group transformation in a real space. We regard the running energy scale or the repetition number of RG transformation as a new emergent direction of the (...) class='Hi'>spacetime, thus constructing a one dimensional higher spacetime. The solution for the beta function is plugged into the effective action and then the RG information is encoded in the curvature of the emergent spacetime. We found that there are two fixed points in which one corresponds to the Lifshitz spacetime with the dynamical critical exponent \ and the other fixed point corresponds to the AdS\ spacetime. The topological superconducting phase induces a naked singularity in the spacetime and the trivial superconducting phase produces regular spacetime. Except the fixed points, each parameter phase shows spatial anisotropic spacetime description as it goes to IR limit. (shrink)

In this essay I begin to lay out a conceptual scheme for: analysing dualities as cases of theoretical equivalence; assessing when cases of theoretical equivalence are also cases of physical equivalence. The scheme is applied to gauge/gravity dualities. I expound what I argue to be their contribution to questions about: the nature of spacetime in quantum gravity; broader philosophical and physical discussions of spacetime. - proceed by analysing duality through four contrasts. A duality will be a suitable isomorphism (...) between models: and the four relevant contrasts are as follows: Bare theory: a triple of states, quantities, and dynamics endowed with appropriate structures and symmetries; vs. interpreted theory: which is endowed with, in addition, a suitable pair of interpretative maps. Extendable vs. unextendable theories: which can, respectively cannot, be extended as regards their domains of application. External vs. internal intepretations: which are constructed, respectively, by coupling the theory to another interpreted theory vs. from within the theory itself. Theoretical vs. physical equivalence: which contrasts formal equivalence with the equivalence of fully interpreted theories. I will apply this scheme to answering questions - for gauge/gravity dualities. I will argue that the things that are physically relevant are those that stand in a bijective correspondence under duality: the common core of the two models. I therefore conclude that most of the mathematical and physical structures that we are familiar with, in these models, are largely, though crucially never entirely, not part of that common core. Thus, the interpretation of dualities for theories of quantum gravity compels us to rethink the roles that spacetime, and many other tools in theoretical physics, play in theories of spacetime. (shrink)

The consensus among spacetime substantivalists is to respond to Leibniz's classic shift arguments, and their contemporary incarnation in the form of the hole argument, by pruning the allegedly problematic metaphysical possibilities that generate these arguments. Some substantivalists do so by directly appealing to a modal doctrine akin to anti-haecceitism. Other substantivalists do so by appealing to an underlying hyperintensional doctrine that implies some such modal doctrine. My first aim in this paper is to pose a challenge for all extant (...) forms of this consensus position. My second aim is to show what form substantivalism must take in order to uphold the consensus while addressing this challenge. The result is a novel "plenitudinous" substantivalist view, which predicts that certain modal facts about spacetime are vague or indeterminate. I then argue against this view on independent grounds, concluding that substantivalists should reject the consensus position. The paper also discusses the way forward for substantivalists in light of this conclusion. (shrink)