Quantum gravity poses the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a (...) detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time. (shrink)

A number of philosophers have argued in favour of extended simples on the grounds that they are needed by fundamental physics. The arguments typically appeal to theories of quantum gravity. To date, the argument in favour of extended simples has ignored the fact that the very existence of spacetime is put under pressure by quantum gravity. We thus consider the case for extended simples in the context of different views on the existence of spacetime. We show (...) that the case for extended simples based on physics is far more complex than has been previously thought. We present and then map this complexity, in order to present a much more textured picture of the argument for extended simples. (shrink)

A number of recent theories of quantum gravity lack a one-dimensional structure of ordered temporal instants. Instead, according to many of these views, our world is either best represented as a single three-dimensional object, or as a configuration space composed of such three-dimensional objects, none of which bear temporal relations to one another. Such theories will be empirically self-refuting unless they can accommodate the existence of conscious beings capable of representation. For if representation itself is impossible in a (...) timeless world, then no being in such a world could entertain the thought that a timeless theory is true, let alone believe such a theory or rationally believe it. This paper investigates the options for understanding representation in a three-dimensional, timeless, world. Ultimately it concludes that the only viable option is one according to which representation is taken to be deeply non-naturalistic. Ironically then we are left with two seemingly very unattractive options. Either a very naturalistic motivation—taking seriously a live view in fundamental physics—leads us to a very non-naturalistic view of the mental, or else views in the philosophy of mind partly dictate what is an acceptable theory in physics. (shrink)

‘Quantum Gravity’ does not denote any existing theory: the field of quantum gravity is very much a ‘work in progress’. As you will see in this chapter, there are multiple lines of attack each with the same core goal: to find a theory that unifies, in some sense, general relativity (Einstein’s classical field theory of gravitation) and quantum field theory (the theoretical framework through which we understand the behaviour of particles in non-gravitational fields). Quantum (...) field theory and general relativity seem to be like oil and water, they don’t like to mix—it is fair to say that combining them to produce a theory of quantum gravity constitutes the greatest unresolved puzzle in physics. Our goal in this chapter is to give the reader an impression of what the problem of quantum gravity is; why it is an important problem; the ways that have been suggested to resolve it; and what philosophical issues these approaches, and the problem itself, generate. This review is extremely selective, as it has to be to remain a manageable size: generally, rather than going into great detail in some area, we highlight the key features and the options, in the hope that readers may take up the problem for themselves—however, some of the basic formalism will be introduced so that the reader is able to enter the physics and (what little there is of) the philosophy of physics literature prepared. I have also supplied references for those cases where I have omitted some important facts. Hence, this chapter is intended primarily as a catalyst for future research projects by philosophers of physics, both budding and well-matured. (shrink)

The correspondence principle made of unitarity, locality and renormalizability has been very successful in quantum field theory. Among the other things, it helped us build the standard model. However, it also showed important limitations. For example, it failed to restrict the gauge group and the matter sector in a powerful way. After discussing its effectiveness, we upgrade it to make room for quantum gravity. The unitarity assumption is better understood, since it allows for the presence of physical (...) particles as well as fake particles (fakeons). The locality assumption is applied to an interim classical action, since the true classical action is nonlocal and emerges from the quantization and a later process of classicization. The renormalizability assumption is refined to single out the special role of the gauge couplings. We show that the upgraded principle leads to an essentially unique theory of quantum gravity. In particular, in four dimensions, a fakeon of spin 2, together with a scalar field, is able to make the theory renormalizable while preserving unitarity. We offer an overview of quantum field theories of particles and fakeons in various dimensions, with and without gravity. (shrink)

