Studies in History and Philosophy of Modern Physics 46 (2014) 186–199 Contents lists available at ScienceDirect Studies in History and Philosophy of Modern Physics journal homepage: www.elsevier.com/locate/shpsb Disappearance and emergence of space and time in quantum gravity Daniele Oriti Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Golm, Germany article info abstract Article history: We discuss the hints for the disappearance of continuum space and time at microscopic scale. These Received 12 February 2013 include arguments for a discrete nature of them or for a fundamental non-locality, in a quantum theory Accepted 31 October 2013 of gravity. We discuss how these ideas are realized in specific quantum gravity approaches. Turning then Available online 25 December 2013 the problem around, we consider the emergence of continuum space and time from the collective Keywords: behaviour of discrete, pre-geometric atoms of quantum space, and for understanding spacetime as a kind Quantum gravity of “condensate”, and we present the case for this emergence process being the result of a phase Emergence transition, dubbed “geometrogenesis”. We discuss some conceptual issues of this scenario and of the idea Spacetime of emergent spacetime in general. As a concrete example, we outline the GFT framework for quantum Cosmology gravity, and illustrate a tentative procedure for the emergence of spacetime in this framework. Last, we Condensed matter theory re-examine the conceptual issues raised by the emergent spacetime scenario in light of this concrete Quantum condensates example. & 2013 Elsevier Ltd. All rights reserved. When citing this paper, please use the full journal title Studies in History and Philosophy of Modern Physics 1. Introduction: philosophy of quantum gravity “in the There has been an enormous progress in several approaches to making” quantum gravity, in recent years, and in particular in the ones we will be focusing on, group field theories, spin foam models and Quantum Gravity is a hard problem. Besides the technical loop quantum gravity. This has led to concrete suggestions for the difficulties of developing and applying the right mathematics, fundamental degrees of freedom, to interesting proposals for the adapted to a background independent context, the main difficul- fundamental quantum dynamics, and even physical applications in ties are conceptual. One is to imagine first, and then identify in simplified context (e.g. symmetry reduced models in cosmology). mathematical terms, the fundamental degrees of freedom of the The “problem of the continuum” or “the issue of the emergence of theory. The next one is to show how the quantum dynamics of spacetime and geometry” remains open. This is, in our opinion, the such fundamental degrees of freedom leads to an effective most pressing issue that quantum gravity approaches have to classical behaviour described, at least in some approximation, by tackle. Indeed, it is the real challenge even assuming that the true General Relativity. If the fundamental degrees of freedom are not fundamental degrees of freedom of quantum gravity have been spatio-temporal in the usual sense, that is, they are not associated found. Such degrees of freedom would be of a different nature to a smooth spacetime manifold (as the basic variable of GR, the than anything else we have learned to deal with up to now, in spacetime metric), then one faces an additional challenge: to show usual spacetime-based physics, and many of the tools that we have that the spacetime continuum itself, and the relative geometric developed to describe similar micro-to-macro and few-to-many variables1 arise at least as a useful approximation to the more transitions in ordinary physical systems, e.g. in condensed matter fundamental structures the theory is based on. theory, would have to be at the very least adapted to this new background independent context and reinterpreted accordingly. Beyond the technical difficulties, this is necessarily going to be a conceptual tour-de-force. E-mail address: [email protected] It is here that philosophy can and should help the development of 1 In this paper, we focus on pure gravity and geometry, leaving aside the theoretical physics. Clarify the conceptual basis of quantum gravity coupling (or the emergence) of matter and gauge fields. While this is of course an approaches, smoothen the tortuous reasoning of theoretical physicists important issue, we do not feel that the problem of emergence of spacetime, as phrased here will be much affected by adding other degrees of freedom in the towards a solution of the continuum conundrum, alert them of hidden picture. assumptionsorprejudicesandofshaky conceptual foundations for 1355-2198/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.shpsb.2013.10.006 D. Oriti / Studies in History and Philosophy of Modern Physics 46 (2014) 186–199 187 their theories, force them to be honest and rigorous in their thinking, One preliminary thing to notice is that, even if the strategy of and not only in their mathematics. This is what we believe philoso- simply applying standard quantization methods to the metric field phers working on the foundations of spacetime theories, and of was successful (and within the usual interpretative framework of quantum gravity in particular, should do. In this respect, we cannot quantum mechanics now applied to spacetime as a whole), the but agree with Huggett and Wütrich (2013) on the need to perform resulting picture of spacetime would be highly non-standard. The philosophical investigations in parallel with the formal development of basic quantum observables would be operators corresponding to the the theory, rather than arrive on the stage after the show has taken metric field (or to equivalent geometric quantities, like the gravita- place, only to elaborate on it, while theoretical physicists are then tional connection) and quantum states would carry a representation of struggling with preparing a new one.2 such observables. Straightforward consequences of the quantum The obvious problem is that a philosophical reflection based on formalism would be the quantum uncertainties in the determination the ongoing, tentative work of theoretical physicists on models of the same geometric quantities, possibly a discrete structure of their that, most likely, will turn out to be incorrect or only partially spectra, the superposition of metric states and thus of causal struc- understood in the future will also be resting on shaky grounds, tures, and so on. A description of spacetime in which these phenom- sharing the same risks of future irrelevance. In addition, if the ena take place could hardly be considered as a minor modification of ground on which these philosophical reflections take place is that the classical one. Still, one could argue that the resulting weirdness of quantum gravity theories, they will also have to struggle among would be purely a result of the quantization process, to be removed in very abstract or yet-to-be developed mathematics and some a classical limit. In a sense, the usual continuum spacetime concepts conceptual darkness, and without much input from experiments would simply be mapped to weirder ones, their quantum counter- (which is much less true in other areas of theoretical physics). parts, by the quantization map, but not dismissed altogether for a new Well, the only reaction we feel is appropriate to these last worries conceptual scheme. As said, to cope conceptually with the resulting is “Welcome to the club!” quantum framework would be already challenging (as it can be seen Another point we agree on with Huggett and Wütrich (2013) is in simplified schemes like quantum cosmologies, Ashtekar & Singh, that philosophical reflection, if it has to be serious and concrete, 2011), but something even more radical seems to be needed.4 needs concrete examples, on which general reasoning can be applied. The notion of spacetime localization is challenged already in semi- Thus, in this paper, we offer to philosophers a brief discussion classical GR, i.e. simply considering quantum fields in a curved of the hints of a non-fundamental nature of continuum space and spacetime, the intuitive idea being that any attempt at exact localiza- time and the usual spacetime physics, a flying survey of how these tion would imply probing spacetime events with such a concentration hints are realized in some quantum gravity approaches, a scenario of energy in such small spacetime regions, that the event itself would for the emergence of spacetime in quantum gravity, a concrete be hidden by the formation of a horizon. This idea is at the root of framework for realizing this scenario (the group field theory some models of quantum spacetime based on non-commutative framework) and an explicit (if tentative) working example of what geometry (Dolplicher, Fredenhagen, & Roberts, 1995), and it is only such an emergence process could be like, in this framework. Along one of the many general arguments for the existence of a minimal the way, while we will not enter into any detailed discussion of length scale, usually associated to the Planck scale, beyond which the philosophical issues related to the idea of emergent spacetime local description of events of a spacetime continuum ceases to make (let alone emergence tout court), we will not refrain for comment- sense. The associated model building, aimed at an effective level of ing on some of