ABSTRACT Unlike the relativity theory it seeks to replace, causal set theory has been interpreted to leave space for a substantive, though perhaps ‘localized’, form of ‘becoming’. The possibility of fundamental becoming is nourished by the fact that the analogue of Stein’s theorem from special relativity does not hold in CST. Despite this, we find that in many ways, the debate concerning becoming parallels the well-rehearsed lines it follows in the domain of relativity. We present, however, some new twists and (...) challenges. In particular, we show that a novel and exotic notion of becoming is compatible with causal sets. In contrast to the localized becoming considered compatible with the dynamics of CST by its advocates, our novel kind of becoming, while not answering to the typical A-theoretic demands, is global and objective. _1_ Introduction _2_ The Basics of Causal Set Theory _3_ Facing the Same Dilemma? _4_ Taking Growth Seriously _5_ Conclusion. (shrink)

Philosophy Beyond Spacetime assesses the state of play in the philosophy of quantum gravity. Research in this field aims at a unified theory in which quantum matter is related dynamically to relativistic spacetime. This volume highlights the conceptual questions involved, showing how physics and metaphysics can illuminate each other.

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)

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.

Quantum gravity--the marriage of quantum physics with general relativity--is bound to contain deep and important lessons for the nature of physical time. Some of these lessons shall be canvassed here, particularly as they arise from quantum general relativity and string theory and related approaches. Of particular interest is the question of which of the intuitive aspects of time will turn out to be fundamental, and which 'emergent' in some sense.

This paper is an enquiry into the logical, metaphysical, and physical possibility of time travel understood in the sense of the existence of closed worldlines that can be traced out by physical objects. We argue that none of the purported paradoxes rule out time travel either on grounds of logic or metaphysics. More relevantly, modern spacetime theories such as general relativity seem to permit models that feature closed worldlines. We discuss, in the context of Gödel's infamous argument for the ideality (...) of time based on his eponymous spacetime, what this apparent physical possibility of time travel means. Furthermore, we review the recent literature on so-called time machines, i.e., of devices that produce closed worldlines where none would have existed otherwise. Finally, we investigate what the implications of the quantum behaviour of matter for the possibility of time travel might be and explicate in what sense time travel might be possible according to leading contenders for full quantum theories of gravity such as string theory and loop quantum gravity. (shrink)

Research in quantum gravity strongly suggests that our world in not fundamentally spatiotemporal, but that spacetime may only emerge in some sense from a non-spatiotemporal structure, as this paper illustrates in the case of causal set theory and loop quantum gravity. This would raise philosophical concerns regarding the empirical coherence and general adequacy of theories in quantum gravity. If it can be established, however, that spacetime emerges in the appropriate circumstances and how all its relevant aspects are explained in fundamental (...) non-spatiotemporal terms, then the challenge is fully met. It is argued that a form of spacetime functionalism offers the most promising template for this project. (shrink)

More often than not, recently popular structuralist interpretations of physical theories leave the central concept of a structure insufficiently precisified. The incipient causal sets approach to quantum gravity offers a paradigmatic case of a physical theory predestined to be interpreted in structuralist terms. It is shown how employing structuralism lends itself to a natural interpretation of the physical meaning of causal set theory. Conversely, the conceptually exceptionally clear case of causal sets is used as a foil to illustrate how a (...) mathematically informed rigorous conceptualization of structure serves to identify structures in physical theories. Furthermore, a number of technical issues infesting structuralist interpretations of physical theories such as difficulties with grounding the identity of the places of highly symmetrical physical structures in their relational profile and what may resolve these difficulties can be vividly illustrated with causal sets. (shrink)

Defining ‘presentism’ in a way that saves it from being trivially false yet metaphysically substantively distinct from eternalism is no mean feat, as the first part of this collection testifies. In Wuthrich (forthcoming), I have offered an attempt to achieve just this, arguing that this is best done in the context of modern spacetime theories. Here, I shall refrain from going through all the motions again and simply state the characterization of an ersatzist version of presentism as it has (...) emerged from considerations there. Any acceptable formulation of presentism should remain neutral among competing spacetime theories in order to enable the present project of assessing the compatibility of presentism with various theories of modern physics, including both spacetime theories and theories of physical processes situated in a spatiotemporal setting. (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)

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: wuthrich@ucsd.edu. (shrink)