We present a reformulation of loop quantum gravity with a cosmological constant and no matter as a Fermi-liquid theory. When the topological sector is deformed and large gauge symmetry is broken, we show that the Chern–Simons state reduces to Jacobson’s degenerate sector describing 1+1 dimensional propagating fermions with nonlocal interactions. The Hamiltonian admits a dual description which we realize in the simple BCS model of superconductivity. On one hand, Cooper pairs are interpreted as wormhole correlations at the de (...) Sitter horizon; their number yields the de Sitter entropy. On the other hand, BCS is mapped into a deformed conformal field theory reproducing the structure of quantum spin networks. When area measurements are performed, Cooper-pair insertions are activated on those edges of the spin network intersecting the given area, thus providing a description of quantum measurements in terms of excitations of a Fermi sea to superconducting levels. The cosmological constant problem is naturally addressed as a nonperturbative mass-gap effect of the true Fermi-liquid vacuum. (shrink)

Relationships between current theories, and relationships between current theories and the sought theory of quantum gravity (QG), play an essential role in motivating the need for QG, aiding the search for QG, and defining what would count as QG. Correspondence is the broad class of inter-theory relationships intended to demonstrate the necessary compatibility of two theories whose domains of validity overlap, in the overlap regions. The variety of roles that correspondence plays in the search for QG are illustrated, (...) using examples from specific QG approaches. Reduction is argued to be a special case of correspondence, and to form part of the definition of QG. Finally, the appropriate account of emergence in the context of QG is presented, and compared to conceptions of emergence in the broader philosophy literature. It is argued that, while emergence is likely to hold between QG and general relativity, emergence is not part of the definition of QG, and nor can it serve usefully in the development and justification of the new theory. (shrink)

What it would take to vindicate folk temporal error theory? This question is significant against a backdrop of new views in quantum gravity—so-called timeless physical theories—that claim to eliminate time by eliminating a one-dimensional substructure of ordered temporal instants. Ought we to conclude that if these views are correct, nothing satisfies the folk concept of time and hence that folk temporal error theory is true? In light of evidence we gathered, we argue that physical theories that entirely eliminate (...) an ordered substructure vindicate folk temporal error theory. (shrink)

The central thesis of this paper is that contemporary theoretical physics is grounded in philosophical presuppositions that make it difficult to effectively address the problems of subject-object interaction and discontinuity inherent to quantum gravity. The core objectivist assumption implicit in relativity theory and quantum mechanics is uncovered and we see that, in string theory, this assumption leads into contradiction. To address this challenge, a new philosophical foundation is proposed based on the phenomenology of Maurice Merleau-Ponty and Martin (...) Heidegger. Then, through the application of qualitative topology and hypernumbers, phenomenological ideas about space, time, and dimension are brought into focus so as to provide specific solutions to the problems of force-field generation and unification. The phenomenological string theory that results speaks to the inconclusiveness of conventional string theory and resolves its core contradiction. (shrink)

The quest for a theory of quantum gravity is usually understood to be driven by philosophical assumptions external to physics proper. It is suspected that specifically approaches in the context of particle physics are rather based on metaphysical premises than experimental data or physical arguments. I disagree. In this paper, I argue that the quest for a theory of quantum gravity sets an important example of physics’ internal unificatory practice. It is exactly Weinberg’s and others’ particle (...) physics stance that reveals the issue of quantum gravity as a genuine physical problem arising within the framework of quantum field theory. (shrink)

The search for a quantum theory of the gravitational field is one of the great open problems in theoretical physics. This book presents a self-contained discussion of the concepts, methods and applications that can be expected in such a theory. The two main approaches to its construction - the direct quantisation of Einstein's general theory of relativity and string theory - are covered. Whereas the first attempts to construct a viable theory for the gravitational field alone, string theory assumes (...) that a quantum theory of gravity will be achieved only through a unification of all the interactions. However, both employ the general method of quantisation of constrained systems, which is described together with illustrative examples relevant for quantum gravity. There is a detailed presentation of the main approaches employed in quantum general relativity: path-integral quantisation, the background-field method and canonical quantum gravity in the metric, connection and loop formulations. The discussion of string theory centres around its quantum-gravitational aspects and the comparison with quantum general relativity. Physical applications discussed at length include the quantisation of black holes, quantum cosmology, the indications of a discrete structure of spacetime, and the origin of irreversibility. This book will be of interest to researchers and students working in relativity and gravitation, cosmology, quantum field theory and related topics. It will also be of interest to mathematicians and philosophers of science. (shrink)

