Quantum Gravity: A Primer for Philosophers∗ Dean Rickles ‘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.1 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. 1 The Strange Case of Quantum Gravity Quantum gravity involves the unification of the principles of quantum theory and gen- eral relativity. Constructing such a theory constitutes one of the greatest challenges in theoretical physics. It is a particularly hard challenge for many reasons, both formal and conceptual, some of which I aim to elucidate in what follows. Even up until the 1970s, quantum gravity was, as Michael Duff remarks, “a subject ... pursued only by mad dogs and Englishmen” ([Duff, 1999], p. 185). That is something of an exagger- ation, of course: for starters, when Duff speaks of quantum gravity, he has in mind the particle physicist’s approach to the problem, according to which the gravitational ∗Appeared in D. Rickles (ed.), The Ashgate Companion to Contemporary Philosophy of Physics. Ash- gate, 2008. Please cite the published version. 1Unlike the chapters on quantum theory and statistical mechanics—less so quantum information theory— this chapter is, therefore, mainly devoted to spelling the various research programmes out, without quite so much emphasis on the nitty gritty philosophical problems. 1 interaction involves an exchange of gravitons (the quanta of the gravitational field). However, quantum gravity, understood as the general unificatory problem sketched above, has been pursed for around eighty years in some form or another, by many of the greatest physicists, many of whom were not English! The remark has more than a grain truth to it though; even now quantum gravity research is looked upon with some trepidation and, often, bemusement. This attitude stems primarily from the extreme de- tachment of quantum gravity research from experimental physics—a feature that leads Nambu [1985] to refer to quantum gravity research as “postmodern physics”! As a re- sult, much of the research conducted in quantum gravity looks like an exercise in pure mathematics or, sometimes, metaphysics. This aspect makes quantum gravity espe- cially interesting from a philosophical point of view, as I shall attempt to demonstrate throughout this chapter. Quantum gravity is, in fact, rather curious from the point of view of the philosopher of physics because it is one of the few areas of contemporary physics where (some of) the physicists who are central figures in the field actively engage with philosophers, col- laborating with them, participating in philosophy conferences, and contributing chap- ters to philosophical books and journals (a pair of recent examples are: [Callender and Huggett, 2001], and [Rickles et al., 2006]). Carlo Rovelli, co-founder of one of the main lines of attack known as ‘loop quantum gravity’, explicitly invites philosophers’ cooperation, writing (in an essay from another philosophy collection: [Earman and Norton, 1997]): As a physicist involved in this effort [quantum gravity—DR], I wish the philosophers who are interested in the scientific description of the world would not confine themselves to commenting and polishing the present fragmentary physical theories, but would take the risk of trying to look ahead.([Rovelli, 1997], p. 182) Similarly, John Baez—a mathematical physicist who has done important work in mak- ing loop gravity rigorous—(again writing in a philosophical collection: [Callender and Huggett, 2001]) writes: Can philosophers really contribute to the project of reconciling general relativity and quantum field theory? Or is this a technical business best left to the experts? [...] General relativity and quantum field theory are based on some profound insights about the nature of reality. These insights are crystallized in the form of mathematics, but there is a limit to how much progress we can make by just playing around with this mathematics. We need to go back to the insights behind general relativity and quantum field theory, learn to hold them together in our minds, and dare to imagine a world more strange, more beautiful, but ultimately more reasonable than our current theories of it. For this daunting task, philosophical reflection is bound to be of help. ([Baez, 2001], p. 177) This ‘intellectually open’ attitude, coupled with what we might call the ‘fluid’ state of play in quantum gravity, makes it possible that philosophers of physics might get involved with the constructive business of physics, as the philosopher Tian Yu Cao 2 points out, “with a good chance to make some positive contributions, rather than just analysing philosophically what physicists have already established” ([Cao, 2001], p. 183).2 However, the exact nature of these ‘positive contributions’ is still unclear at the present stage, though this primer will point out some possible directions. However, perhaps the most important reason for the introduction of philosophical reflection in the area of quantum gravity research is, as suggested above, the fact that it does not (thus far) have the character of an empirical problem: current physics, as exemplified by the standard model of particle physics plus general relativity, does not contradict any piece of experimental evidence.3 What matters most, in quantum grav- ity, is internal consistency, in the sense of some particular approach to the problem being logically coherent, and external compatibility, in the sense of the particular ap- proach being compatible with our most well-established background knowledge (i.e. with what we know from both theory and experiment)—cf. [t’Hooft, 2001]. These constraints do not appear to be sufficiently stringent to uniquely determine the desired theory of quantum gravity; instead there are multiple research avenues that each seem to satisfy the constraints (or at least approximate them). The extent to which the vari- ous approaches are really quantum theories of gravity is somewhat controversial: string theory is only known at a perturbative level (as is quantum electrodynamics), which is not sufficient to provide the full theory of quantum gravity we are seeking; loop quan- tum gravity faces (amongst other problems) a ‘reconstruction problem’ according to which classical general relativity is not demonstrably proven to be its classical limit. This problem aside, satisfying these demands can often direct the specific research programmes into conceptual problems that philosophers are well acquainted with— problems to do with the nature of space, time, matter, causality, change, identity, sub- stance, and so on (i.e. the warhorses of traditional philosophy). We discuss this aspect in the next section, and also consider what the possible motivations of quantum gravity research might be if not empirical ones. Let us now turn to the general characterization of quantum gravity—this primarily involves explaining the nature of the problem that such a theory is intended to resolve. We will then give a brief history of quantum gravity. After this, we shall present the central ideas required from the ingredient theories of quantum gravity, namely quantum theory and general relativity. Then we can turn our attention to the various approaches aimed at reconciling these two theories. We then consider several issues of ‘special interest’: the nature and roleˆ of background independence, the experimental status of 2We should not get too carried away though, and ought to heed Dirac’s warning—self-professed enemy of philosophy though he was—that “[u]nless such [philosophical] ideas have a mathematical basis they will be ineffective” ([Dirac, 1978], p. 1). What the above quotations are intended to convey is the fact that ‘mathematical’ and ‘philosophical’ are woven together more tightly than usual in a great deal of quantum gravity research, not that we can make scientific progress by idle philosophical speculation. 3Very roughly, the standard model of particle physics is our best description of the strong nuclear, weak nuclear, and electromagnetic forces (or interactions)—of course, the standard model unifies the weak and electromagnetic into a single ‘electroweak’ force. It tells us that matter is composed of particles called ‘fermions’ bound together by the exchange of (strong, weak, and electromagnetic) force-carrying particles called ‘bosons’. Gravity is not included in the interactions treated in the standard model. Some quantum gravity researchers—especially those from the particle physics community—view the search for a quantum theory of gravity as tantamount to the search for a unified description of all interactions.