Approaches to quantum gravity often involve the disappearance of space and time at the fundamental level. The metaphysical consequences of this disappearance are profound, as is illustrated with David Lewis's analysis of modality. As Lewis's possible worlds are unified by the spatiotemporal relations among their parts, the non-fundamentality of spacetime---if borne out---suggests a serious problem for his analysis: his pluriverse, for all its ontological abundance, does not contain our world. Although the mere existence---as opposed to the fundamentality---of spacetime must be (...) recovered from the fundamental structure in order to guarantee the empirical coherence of the non-spatiotemporal fundamental theory, it does not suffice to salvage Lewis's theory of modality from the charge of rendering our actual world impossible. (shrink)

Information theory presupposes the notion of an epistemic agent, such as a scientist or an idealized human. Despite that, information theory is increasingly invoked by physicists concerned with fundamental physics, physics at very high energies, or generally with the physics of situations in which even idealized epistemic agents cannot exist. In this paper, I shall try to determine the extent to which the application of information theory in those contexts is legitimate. I will illustrate my considerations using the case of (...) black hole thermodynamics and Bekenstein's celebrated argument for his formula for the entropy of black holes. This example is particularly pertinent to the theme of the present collection because it is widely accepted as `empirical data' in notoriously empirically deprived quantum gravity, even though the laws of black hole thermodynamics have so far evaded direct empirical confirmation. (shrink)

Unlike the relativity theory it seeks to replace, causal set theory has been interpreted to leave space for a substantive, though perhaps ‘localized’, form of ‘becoming’. The possibility of fundamental becoming is nourished by the fact that the analogue of Stein’s theorem from special relativity does not hold in causal set theory. Despite this, we find that in many ways, the debate concerning becoming parallels the well-rehearsed lines it follows in the domain of relativity. We present, however, some new twists (...) and challenges. In particular, we show that a novel and exotic notion of becoming is compatible with causal sets. In contrast to the ‘localized’ becoming considered compatible with the dynamics of causal set theory by its advocates, our novel kind of becoming, while not answering to the typical A-theoretic demands, is ‘global’ and objective. (shrink)

Does the need to find a quantum theory of gravity imply that the gravitational field must be quantized? Physicists working in quantum gravity routinely assume an affirmative answer, often without being aware of the metaphysical commitments that tend to underlie this assumption. The ambition of this article is to probe these commitments and to analyze some recently adduced arguments pertinent to the issue of quantization. While there exist good reasons to quantize gravity, as this analysis will show, alternative approaches to (...) gravity challenge the received wisdom. These renegade approaches do not regard gravity as a fundamental force, but rather as effective, i.e. as merely supervening on fundamental physics. I will urge that these alternative accounts at least prove the tenability of an opposition to quantization. (shrink)

These works concern fundamental philosophical problems of time and spacetime, such as the implications of the absolute and relations concepts of motion for the disputes about the character of spacetime, the role of relativity, quantum mechanics, quantum gravity and noncommutative geometry with respect to the controversy concerning the objectivity of the flow of time, the existence of the future, the concept of branching spacetime. One paper presents the views on time of an outstanding representative of phenomenology, Roman Ingarden, thus enriching (...) the book with some questions of philosophical anthropology and ethics. The collection is mainly addressed to research workers and graduate students. (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)

This essay considers and evaluates recent results and arguments from classical chaotic systems theory and non-relativistic quantum mechanics that pertain to the question of whether our world is deterministic or indeterministic. While the classical results are inconclusive, quantum mechanics is often assumed to establish indeterminism insofar as the measurement process involves an ineliminable stochastic element, even though the dynamics between two measurements is considered fully deterministic. While this latter claim concerning the Schrödinger evolution must be qualified, the former fully depends (...) on a resolution of the measurement problem. Two alleged proofs that nature is indeterministic, relying, in turn, on Gleason's theorem and Conway and Kochen's recent 'free will theorem', are shown to be wanting qua proofs of indeterminism. We are thus left with the conclusion that the determinism question remains open. (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)

Radical ontic structural realism (ROSR) asserts an ontological commitment to ‘free-standing’ physical structures understood solely in terms of fundamental relations, without any recourse to relata that stand in these relations. Bain ([2013], pp.1621–35) has recently defended ROSR against the common charge of incoherence by arguing that a reformulation of fundamental physical theories in category-theoretic terms (rather than the usual set-theoretic ones) offers a coherent and precise articulation of the commitments accepted by ROSR. In this essay, we argue that category theory (...) does not offer a more hospitable environment to ROSR than set theory. We also show that the application of category-theoretic tools to topological quantum field theory and to algebraic generalizations of general relativity do not warrant the claim that these theories describe ‘object-free’ structures. We conclude that category theory offers little if any comfort to ROSR. 1 Introduction: Ridding Structures of Objects2 The Set-theoretic Peril for Radical Ontic Structural Realism3 Bain’s Categorial Strategy to Save Radical Ontic Structural Realism4 Throwing out the Relations with the Relata5 Categorial and Set-theoretical Structures6 Radical Suggestions from Topological Quantum Field Theory?7 Sheaves of Einstein Algebras as Radical Structures?8 Conclusions. (shrink)