It has long been thought that observing distinctive traces of quantum gravity in a laboratory setting is effectively impossible, since gravity is so much weaker than all the other familiar forces in particle physics. But the quantum gravity phenomenology community today seeks to do the (effectively) impossible, using a challenging novel class of `tabletop' Gravitationally Induced Entanglement (GIE) experiments, surveyed here. The hypothesized outcomes of the GIE experiments are claimed by some (but disputed by others) (...) to provide a `witness' of the underlying quantum nature of gravity in the non-relativistic limit, using superpositions of Planck-mass bodies. We inspect what sort of achievement it would possibly be to perform GIE experiments, as proposed, ultimately arguing that the positive claim of witness is equivocal. Despite various sweeping arguments to the contrary in the vicinity of quantum information theory or given low-energy quantum gravity, whether or not one can claim to witness the quantum nature of the gravitational field in these experiments decisively depends on which out of two legitimate modelling paradigms one finds oneself in. However, by situating GIE experiments in a tradition of existing experiments aimed at making gravity interestingly quantum in the laboratory, we argue that, independently of witnessing or paradigms, there are powerful reasons to perform the experiments, and that their successful undertaking would indeed be a major advance in physics. (shrink)

In the author’s previous contribution to this journal (Rosen 2015), a phenomenological string theory was proposed based on qualitative topology and hypercomplex numbers. The current paper takes this further by delving into the ancient Chinese origin of phenomenological string theory. First, we discover a connection between the Klein bottle, which is crucial to the theory, and the Ho-t’u, a Chinese number archetype central to Taoist cosmology. The two structures are seen to mirror each other in expressing the psychophysical (phenomenological) action (...) pattern at the heart of microphysics. But tackling the question of quantum gravity requires that a whole family of topological dimensions be brought into play. What we find in engaging with these structures is a closely related family of Taoist forebears that, in concert with their successors, provide a blueprint for cosmic evolution. Whereas conventional string theory accounts for the generation of nature’s fundamental forces via a notion of symmetry breaking that is essentially static and thus unable to explain cosmogony successfully, phenomenological/Taoist string theory entails the dialectical interplay of symmetry and asymmetry inherent in the principle of synsymmetry. This dynamic concept of cosmic change is elaborated on in the three concluding sections of the paper. Here, a detailed analysis of cosmogony is offered, first in terms of the theory of dimensional development and its Taoist (yin-yang) counterpart, then in terms of the evolution of the elemental force particles through cycles of expansion and contraction in a spiraling universe. The paper closes by considering the role of the analyst per se in the further evolution of the cosmos. (shrink)

A nonstandard viewpoint to quantum gravity is discussed. General relativity and quantum mechanics are to be related as two descriptions of the same, e.g. as Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics merged in the contemporary quantum mechanics. From the viewpoint of general relativity one can search for that generalization of relativity implying the in-variance “within – out of” of the same system.

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)

EPR-type measurements on spatially separated entangled spin qubits allow one, in principle, to detect curvature. Also the entanglement of the vacuum state is affected by curvature. Here, we ask if the curvature of spacetime can be expressed entirely in terms of the spatial entanglement structure of the vacuum. This would open up the prospect that quantum gravity could be simulated on a quantum computer and that quantum information techniques could be fully employed in the study of (...) quantum gravity. (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)

This is a nontechnical overview of how various approaches to quantum gravity suggest modifications to the way we conceptualize space and time. A theory of quantum gravity is needed to reconcile quantum physics with general relativity, our best theory for gravity. The most popular approaches to quantum gravity are string theory and loop quantum gravity. So far, no approach has been empirically successful, and there is no commonly accepted theory. Thus, (...) the conclusions presented here are tentative. Many approaches suggest that space and time—or perhaps, it is better to talk about spacetime—might not be fundamental. Various views on how to think about time in quantum gravity are briefly presented. (shrink)

I examine the early history of quantum gravity and comment on its suitability as an episode that demands an integrated approach to history and philosophy of science.

