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)

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)

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)

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)

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)

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)

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)

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 argue that the need to understand spacetime structure as emergent in quantum gravity is less radical and surprising it might appear. A clear understanding of the link between general relativity's geometrical structures and empirical geometry reveals that this empirical geometry is exactly the kind of thing that could be an effective and emergent matter. Furthermore, any theory with torsion will involve an effective geometry, even though these theories look, at first glance, like theories with straightforward spacetime geometry. (...) As it's highly likely that there will be a role for torsion in quantum gravity, it's also highly likely that any theory of quantum gravity will require us to get to grips with emergent spacetime structure. (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)

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)

Several different quantum gravity research programmes suggest, for various reasons, that spacetime is not part of the fundamental ontology of physics. This gives rise to the problem of empirical coherence: if fundamental physical entities do not occupy spacetime or instantiate spatiotemporal properties, how can fundamental theories concerning those entities be justified by observation of spatiotemporally located things like meters, pointers and dials? I frame the problem of empirical coherence in terms of entailment: how could a non-spatiotemporal fundamental theory (...) entail spatiotemporal evidence propositions? Solutions to this puzzle can be classified as realist or antirealist, depending on whether or not they posit a non-fundamental spacetime structure grounded in or caused by the fundamental structure. These approaches place different constraints on our everyday concepts of space and time. Applying lessons from the philosophy of mind, I argue that only realism is both conceptually plausible and suitable for addressing the problem at hand. I suggest a role functionalist version of realism, which is consistent with both grounding and causation, and according to which our everyday concepts reveal something of the true nature of emergent spacetime. (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)

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)

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)

A number of approaches to quantum gravity (QG) seem to imply that spacetime does not exist. Philosophers are quick to point out, however, that the loss of spacetime should not be regarded as total. Rather, we should interpret these approaches as ones that threaten the fundamentality but not the existence of spacetime. In this paper, I argue for two claims. First, I argue that spacetime realism is not forced by QG; spacetime eliminativism remains an option. (...) Second, I argue that eliminativism provides a useful framework for developing two existing approaches to the metaphysics of QG, involving functionalism and mereology respectively. (shrink)

Important features of space and time are taken to be missing in quantum gravity, allegedly requiring an explanation of the emergence of spacetime from non-spatio-temporal theories. In this paper, we argue that the explanatory gap between general relativity and non-spatio- temporal quantum gravity theories might significantly be reduced with two moves. First, we point out that spacetime is already partially missing in the context of general relativity when understood from a dynamical perspective. Second, we argue that most approaches (...) to quantum gravity already start with an in-built distinction between structures to which the asymmetry between space and time can be traced back. (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)

In prior work, we have argued that spacetime functionalism provides tools for clarifying the conceptual difficulties specifically linked to the emergence of spacetime in certain approaches to quantum gravity. We argue in this article that spacetime functionalism in quantum gravity is radically different from other functionalist approaches that have been suggested in quantum mechanics and general relativity: in contrast to these latter cases, it does not compete with purely interpretative alternatives, but is rather intertwined with the physical (...) theorizing itself at the level of quantum gravity. Spacetime functionalism allows one to articulate a coherent realist perspective in the context of quantum gravity, and to relate it to a straightforward realist understanding of general relativity. (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)

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)

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)

The hole argument purports to show that all spacetime theories of a certain form are indeterministic, including the General Theory of Relativity. The argument has given rise to an industry of searching for a metaphysics of spacetime that delivers the right modal implications to rescue determinism. In this paper, I first argue that certain prominent extant replies to the hole argument—namely, those that appeal to an essentialist doctrine about spacetime—fail to deliver the requisite modal implications. As part (...) of my argument, I show that threats to determinism of the sort brought out by the hole argument are more general than has heretofore been recognized. I then use these results to propose a novel essentialist doctrine about spacetime that successfully rescues determinism, what I call sufficiency metric essentialism. However, I go on to argue that once we realize what an essentialist doctrine about spacetime must look like in order to address the hole argument, we should reject all such doctrines, because they can't fulfill their ambition of improving on standard modal replies to the argument. I close by suggesting some lessons for future work on spacetime and the metaphysics of physics more broadly, and also drawing some general morals for contemporary metaphysics, in particular about (i) whether essence can be used to articulate a precise structuralist doctrine, and (ii) the relationship between essence and modality. (shrink)

In prior work, we have argued that spacetime functionalism provides tools for clarifying the conceptual difficulties specifically linked to the emergence of spacetime in certain approaches to quantum gravity. We argue in this article that spacetime functionalism in quantum gravity is radically different from other functionalist approaches that have been suggested in quantum mechanics and general relativity: in contrast to these latter cases, it does not compete with purely interpretative alternatives, but is rather intertwined with the physical (...) theorizing itself at the level of quantum gravity. Spacetime functionalism allows one to articulate a coherent realist perspective in the context of quantum gravity, and to relate it to a straightforward realist understanding of general relativity. (shrink)

In a recent article, Ned Markosian gives an argument against four-dimensionalism understood as the view that time is one of four identical dimensions that constitute a single four-dimensional manifold. In this paper, I show that Markosian attacks a straw man as his argument targets a theory known to be false on empirical grounds. Four-dimensionalism rightly conceived in no way entails that time is identical to space. I then address two objections raised by Markosian against four-dimensionalism rightly conceived.