The present volume collects essays on the philosophical foundations of quantum theories of gravity, such as loop quantum gravity and string theory. Central for philosophical concerns is quantum gravity's suggestion that space and time, or spacetime, may not exist fundamentally, but instead be a derivative entity emerging from non-spatiotemporal degrees of freedom. In the spirit of naturalised metaphysics, contributions to this volume consider the philosophical implications of this suggestion. In turn, philosophical methods and insights are brought to bear on the (...) foundations of quantum gravity itself. For instance, the idea of functionalism, borrowed from the philosophy of mind and discussed by several essays, exemplifies this mutual interaction the collection seeks to foster. (shrink)

This paper argues that recent arguments to the effect that the debate between presentism and eternalism lacks any metaphysical substance ultimately fail, although important lessons can be gleaned from them in how to formulate a non-vacuous version of presentism. It suggests that presentism can best be characterized in the context of spacetime theories. The resulting position is an ersatzist version of presentism that admits merely non-present entities as abstracta deprived of physical existence. Ersatzist presentism both escapes the charges of triviality (...) and promises to offer a route to solving the grounding problem which befalls its more traditional cousins. (shrink)

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter investigates the meaning and significance of string theoretic dualities, arguing they reveal a surprising physical indeterminateness to spacetime.

This paper examines two cosmological models of quantum gravity to investigate the foundational and conceptual issues arising from quantum treatments of the big bang. While the classical singularity is erased, the quantum evolution that replaces it may not correspond to classical spacetime: it may instead be a non-spatiotemporal region, which somehow transitions to a spatiotemporal state. The different kinds of transition involved are partially characterized, the concept of a physical transition without time is investigated, and the problem of empirical incoherence (...) for regions without spacetime is discussed. (shrink)

There exists a growing literature on the so-called physical Church-Turing thesis in a relativistic spacetime setting. The physical Church-Turing thesis is the conjecture that no computing device that is physically realizable can exceed the computational barriers of a Turing machine. By suggesting a concrete implementation of a beyond-Turing computer in a spacetime setting, Istvan Nemeti and Gyula David have shown how an appreciation of the physical Church-Turing thesis necessitates the confluence of mathematical, computational, physical, and indeed cosmological ideas. In this (...) essay, I will honour Istvan's seventieth birthday, as well as his longstanding interest in, and his seminal contributions to, this field going back to as early as 1987 by modestly proposing how the concrete implementation in Nemeti and D\'avid might be complemented by a quantum-information-theoretic communication protocol between the computing device and the logician who sets the beyond-Turing computer a task such as determining the consistency of Zermelo-Fraenkel set theory. This suggests that even the foundations of quantum theory and, ultimately, quantum gravity may play an important role in determining the validity of the physical Church-Turing thesis. (shrink)

Although general relativity is a predictively successful theory, it treats matter as classical rather than as quantum. For this reason, it will have to be replaced by a more fundamental quantum theory of gravity. Attempts to formulate a quantum theory of gravity suggest that such a theory may have radical consequences for the nature, and indeed the fate, of spacetime. The present article articulates what this problem of spacetime is and traces it three approaches to quantum gravity taking general relativity (...) as their vantage point: semi-classical gravity, causal set theory, and loop quantum gravity. (shrink)

Most approaches to quantum gravity suggest that relativistic spacetime is not fundamental, but instead emerges from some non-spatiotemporal structure. This paper investigates the implications of this suggestion for the possibility of time travel in the sense of the existence of closed timelike curves in some relativistic spacetimes. In short, will quantum gravity reverse or strengthen general relativity’s verdict that time travel is possible?

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no-go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time machine. (...) We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently “potent” to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident “yes” has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer. (shrink)

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter introduces causal set theory and identifies and articulates a 'problem of space' in this theory.