Eternalism, the view that what we regard locally as being located in the past, the present and the future equally exists, is the best ontological account of temporal existence in line with special and general relativity. However, special and general relativity are not fundamental theories and several research programs aim at finding a more fundamental theory of quantum gravity weaving together all we know from relativistic physics and quantum physics. Interestingly, some of these approaches assert that time (...) is not fundamental. If time is not fundamental, what does it entail for eternalism and the standard debate over existence in time? First, I will argue that the non-fundamentality of time to be found in string theory entails standard eternalism. Second, I will argue that the non-fundamentality of time to be found in loop quantum gravity entails atemporal eternalism, namely a novel position in the spirit of standard eternalism. (shrink)

The quest for a theory of quantum gravity is usually understood to be driven by philosophical assumptions external to physics proper. It is suspected that specifically approaches in the context of particle physics are rather based on metaphysical premises than experimental data or physical arguments. I disagree. In this paper, I argue that the quest for a theory of quantum gravity sets an important example of physics’ internal unificatory practice. It is exactly Weinberg’s and others’ particle (...) physics stance that reveals the issue of quantum gravity as a genuine physical problem arising within the framework of quantum field theory. (shrink)

I propose an experiment that may be performed, with present low temperature and cryogenic technology, to reveal Wheeler’s quantum foam. It involves coupling an optical photon’s momentum to the center of mass motion of a macroscopic transparent block with parameters such that the latter is displaced in space by approximately a Planck length. I argue that such displacement is sensitive to quantum foam and will react back on the photon’s probability of transiting the block. This might allow determination (...) of the precise scale at which quantum fluctuations of space–time become large, and so differentiate between the brane-world and the traditional scenarios of spacetime. (shrink)

This is an essay review of two textbooks on quantum gravity by Carlo Rovelli and Claus Kiefer.

In this paper, I discuss whether the results of loop quantum gravity (LQG) constitute a fatal blow to Humeanism. There is at least a prima facie reason for believing so: while Humeanism regards spatiotemporal relations as fundamental, LQG describes the fundamental layer of our reality in terms of spin networks, which are not in spacetime. However, the question should be tackled more carefully. After explaining the importance of the debate on the tenability of Humeanism in light of LQG, (...) and having presented the Humean doctrine, I review two cases which present serious threats to Humeanism, one concerning the fundamentality of vectorial quantities and the other concerning quantum entanglement. In particular, I recall the strategies that are usually employed in these two cases in order to save Humeanism: in the first case, the strategy consists in amending the characterization of the Humean mosaic; in the second case, it consists in adopting a realist or nomological interpretation of the wave function. These solutions will turn out to be helpful in my discussion of LQG where, after describing LQG, I show that Humeans might save their doctrine either by endorsing a realist interpretation of spin networks, or by giving them a nomological status and, at the same time, by revisiting the characterization of the Humean mosaic. However, I conclude that both solutions are wanting. (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)

What is spacetime? General relativity and quantum field theory answer this question in very different ways. This collection of essays by physicists and philosophers looks at the problem of uniting these two most fundamental theories of our world, focusing on the nature of space and time within this new quantum framework, and the kind of metaphysical picture suggested by recent developments in physics and mathematics. This is a book that will inspire further philosophical reflection on recent advances in (...) modern physics. (shrink)

In a case study Kuhn's morphology of scientific revolutions is put to the test in confronting it with the contemporary developments in physics. It is shown in detail, that Kuhn's scheme is not compatible with the situation in physics today.

This self-contained letter shows how ψ-epistemic quantum gravity (QG), that is, QG with a ψ-epistemic interpretation of quantum theory, in principle obtains from a deterministic model of the Elementary Process Theory (EPT) that describes an individual process at supersmall (Planck) scale by which a predominantly gravitational interaction takes place. While both ψ-epistemic QG and the model of the EPT remain to be formulated rigorously, this shows how the probabilistic nature of our knowledge of the physical world emerges (...) in a strictly deterministic universe--God does not play dice, it is our knowledge of the outcome of a process that is fundamentally probabilistic. -/- Edit: a completely worked-out and majorly revised version of this letter-type preprint has been published as a book chapter. (shrink)

