Studies in History and Philosophy of Modern Physics

1 Research paperThree principles of quantum gravity in the condensed matter approachJonathan BainnPolytechnic Institute of New York University, Department of Technology, Culture and Society, 6 Metrotech Center, Brooklyn, NY 11201, USAarticle infoArticle History :Received 5 January 2013 Received in revised form22 June 2013 Accepted 15 September 2013 Keywords:Quantum gravityCondensed matterEffectivefield theoryAsymptotic safetyHolographyabstractResearch on quantum gravity (QG) has historically relied on appeals to guiding principles . This essayframes three such principles within the context of the condensed matter approach to QG.

2 Ifirst identifytwo distinct versions of this approach, and then consider the extent to which the principles of asymptoticsafety, relative locality, and holography are supported by these versions. The general hope is that a focuson distinct versions of a single approach may provide insight into the conceptual and foundationalsignificance of these Elsevier Ltd. All rights citing this paper, please use the full journal titleStudies in History and Philosophy of Modern Physics1. IntroductionGuiding principles occur frequently in theory construction andjustification.

3 They appear in historical and conceptual accounts of bothrelativity theory (the principle of relativity, the equivalence principle,the geodesic principle,etc.), and quantum mechanics (the adiabatichypothesis, the principle of mechanical transformability, the corre-spondence principle, the exclusion principle,etc.). Such principles playimportant conceptual roles in stages of theory development duringwhich empirical testability is limited or non-existent. However, theirsignificance is not just restricted to being stand-ins for empiricaladequacy. Some authors have argued that guiding principles are afundamental characteristic of certain types of fully developed , appeals to principles , when combined with appealsto empirical adequacy, can offer powerful arguments in the context oftheory choice.

4 For instance, an argument due to Steven Weinbergclaims that quantumfield theory is the way it is because it is the onlyway to reconcile the empirical evidence for the theory with two basicguiding area of current research in which guiding principles play asignificant role in theory development is thefield of quantumgravity (QG, hereafter). There is currently little contact betweentheoretical work in QG and empirical tests, as a recent reviewmakes clear:Unfortunately, in spite of more than 70 years of theory work onthe quantum-gravity problem, and a certain proliferation oftheoretical frameworks being considered, there is only a smallnumber of physical effects that have been considered withinquantum-gravity theories.

5 Moreover, most of these effectsconcern strong-gravity/large-curvature contexts, such asblack-hole Physics and big-bang Physics , which are exciting atthe level of conceptual analysis and development of formalism,but of course are not very promising for the actual (experi-mental) discovery of manifestations of non-classical propertiesof spacetime and/or gravity (Amelino-Camelia, 2008, p. 7).The general hope is that at some point in the future, empiricaltestability will become more feasible; and even irrespective of this,the burgeoningfield of quantum gravity phenomenology hasmade it clear that there are other, perhaps more indirect, methodsof assessing the empirical status of various approaches to , however, in the absence of immediate empiricaltestability, many approaches to QG have relied on appeals toguiding essay is concerned with the extent to which a particularapproach to QG, the condensed matter approach, satisfies three suchprinciples: asymptotic safety, relative locality, and holography.

6 InContents lists available atScienceDirectjournal in History and Philosophyof Modern Physics1355-2198/$- see front matter&2013 Elsevier Ltd. All rights : 1 literature on Einstein s famous distinction between theories of principleand constructive theories is vast. See, ,Brown & Pooley (2006)and argument is summarized inWeinberg (1997)and analyzed inBain(1999).3 Thanks to a referee for stressing this cite this article as: Bain, J. Three principles of quantum gravity in the condensed matter in History andPhilosophy of Modern Physics (2013), in History and Philosophy of Modern Physics ( ) senses to be made more precise inSections 3 5below, theseprinciples state the following:Asymptotic safety: A theory of QG must scale towards anultra-violet (UV)fixed point with afinite number of UV-irrelevantcouplings.

7 (Weinberg, 1979)Relative locality: A theory of QG must entail that coincidenceof events in spacetime ( locality ) is relative to an observer srest frame. (Amelino-Camelia, Freidel, Kowalski-Gllikman, &Smolin, 2011a;Amelino-Camelia, Freidel, Kowalski-Gllikman,& Smolin, 2011b)Holography: A theory of QG must entail that the number offundamental degrees of freedom in any regionOof spacetimecannot exceedA/4, whereAis the surface area ofO.(Bousso, 2002)Asymptotic safety addresses a particular problem with reconcilinggeneral relativity (GR) and quantumfield theory (QFT); namely, whenGR is constructed as a QFT, it is non-renormalizable.

8 In this context,this means that when one expands relevant quantities in GR in aperturbative power series expansion, there are terms that diverge athigh energies and that cannot be regularized by renormalizing afinitenumber of parameters associated with the (2009), suggests that this has ..led to widespread pessimism about thepossibility of constructing a fundamental QFT of gravity. Instead, wehave become accustomed to thinking of general relativity (GR) as aneffectivefield theory, which only gives an accurate description ofgravitational Physics at low energies.

9 Weinberg (1979)suggested thatthis pessimism would be addressed if it could be shown that GR isasymptotically safe. In a sense to be made more precise below, anasymptotically safe theory is well-behaved at all energy scales andthus, perhaps, warrants the ascription of a fundamental theory. View-ing asymptotic safety as a guiding principle in the search for a theoryof QG takes Weinberg s suggestion seriously: If GR does happen topossess a UVfixed point, our search is over; if it happens that GR doesnot possess a UVfixed point, then we should be looking for QFTsdescribing gravity that locality is motivated by taking seriously the non-linearcomposition law for velocities in special relativity (Amelino-Camelia et al.)

10 , 2011a, p. 11). This law imposes an invariant scale,the speed of lightc, on the theory (provided one upholds theprinciple of relativity), which serves to demarcate the scale atwhich effects due to the non-linearity become relevant. This scalethen makes possible the mixing of spatial and temporal coordi-nates of an event under Lorentz transformations, and this entailsthe relativity of simultaneity ( , the relativity of coincidence oftemporal coordinates). If one assumes a similar non-linearity inthe composition of momenta, one is led to a mixing of spatio-temporal and 4-momentum coordinates of an event.