This paper issues a call to arms and seeks to entice the reader with some of the most captivating philosophical puzzles arising in quantum gravity. The analysis will be prefaced, in Section 1, by general considerations concerning the need for finding a quantum theory of gravity and the methods used in the pursuit of this goal. After mapping the field in Section 2, loop quantum gravity is introduced as an important competitor and particularly rich source of philosophical trouble in Section (...) 3. The so-called problem of time, i.e. the puzzle that no genuine physical quantity can change, is discussed in Section 4. Finally, Section 5 analyzes how the familiar continuous spacetime structure might re-emerge from the fundamental, non-spatiotemporal structure. (shrink)

This volume offers an integrated understanding of how the theory of general relativity gained momentum after Einstein had formulated it in 1915. Chapters focus on the early reception of the theory in physics and philosophy and on the systematic questions that emerged shortly after Einstein's momentous discovery. They are written by physicists, historians of science, and philosophers, and were originally presented at the conference titled Thinking About Space and Time: 100 Years of Applying and Interpreting General Relativity, held at the (...) University of Bern from September 12-14, 2017. By establishing the historical context first, and then moving into more philosophical chapters, this volume will provide readers with a more complete understanding of early applications of general relativity and of related philosophical issues. Because the chapters are often cross-disciplinary, they cover a wide variety of topics related to the general theory of relativity. These include: Heuristics used in the discovery of general relativity Mach's Principle The structure of Einstein's theory Cosmology and the Einstein world Stability of cosmological models The metaphysical nature of spacetime The relationship between spacetime and dynamics The Geodesic Principle Symmetries Thinking About Space and Time will be a valuable resource for historians of science and philosophers who seek a deeper knowledge of the uses of general relativity, as well as for physicists and mathematicians interested in exploring the wider historical and philosophical context of Einstein's theory. (shrink)

We investigate Kerr–Newman black holes in which a rotating charged ring-shaped singularity induces a region which contains closed timelike curves (CTCs). Contrary to popular belief, it turns out that the time orientation of the CTC is oppo- site to the direction in which the singularity or the ergosphere rotates. In this sense, CTCs “counter-rotate” against the rotating black hole. We have similar results for all spacetimes sufficiently familiar to us in which rotation induces CTCs. This motivates our conjecture that perhaps (...) this counter-rotation is not an accidental oddity particular to Kerr–Newman spacetimes, but instead there may be a general and intuitively comprehensible reason for this. (shrink)

Physical time plays a different role in general relativity than in quantum mechanics and the particle physics based on it. The first section of this chapter provides a brief survey of the main approaches to quantum gravity and then proceeds to consider the lessons that can be drawn from two distinct strategies for discovering a theory of quantum gravity. In the next section, the chapter first explicates the fate of time in approaches to quantum gravity that start with general relativity (...) (GR) and attempt to quantize it. Second, it investigates approaches to quantum gravity that start from quantum particle physics. The third and fourth sections respectively offer an assessment of time as understood in string theory and 'non‐commutative' field theory. One of the important possibilities for time in quantum gravity is that it might fail to commute with space. (shrink)

Recent years have seen a growing consensus in the philosophical community that the grandfather paradox and similar logical puzzles do not preclude the possibility of time travel scenarios that utilize spacetimes containing closed timelike curves. At the same time, physicists, who for half a century acknowledged that the general theory of relativity is compatible with such spacetimes, have intensely studied the question whether the operation of a time machine would be admissible in the context of the same theory and of (...) its quantum cousins. A time machine is a device which brings about closed timelike curves—and thus enables time travel—where none would have existed otherwise. The physics literature contains various no-go theorems for time machines, i.e., theorems which purport to establish that, under physically plausible assumptions, the operation of a time machine is impossible. We conclude that for the time being there exists no conclusive no-go theorem against time machines. The character of the material covered in this article makes it inevitable that its content is of a rather technical nature. We contend, however, that philosophers should nevertheless be interested in this literature for at least two reasons. First, the topic of time machines leads to a number of interesting foundations issues in classical and quantum theories of gravity; and second, philosophers can contribute to the topic by clarifying what it means for a device to count as a time machine, by relating the debate to other concerns such as Penrose's cosmic censorship conjecture and the fate of determinism in general relativity theory, and by eliminating a number of confusions regarding the status of the paradoxes of time travel. The present article addresses these ambitions in as non-technical a manner as possible, and the reader is referred to the relevant physics literature for details. (shrink)

A journey surveying the land of space, time and motion Content Type Journal Article Category Book Review Pages 1-4 DOI 10.1007/s11016-011-9575-8 Authors Christian Wüthrich, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0119, USA Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter sketches how spacetime emerges in causal set theory and demonstrates how this question is deeply entangled with genuinely philosophical concerns.