Quantum gravity is supposed to be the most fundamental theory, including a quantum theory of the metrical field (spacetime). However, it is not clear how a quantum theory of gravity could account for classical phenomena, including notably measurement outcomes. But all the evidence that we have for a physical theory is based on measurement outcomes. We consider this problem in the framework of canonical quantum gravity, pointing out a dilemma: all the available accounts (...) that admit classical phenomena presuppose entities with a well-defined spatio-temporal localization (“local beables” in John Bell's terms) as primitive. But there seems to be no possibility to include such primitives in canonical quantum gravity. However, if one does not do so, it is not clear how entities that are supposed to be ontologically prior to spacetime could give rise to entities that then are spatio-temporally localized. (shrink)

Physicists who work on canonical quantum gravity will sometimes remark that the general covariance of general relativity is responsible for many of the thorniest technical and conceptual problems in their field.1 In particular, it is sometimes alleged that one can trace to this single source a variety of deep puzzles about the nature of time in quantum gravity, deep disagreements surrounding the notion of ‘observable’ in classical and quantum gravity, and deep questions about the (...) nature of the existence of spacetime in general relativity. Philosophers who think about these things are sometimes skeptical about such claims. We have all learned that Kretschmann was quite correct to urge against Einstein that the “General Theory of Relativity” was no such thing, since any theory could be cast in a generally covariant form, and hence the general covariance of general relativity could not have any physical content, let alone bear the kind of weight that Einstein expected it to.2 Friedman’s assessment is widely accepted: “As Kretschmann first pointed out in 1917, the principle of general covariance has no physical content whatever: it specifies no particular physical theory; rather, it merely expresses our commitment to a certain style of formulating physical theories” (1984, p. 44). Such considerations suggest that general covariance, as a technically crucial but physically contentless feature of general relativity, simply cannot be the source of any significant conceptual or physical problems.3 Physicists are, of course, conscious of the weight of Kretschmann’s points against Einstein. Yet they are considerably more ambivalent than their philosophical colleagues. Consider Kuchaˇr’s conclusion at the end of a discussion of this topic. (shrink)

There is a philosophical tradition of arguing against presentism, the thesis that only presently existing things exist, on the basis of its incompatibility with fundamental physics. I grant that presentism is incompatible with special and general relativity, but argue that presentism is not incompatible with quantum gravity, because there are some theories of quantum gravity that utilize a fixed foliation of spacetime. I reply to various objections to this defense of presentism, and point out a flaw (...) in Gödel's modal argument for the ideality of time. This paper provides an interesting case study of the interplay between physics and philosophy. (shrink)

The conceptual incompatibility between General Relativity and Quantum Mechanics is generally seen as a sufficient motivation for the development of a theory of Quantum Gravity. If - so a typical argumentation - Quantum Mechanics gives a universally valid basis for the description of the dynamical behavior of all natural systems, then the gravitational field should have quantum properties, like all other fundamental interaction fields. And, if General Relativity can be seen as an adequate description of (...) the classical aspects of gravity and spacetime - and their mutual relation -, this leads, together with the rather convincing arguments against semi-classical theories of gravity, to a strategy which takes a quantization of General Relativity as the natural avenue to a theory of Quantum Gravity. And, because in General Relativity the gravitational field is represented by the spacetime metric, a quantization of the gravitational field would in some sense correspond to a quantization of geometry. Spacetime would have quantum properties. But, this direct quantization strategy to Quantum Gravity will only be successful, if gravity is indeed a fundamental interaction. Only if it is a fundamental interaction, the given argumentation is valid, and the gravitational field, as well as spacetime, should have quantum properties. - What, if gravity is instead an intrinsically classical phenomenon? Then, if Quantum Mechanics is nevertheless fundamentally valid, gravity can not be a fundamental interaction; a classical and at the same time fundamental gravity is excluded by the arguments against semi-classical theories of gravity. An intrinsically classical gravity in a quantum world would have to be an emergent, induced or residual, macroscopic effect, caused by a quantum substrate dominated by other interactions, not by gravity. Then, the gravitational field (as well as spacetime) would not have any quantum properties. And then, a quantization of gravity (i.e. of General Relativity) would lead to artifacts without any relation to nature. The serious problems of all approaches to Quantum Gravity that start from a direct quantization of General Relativity (e.g. non-perturbative canonical quantization approaches like Loop Quantum Gravity) or try to capture the quantum properties of gravity in form of a 'graviton' dynamics (e.g. Covariant Quantization, String Theory) - together with the, meanwhile, rich spectrum of (more or less advanced) theoretical approaches to an emergent gravity and/or spacetime - make this latter option more and more interesting for the development of a theory of Quantum Gravity. The most advanced emergent gravity (and spacetime) scenarios are of an information-theoretical, quantum-computational type. A paradigmatic model for the emergence of gravity and spacetime comes from the Pregeometric Quantum Causal Histories approach. (shrink)

