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

Summary 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.

A non-Abelian, Universal SpaceTime Ontology is introduced in terms of Categories, Functors, Natural Transformations, Higher Dimensional Algebra and the Theory of Levels. A Paradigm shift towards Non-Commutative Spacetime structures with remarkable asymmetries or broken symmetries, such as the CPT-symmetry violation, is proposed. This has the potential for novel applications of Higher Dimensional Algebra to SpaceTime structure determination in terms of universal, topological invariants of ‘hidden’ symmetry. Fundamental concepts of Quantum Algebra and Quantum Algebraic Topology, such as Quantum Groups, von Neumann (...) and Hopf Algebras are first considered with a view to their possible extensions and future applications in Quantum Field theories. New, non-Abelian results may be obtained through Higher Homotopy, General van Kampen Theorems, Lie Groupoids/Algebroids and Groupoid Atlases, possibly with novel applications to Quantum Dynamics and Local-to-Global Problems, Quantum Logics and Logic Algebras. Many-valued Logics, Łukasiewicz–Moisil Logics lead to Generalized LM-Toposes as global representations of SpaceTime Structures in the presence of intense Quantum Gravitational Fields. Such novel representations have the potential to develop a Quantum/General Relativity Theory in the context of Supersymmetry, Supergravity, Supersymmetry Algebras and the Metric Superfield in the Planck limit of spacetime. Quantum Gravity and Physical Cosmology issues are also considered here from the perspective of multiverses, thus leading also to novel types of Generalized, non-Abelian, Topological, Higher Homotopy Quantum Field Theories (HHQFT) and Non-Abelian Quantum Algebraic Topology (NA-QAT) theories. (shrink)

Substantivalists claim that spacetime enjoys an existence analogous to that of material bodies, while relationalists seek to reduce spacetime to sets of possible spatiotemporal relations. The resulting debate has been central to the philosophy of space and time since the Scientific Revolution. Recently, many philosophers of physics have turned away from the debate, claiming that it is no longer of any relevance to physics. At the same time, there has been renewed interest in the debate among physicists working on quantum (...) gravity, who claim that the conceptual problems which they face are intimately related to interpretative questions concerning general relativity (GR). My goal is to show that the physicists are correct—there is a close relationship between the interpretative issues of classical and quantum gravity. (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. (shrink)

Belot, Earman, and Ruetsche (1999) dismiss the black hole remnant proposal as an inadequate response to the Hawking information loss paradox. I argue that their criticisms are misplaced and that, properly understood, remnants do offer a substantial reply to the argument against the possibility of unitary evolution in spacetimes that contain evaporating black holes. The key to understanding these proposals lies in recognizing that the question of where and how our current theories break down is at the heart of these (...) debates in quantum gravity. I also argue that the controversial nature of assessing the limits of general relativity and quantum field theory illustrates the significance of attempts to establish the proper borders of our effective theories. (shrink)

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)

We discuss from a philosophical perspective the way in which the normal concept of time might be said to `emerge' in a quantum theory of gravity. After an introduction, we briefly discuss the notion of emergence, without regard to time (Section 2). We then introduce the search for a quantum theory of gravity (Section 3); and review some general interpretative issues about space, time and matter (Section 4). We then discuss the emergence of time in simple quantum geometrodynamics, and in (...) the Euclidean approach (Section 5). Section 6 concludes. (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)

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)

Loop quantum gravity predicts that spatial geometry is fundamentally discrete. Whether this discreteness entails a departure from exact Lorentz symmetry is a matter of dispute that has generated an interesting methodological dilemma. On one hand one would like the theory to agree with current experiments, but, so far, tests in the highest energies we can manage show no such sign of departure. On the other hand one would like the theory to yield testable predictions, and deformations of exact Lorentz symmetry (...) in certain yet– to–be–tested regimes may have phenomenological consequences. Exposing their shortcomings, here I discuss two arguments that exemplify this dilemma, and compare them to other cases from the history of physics that share their symptoms. (shrink)

This essay is a philosophical evaluation of some of the findings of Wald and Penrose in which they claim to have supported an arrow (or the irreversibility) of time in quantum gravity. First, the notion of lawlike irreversibility (or anisotropy) of time is spelled out, then the general situation in quantum mechanics is briefly discussed. Finally, the findings in quantum gravity are evaluated against such a background. My conclusion is that the arrow of time found in quantum gravity is at (...) best de facto (nonlawlike). (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)

‘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)

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

This volume closes that gap, with essays written by some of the leading researchers in the field.

He explores what might be called the metaphysics of physics, or maybe just its geometry: as the series title might suggest, topology plays a major role in the ...

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)

This paper addresses a central question of contemporary theoretical physics: Can a unified account be provided for the known forces of nature? The issue is brought into focus by considering the recently revived Kaluza-Klein approach to unification, a program entailing dimensional transformation through cosmogony. First it is demonstrated that, in a certain sense, revitalized Kaluza-Klein theory appears to undermine the intuitive foundations of mathematical physics, but that this implicit consequence has been repressed at a substantial cost. A fundamental reformulation of (...) the Kaluza-Klein strategy is then undertaken, one that casts it within a new intuitive context. This is followed by a provisional application of the suggested approach to the specific problem of cosmic evolution. The paper concludes by exploring the far-reaching epistemological implications of the "neo-intuitive" proposal set forth. (shrink)

Biographical Information: The author is a Professor of Physics at New York University. He has lectured widely in Europe and Latin America, including at the Università di Roma ``La Sapienza'' and, during the Sandinista government, at the Universidad Nacional Autónoma de Nicaragua. He is co-author with Roberto Fernández and Jürg Fröhlich of Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory (Springer, 1992).

An ontological approach to the analysis of conceptual frameworks of physical theories is introduced and then applied to the case of quantum gravity. The tension between the theoretical constraints posed, respectively, by general relativity and quantum field theory, is analysed. A possible solution to the difficulties created by the tension, based on the notion of ontological synthesis, is suggested.

This essay offers a reaction to the recent resurgence of presentism in the philosophy of time. What is of particular interest in this renaissance is that a number of recent arguments supporting presentism are crafted in an untypically naturalistic vein, breathing new life into a metaphysics of time with a bad track record of co-habitation with modern physics. Against this trend, the present essay argues that the pressure on presentism exerted by special relativity and its core lesson of Lorentz symmetry (...) cannot easily be shirked. A categorization of presentist responses to this pressure is offered. As a case in point, I analyze a recent argument by Monton (2006) presenting a case for the compatibility of presentism with quantum gravity. Monton claims that this compatibility arises because there are quantum theories of gravity that use fixed foliations of spacetime and that such fixed foliations provide a natural home for a metaphysically robust notion of the present. A careful analysis leaves Monton's argument wanting. In sum, the prospects of presentism to be alleviated from the stress applied by fundamental physics are faint. (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 physical—as opposed to metaphysical—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)

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)

This paper investigates some of the philosophical and conceptual issues raised by the search for a quantum theory of gravity. It is critically discussed whether such a theory is necessary in the first place, and how much would be accomplished if it is eventually constructed. I argue that the motivations behind, and expectations to, a theory of quantum gravity are entangled with central themes in the philosophy of science, in particular unification, reductionism, and the interpretation of quantum mechanics. I further (...) argue that there are —contrary to claims made on behalf of string theory— no good reasons to think that a quantum theory of gravity, if constructed, will provide a theory of everything, that is, a fundamental theory from which all physics in principle can be derived. (shrink)