We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general relativity), as a 4-dimensional manifold equipped with a Lorentzian metric. After an introduction (Section 1), we briefly review the conceptual problems of the ingredient theories (Section 2) and introduce the enterprise of quantum gravity (Section 3). We then describe how three main research programmes in (...) quantum gravity treat four topics of particular importance: the scope of standard quantum theory; the nature of spacetime; spacetime diffeomorphisms, and the so-called `problem of time' (Section 4). These programmes are the old particle-physics approach, superstring theory, and canonical quantum gravity. By and large, these programmes accept most of the ingredient theories' treatment of spacetime, albeit with a metric with some type of quantum nature; but they also suggest that the treatment has fundamental limitations. This prompts the idea of going further: either by quantizing structures other than the metric, such as the topology; or by regarding such structures as phenomenological. We discuss this in Section 5. (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.

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.

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)

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)

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)

The existence and fundamentality of spacetime has been questioned in quantum gravity where spacetime is frequently described as emerging from a more fundamental non-spatiotemporal ontology. This is supposed to lead to various philosophical issues such as the problem of empirical coherence. Yet those issues assume beforehand that we actually understand and agree on the nature of spacetime. Reviewing popular conceptions of spacetime, we find that there is substantial disagreement on this matter, and little hope of resolving (...) it. However, we argue that this should not trouble us as these issues, which seem to suggest the need for an account of spacetime in quantum gravity, can be addressed without one. (shrink)

Spacetime substantivalism leads to a radical form of indeterminism within a very broad class of spacetime theories which include our best spacetime theory, general relativity. Extending an argument from Einstein, we show that spacetime substantivalists are committed to very many more distinct physical states than these theories' equations can determine, even with the most extensive boundary conditions.

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)

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)

Newton's Principia introduced conceptions of space and time that launched one of themost famous and sustained debates in the history of physics, a controversy that involves fundamentalconcerns in the foundations of physics, metaphysics, and scientific epistemology.This bookintroduces and clarifies the historical and philosophical development of the clash between Newton'sabsolute conception of space and Leibniz's relational one. It separates the issues and provides newperspectives on absolute relational accounts of motion and relational-substantival accounts of theontology of space time.Earman's sustained treatment and imaginative (...) insights raise to a new levelthe debate on these important issues at the boundary of philosophy and physics. He surveys thehistory of the controversy from Newton to Einstein develops the mathematics and physics needed topose the issues in sharp form and provides a persuasive assessment of the philosophical problemsinvolved.Most importantly, Earman revitalizes the connection of the debate to contemporary science.He shows, for example, how concerns raised by Leibniz form the core of ongoing debate on thefoundations of general theory of relativity, moving the discussion into a new and vital arena andintroducing arguments that will be discussed for years to come.John Earman is Professor of Historyand Philosophy of Science at the University of Pittsburgh. A Bradford Book. (shrink)

Graduate-level textbook in general relativity.

Priority Monism, as defined by Jonathan Schaffer, has a number of components. It is the view that: the cosmos exists; the cosmos is a maximal actual concrete object, of which all actual concrete objects are parts; the cosmos is basic—there is no object upon which the cosmos depends, ontologically; ontological dependence is a primitive and unanalysable relation. In a recent attack, Lowe has offered a series of arguments to show that Monism fails. He offers up four tranches of argument, with (...) different focuses. These focal points are: being a concrete object; aggregation and dependence; analyses of ontological dependence; Schaffer’s no-overlap principle. These are all technical notions, but each figures at the heart of a cluster of arguments that Lowe puts forward. To respond, I work through each tranche of argument in turn. Before that, in the first section, I offer a cursory statement of Monism, as Schaffer presents it in his 2010 paper, Monism: The Priority of the Whole. I then respond to each of Lowe’s criticisms in turn, deploying material from Schaffer’s 2009 paper Spacetime: the One Substance, as well as various pieces of conceptual machinery from Lowe’s own works to deflect Lowe’s attacks. In the process of defending Monism from Lowe, I end up offering some subtle refinements to Schaffer’s view and explain how the resulting ‘hybrid’ view fares in the wider dialectic. (shrink)