In support of a recent conjecture by Nielsen (1999), we prove that the phenomena of ‘incomparable entanglement’— whereby, neither member of a pair of pure entangled states can be transformed into the other via local operations and classical communication (LOCC)—is a generic feature when the states at issue live in an infinite-dimensional Hilbert space.  2002 Elsevier Science B.V. All rights reserved.

Hilary Putnam has argued that from a realist perspective, quantum mechanics stands in need of an interpretation. Ironically, this hypothesis may appear vulnerable against arguments drawing on Putnam's own work. Nancy Cartwright has urged that his 1962 essay on the meaning of theoretical terms suggests that quantum mechanics needs no interpretation and thus stands in tension with his claim of three years later. She furthermore contends that this conflict should be resolved in favour of the earlier work, as quantum mechanics, (...) like all successful theories, does not need an interpretation. The first part of this essay deflates both of these objections. The second part addresses and evaluates Putnam's own assessments of the main interpretative options available in 1965 and 2005. Although we may disagree on some aspects, his pessimistic conclusion will come out largely unscathed, and, in fact, enhanced. I will close by briefly stating the historical relevance of this work. (shrink)

We investigate the fate of determinism in general relativity, comparing the philosopher’s account with the physicist’s well-posed initial value formulations. The fate of determinism is interwoven with the question of what it is for a spacetime to be ‘physically reasonable’. A central concern is the status of global hyperbolicity, a putatively necessary condition for determinism in GR. While global hyperbolicity may fail to be true of all physically reasonable models, we analyze whether global hyperbolicity should be imposed by fiat; established (...) from weaker assumptions, as in cosmic censorship theorems; or justified by beyond-GR physics. (shrink)

Quantum gravity’s suggestion that spacetime may be emergent and so only exist contingently would force a radical reconception of extant analyses of laws of nature. Humeanism presupposes a spatiotemporal mosaic of particular matters of fact on which laws supervene; primitivism and dispositionalism conceive of the action of primitive laws or of dispositions as a process of ‘nomic production’ unfolding over time. We show how the Humean supervenience basis of non-modal facts and primitivist or dispositionalist accounts of nomic production can be (...) reconceived, avoiding a reliance on fundamental spacetime. However, it is unclear that naturalistic forms of Humeanism can maintain their commitment to there being no necessary connections among distinct entities. Furthermore, non-temporal conceptions of production render this central concept more elusive than before. In fact, the challenges run so deep that the survival of the investigated analyses into the era of quantum gravity is questionable. (shrink)

We discuss the possibility to build and operate a time machine, a device that produces closed timelike curves. We specify the spacetime structure needed to implement a time machine and assess attempted no-go results against time machines in classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and in Euclidean quantum gravity. Such no-go theorems for time machines would show that, under physically reasonable conditions, CTCs cannot develop in spacetimes initially free of these pathologies. Our review indicates (...) that an investigation of the prospects of achieving no-go results has not been entirely successful in establishing such generality. At the same time, the pursuit of chronology protection results has proved to be a fruitful way to probe the foundations of classical GTR and the interface between general relativity and quantum field theory. (shrink)

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. This chapter analyses the nature and derivation of spacetime topology and geometry according to string theory.

We address the question of whether it is possible to operate a time machine by manipulating matter and energy so as to manufacture closed timelike curves. This question has received a great deal of attention in the physics literature, with attempts to prove no- go theorems based on classical general relativity and various hybrid theories serving as steps along the way towards quantum gravity. Despite the effort put into these no-go theorems, there is no widely accepted definition of a time (...) machine. We explain the conundrum that must be faced in providing a satisfactory definition and propose a resolution. Roughly, we require that all extensions of the time machine region contain closed timelike curves; the actions of the time machine operator are then sufficiently "potent" to guarantee that closed timelike curves appear. We then review no-go theorems based on classical general relativity, semi-classical quantum gravity, quantum field theory on curved spacetime, and Euclidean quantum gravity. Our verdict on the question of our title is that no result of sufficient generality to underwrite a confident "yes" has been proven. Our review of the no-go results does, however, highlight several foundational problems at the intersection of general relativity and quantum physics that lend substance to the search for an answer. (shrink)

This is a chapter of the planned monograph "Out of Nowhere: The Emergence of Spacetime in Quantum Theories of Gravity", co-authored by Nick Huggett and Christian Wüthrich and under contract with Oxford University Press. (More information at www<dot>beyondspacetime<dot>net.) This chapter introduces the problem of emergence of spacetime in quantum gravity. It introduces the main philosophical challenge to spacetime emergence and sketches our preferred solution to it.

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 the fundamental entities can't be smaller than the derived by assumption and so can't '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)

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.