Recently there has been a great deal of interest in tabletop experiments intended to exhibit the quantum nature of gravity by demonstrating that it can induce entanglement. In order to evaluate these experiments, we must determine if there is any interesting class of possibilities that will be convincingly ruled out if it turns out that gravity can indeed induce entanglement. In particular, since one argument for the significance of these experiments rests on the claim that they demonstrate (...) the existence of superpositions of spacetimes, it is important to keep in mind that different interpretations of quantum mechanics may make different predictions about superpositions of spacetimes. ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-complete interpretations of quantum mechanics, like the Everett interpretation, almost universally predict the existence of superpositions of spacetimes, whereas in ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete, ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-nonphysical interpretations it seems more natural to predict that spacetime superpositions are not possible. Meanwhile ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete, ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-supplemented interpretations present us with a more complex picture where we may or may not end up predicting that spacetime superpositions are possible, depending on the particular way in which the coupling between spacetime and matter is constructed. This line of reasoning suggests that what would be ruled out by a successful result to these tabletop experiments is a class of quantum gravity models that we refer to as ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete quantum gravity —i.e. models of the interaction between quantum mechanics and gravity in which gravity is coupled to non-quantum beables rather than quantum beables. It follows that the results of tabletop experiments can also be regarded as giving us new evidence about the interpretation of quantum mechanics: roughly speaking, a positive result to these experiments should increase our confidence in ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-complete interpretations, whilst a negative result should instead increase our confidence in ψ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\psi$$\end{document}-incomplete interpretations. We introduce these ideas in Sect. 1, and then in Sect. 2 we make the reasoning more precise by presenting a set of inferences that may be made about the ontology of quantum mechanics based on the results of tabletop experiments. In Sect. 3 we discuss some existing PIQG models and consider what more needs to be done to make these sorts of approaches more appealing. There are two competing paradigms for the interpretation of these experiments, which have been dubbed the ‘Newtonian’ paradigm and the ‘tripartite’ paradigm: here we largely work within the tripartite paradigm, because the tripartite view is specifically concerned with ontological aspects of the mediating gravitational interaction and that makes it a suitable setting for enquiries about the ontology of quantum mechanics, but in Sect. 4 we consider what conclusions can be drawn if one does not presuppose the tripartite view. Finally in Sect. 5 we discuss a cosmological phenomenon which could be regarded as providing evidence for PIQG models. (shrink)