Several approaches to developing a theory of quantum gravity suggest that spacetime—as described by general relativity—is not fundamental. Instead, spacetime is supposed to be explained by reference to the relations between more fundamental entities, analogous to `atoms' of spacetime, which themselves are not (fully) spatiotemporal. Such a case may be understood as emergence of \textit{content}: a `hierarchical' case of emergence, where spacetime emerges at a `higher', or less-fundamental, level than its `lower-level' non-spatiotempral basis. But quantum gravity (...) cosmology also presents us with the possibility of emergence of \textit{context}: where spacetime emerges from some `prior' non-spatiotemporal state (replacing the Big Bang), due to particular conditions in the early universe. I present a general conception of emergence which is plausibly able to accommodate both pictures. This is a positive conception that does not rely on a failure of reduction or explanation in any sense (indeed, reduction is a necessary feature of quantum gravity, and is useful in understanding emergence in this case). I also consider the possibility that the distinction between content- and context- based explanations is blurred, or usefully `collapsed', in the case of spacetime emergence. (shrink)

What ontology does realism about the quantum state suggest? The main extant view in contemporary philosophy of physics is wave-function realism . We elaborate the sense in which wave-function realism does provide an ontological picture, and defend it from certain objections that have been raised against it. However, there are good reasons to be dissatisfied with wave-function realism, as we go on to elaborate. This motivates the development of an opposing picture: what we call spacetime state realism , a (...) view which takes the states associated to spacetime regions as fundamental. This approach enjoys a number of beneficial features, although, unlike wave-function realism, it involves non-separability at the level of fundamental ontology. We investigate the pros and cons of this non-separability, arguing that it is a quite acceptable feature, even one which proves fruitful in the context of relativistic covariance. A companion paper discusses the prospects for combining a spacetime-based ontology with separability, along lines suggested by Deutsch and Hayden. (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 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)

This paper introduces and examines the prospects of the recent research in a holographic relation between entanglement and spacetime pioneered by Mark van Raamsdonk and collaborators. Their thesis is that entanglement in a holographic quantum state is crucial for connectivity in its spacetime dual. Utilizing this relation, the paper develops a thought experiment that promises to probe the nature of spacetime by monitoring the behavior of a spacetime when all entanglement is removed between local degrees of (...) freedom in its dual quantum state. The thought experiment suggests a picture of spacetime as consisting of robust nodes that are connected by non-robust bulk spacetime that is sensitive to changes in entanglement in the dual quantum state. However, rather than pursuing the thought experiment in further detail, the credibility of the relation between spacetime and entanglement in this zero entanglement limit is questioned. The energy of a quantum system generally increases when all entanglement is removed between subsystems, and so does the energy of its spacetime dual. If a system is subdivided into an infinite number of subsystems and all entanglement between them is removed, then the energy of the quantum system and the energy of its spacetime dual are at risk of diverging. While this is a prima facie worry for the thought experiment, it does not constitute a conclusive refutation. (shrink)

This is a contribution to a book on quantum gravity and philosophy. I discuss nature and origin of the problem of quantum gravity. I examine the knowledge that may guide us in addressing this problem, and the reliability of such knowledge. In particular, I discuss the subtle modification of the notions of space and time engendered by general relativity, and how these might merge into quantum theory. I also present some reflections on methodological questions, and on some general issues in (...) philosophy of science which are are raised by, or a relevant for, the research on quantum gravity. (shrink)

The Relational Blockworld (RBW) interpretation of non-relativistic quantum mechanics (NRQM) is introduced. Accordingly, the spacetime of NRQM is a relational, non-separable blockworld whereby spatial distance is only defined between interacting trans-temporal objects. RBW is shown to provide a novel statistical interpretation of the wavefunction that deflates the measurement problem, as well as a geometric account of quantum entanglement and non-separability that satisfies locality per special relativity and is free of interpretative mystery. We present RBW’s acausal and adynamical resolution of (...) the so-called “quantum liar paradox,” an experimental set-up alleged to be problematic for a spacetime conception of reality, and conclude by speculating on RBW’s implications for quantum gravity. (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)

For Anselm, the attribute of omnipresence is not merely concerned with where God exists, but with where and when God exists. His account of this attribute thus precipitates a discourse on the nature of space and time: how they are related to God, to one another, and to the rest of the created order. In the course of this analysis Anselm articulates a number of positions which are generally thought to be the sole possession of modernity. In Part One of (...) what follows I argue, first, that Anselm provides us with an analysis of objects which have both spatial and temporal parts, and second, that he provides us with a clear distinction between those objects which persist by enduring through time in their entirety and those which persist by being temporally extended. In Part Two I argue that Anselm's analysis of omnipresence is consciously informed by a conception of spacetime, according to which space and time form a single, four-dimensional manifold in which objects both persist and move. (shrink)

Introduction for the Synthese Special Issue on Spacetime Functionalism.

The causal set programme towards a quantum theory of gravity is situated vis-à-vis the long-standing debate between eternalism (block theory) and past-presentism or possibilism (growing block theory) in the philosophy of time. It is argued that despite 'appearances' and declarations to the contrary, the programme does not side with growing block theorists when it comes to harboring a robust notion of Becoming - at least, not more than familiar relativistic theories on continuous spacetime manifolds. The problem stems mainly from (...) the postulate of discrete general covariance - a requirement imposed upon the only fully worked out kind of dynamics for causal sets to date, a dynamics of a classical stochastic process. (shrink)