The mutual conceptual incompatibility between General Relativity and Quantum Mechanics / Quantum Field Theory is generally seen as the most essential motivation for the development of a theory of Quantum Gravity. It leads to the insight that, if gravity is a fundamental interaction and Quantum Mechanics is universally valid, the gravitational field will have to be quantized, not at least because of the inconsistency of semi-classical theories of gravity. The objective of a theory (...) of Quantum Gravity would then be to identify the quantum properties and the quantum dynamics of the gravitational field. If this means to quantize General Relativity, the general-relativistic identification of the gravitational field with the spacetime metric has to be taken into account. The quantization has to be conceptually adequate, which means in particular that the resulting quantum theory has to be background-independent. This can not be achieved by means of quantum field theoretical procedures. More sophisticated strategies, like those of Loop Quantum Gravity, have to be applied. One of the basic requirements for such a quantization strategy is that the resulting quantum theory has a classical limit that is (at least approximately, and up to the known phenomenology) identical to General Relativity. However, should gravity not be a fundamental, but an induced, residual, emergent interaction, it could very well be an intrinsically classical phenomenon. Should Quantum Mechanics be nonetheless universally valid, we had to assume a quantum substrate from which gravity would result as an emergent classical phenomenon. And there would be no conflict with the arguments against semi-classical theories, because there would be no gravity at all on the substrate level. The gravitational field would not have any quantum properties to be captured by a theory of Quantum Gravity, and a quantization of General Relativity would not lead to any fundamental theory. The objective of a theory of 'Quantum Gravity' would instead be the identification of the quantum substrate from which gravity results. The requirement that the substrate theory has General Relativity as a classical limit – that it reproduces at least the known phenomenology – would remain. The paper tries to give an overview over the main options for theory construction in the field of Quantum Gravity. Because of the still unclear status of gravity and spacetime, it pleads for the necessity of a plurality of conceptually different approaches to Quantum Gravity. (shrink)

The paper surveys the possibility of keeping a neo-Kantian approach in the face of Loop Quantum Gravity. Together with a preliminary analysis of Cassirer’s re-interpretation of Kantian philosophy that allowed him to harmonize the a priori cognitions with the theory of relativity and quantum mechanics, it will focus on the distinction between constitutive and regulativea priori. In this way, the paper will suggest that despite Rovelli’s refutation of Kant’s interpretation of space and time, he seems, at least (...) implicitly, to hold to a couple of neo-Kantian assumptions: the usage of constitutivea priori principlessuch as granularity, indeterminism and partially relation, and the claim for functionalism as a rule in ordering the ‘appearances’. (shrink)

Introduction: The Winding Road to Quantum Gravity Abhay Ashtekar Traveler, there are no paths; Paths are made by walking. ...

In this paper we consider a naive conception of what a quantum theory of gravity might entail: a quantum-mechanically fluctuating gravitational field at each spacetime point. We argue that this idea is problematic both conceptually and technically.

We review connections between the metric of spacetime and the quantum fluctuations of fields. We start with the finding that the spacetime metric can be expressed entirely in terms of the 2-point correlator of the fluctuations of quantum fields. We then discuss the open question whether the knowledge of only the spectra of the quantum fluctuations of fields also suffices to determine the spacetime metric. This question is of interest because spectra are geometric invariants and their quantization (...) would, therefore, have the benefit of not requiring the modding out of diffeomorphisms. Further, we discuss the fact that spacetime at the Planck scale need not necessarily be either discrete or continuous. Instead, results from information theory show that spacetime may be simultaneously discrete and continuous in the same way that information can. Finally, we review the recent finding that a covariant natural ultraviolet cutoff at the Planck scale implies a signature in the cosmic microwave background that may become observable. (shrink)

We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory contains an evolution equation distinct from standard Wheeler–DeWitt cosmology. Furthermore, the local symmetry principle—and corresponding observables—of the theory have a direct interpretation in terms of a conventional gauge theory, where the gauge symmetry group is that of spatial conformal diffeomorphisms (that preserve the spatial volume of the (...) Universe). The global evolution is in terms of an arbitrary parameter that serves only as an unobservable label for successive states of the Universe. Our proposal follows unambiguously from a suggestion of York whereby the independently specifiable initial data in the action principle of General Relativity is given by a conformal geometry and the spatial average of the York time on the spacelike hypersurfaces that bound the variation. Remarkably, such a variational principle uniquely selects the form of the constraints of the theory so that we can establish a precise notion of both symmetry and evolution in quantum gravity. (shrink)

The local Lorentz and diffeomorphism symmetries of Einstein's gravitational theory are spontaneously broken by a Higgs mechanism by invoking a phase transition in the early universe, at a critical temperature Tc below which the symmetry is restored. The spontaneous breakdown of the vacuum state generates an external time, and the wave function of the universe satisfies a time-dependent Schrödinger equation, which reduces to the Wheeler-deWitt equation in the classical regime for T (...) The conservation of energy is spontaneously violated for T>Tc, and matter is created fractions of seconds after the big bang, generating the matter in the Universe. The time direction of the vacuum expectation value of the scalar Higgs field generates a time asymmetry, which defines the cosmological arrow of time and the direction of increasing entropy as the Lorentz symmetry is restored at low temperatures. (shrink)

This essay presents an alternative to contemporary substantivalist and relationist interpretations of quantum gravity hypotheses by means of an historical comparison with the ontology of space in the seventeenth century. Utilizing differences in the spatial geometry between the foundational theory and the theory derived from the foundational, in conjunction with nominalism and platonism, it will be argued that there are crucial similarities between seventeenth century and contemporary theories of space, and that these similarities reveal a host of underlying (...) conceptual issues that the substantival/relational dichotomy fails to distinguish. (shrink)

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.

The paper discusses the philosophical conclusions, which the interrelation between quantum mechanics and general relativity implies by quantum measure. Quantum measure is three-dimensional, both universal as the Borel measure and complete as the Lebesgue one. Its unit is a quantum bit (qubit) and can be considered as a generalization of the unit of classical information, a bit. It allows quantum mechanics to be interpreted in terms of quantum information, and all physical processes to be (...) seen as informational in a generalized sense. This implies a fundamental connection between the physical and material, on the one hand, and the mathematical and ideal, on the other hand. Quantum measure unifies them by a common and joint informational unit. Furthermore the approach clears up philosophically how quantum mechanics and general relativity can be understood correspondingly as the holistic and temporal aspect of one and the same, the state of a quantum system, e.g. that of the universe as a whole. The key link between them is the notion of the Bekenstein bound as well as that of quantum temperature. General relativity can be interpreted as a special particular case of quantum gravity. All principles underlain by Einstein (1918) reduce the latter to the former. Consequently their generalization and therefore violation addresses directly a theory of quantum gravity. Quantum measure reinterprets newly the “Bing Bang” theories about the beginning of the universe. It measures jointly any quantum leap and smooth motion complementary to each other and thus, the jump-like initiation of anything and the corresponding continuous process of its appearance. Quantum measure unifies the “Big Bang” and the whole visible expansion of the universe as two complementary “halves” of one and the same, the set of all states of the universe as a whole. It is a scientific viewpoint to the “creation from nothing”. (shrink)

I argue that all current research programs in quantum gravity conform to the 17th century hypothetico-deductive model of scientific inquiry, perhaps of necessity given the current state of technology. In so far as they do not recognize and advertise the shortcomings of the research method they use, they do a disservice to the integrity of science, for the method admits of far less certainty accruing to its products than one would be led to believe by the pronouncements of (...) researchers in the area. (shrink)

A solution to the issue of time in quantum gravity is proposed. The hypothesis that time is not defined at the fundamental level (at the Planck scale) is considered. A natural extension of canonical Heisenberg-picture quantum mechanics is defined. It is shown that this extension is well defined and can be used to describe the "non-Schrödinger regime," in which a fundamental time variable is not defined. This conclusion rests on a detailed analysis of which quantities are the (...) physical observables of the theory; a main technical result of the paper is the identification of a class of gauge-invariant observables that can describe the (observable) evolution in the absence of a fundamental definition of time. The choice of the scalar product and the interpretation of the wave function are carefully discussed. The physical interpretation of the extreme "no time" quantum gravitational physics is considered. (shrink)

The theory of unconstrained membranes of arbitrary dimension is presented. Their relativistic dynamics is described by an action which is a generalization of the Stueckelberg point-particle action. In the quantum version of the theory, the evolution of a membrane's state is governed by the relativistic Schrödinger equation. Particular stationary solutions correspond to the conventional, constrained membranes. Contrary to the usual practice, our spacetime is identified, not with the embedding space (which brings the problem of compactification), but with a membrane (...) of dimension 4 or higher. A 4-membrane is thus assumed to represent spacetime. The Einstein-Hilbert action emerges as an effective action after functionally integrating out the membrane's embedding functions. (shrink)