Classical and Quantum Aspects of Gravity in Relation to the Emergent Paradigm PDF
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Springer Theses Recognizing Outstanding Ph.D. Research Sumanta Chakraborty Classical and Quantum Aspects of Gravity in Relation to the Emergent Paradigm Springer Theses Recognizing Outstanding Ph.D. Research Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected foritsscientificexcellenceandthehighimpactofitscontentsforthepertinentfield of research. For greater accessibility to non-specialists, the published versions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explainingthespecialrelevanceoftheworkforthefield.Asawhole,theserieswill provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists. Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria (cid:129) They must be written in good English. (cid:129) ThetopicshouldfallwithintheconfinesofChemistry,Physics,EarthSciences, Engineeringandrelatedinterdisciplinary fields such asMaterials,Nanoscience, Chemical Engineering, Complex Systems and Biophysics. (cid:129) The work reported in the thesis must represent a significant scientific advance. (cid:129) Ifthethesisincludespreviouslypublishedmaterial,permissiontoreproducethis must be gained from the respective copyright holder. (cid:129) They must have been examined and passed during the 12 months prior to nomination. (cid:129) Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. (cid:129) The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field. More information about this series at http://www.springer.com/series/8790 Sumanta Chakraborty Classical and Quantum Aspects of Gravity in Relation to the Emergent Paradigm Doctoral Thesis accepted by Jawaharlal Nehru University, Pune, India 123 Author Supervisor Dr. SumantaChakraborty Prof. ThanuPadmanabhan Department ofTheoretical Physics Inter-University Centre for Astronomyand Indian Association for the Cultivation of Astrophysics (IUCAA) Science Pune Jadavpur, Kolkata, West Bengal India India ISSN 2190-5053 ISSN 2190-5061 (electronic) SpringerTheses ISBN978-3-319-63732-7 ISBN978-3-319-63733-4 (eBook) DOI 10.1007/978-3-319-63733-4 LibraryofCongressControlNumber:2017946667 ©SpringerInternationalPublishingAG2017 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. 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Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAG Theregisteredcompanyaddressis:Gewerbestrasse11,6330Cham,Switzerland To my grandparents—Prakash, Jharna, Samir and Binapani—for their love, inspiration and knowledge. To my parents—Subenoy and Archana—for everything. To my cousins—Sukriti and Poulomi—for their love and support. ’ Supervisor s Foreword CombiningtheprinciplesofGeneralRelativityandQuantumTheory—thetwokey developments in theoretical physics in twentieth century—is a major challenge which has attracted the attention of the community for more than half a century. Thesedecadesofexplorationhaveessentiallyledtoaseriesofresoundingfailures, very often after a period of initial hope and hype with regard to each of the approaches.(Infact,atanygiventimeduringlast50yearsorso,therewasasetof people who were ‘true believers’ in some particular approach they were pursuing, with the hope that the solution was just around the corner!). The current situation actuallyhasahistoricparallel.Atleasttwiceinthehistoryofphysics,verytalented people have got themselves stuck in a “local minimum” of a completely wrong idea.Thefirstwasinthecaseofthecalorifictheoryforheat;thesecondwasinthe theory of aether with matter arising as vortices and excitations of the aether. Ibelievethecurrentlypopularparadigmsofquantumgravitybelongtoyetanother case of very smart physicists pursuing very wrong ideas. So what could be a possible alternative route which can lift us above the “local minimum”? A major paradigm shift isrequired, which I can best illustrate with an analogy. We know that the elasticity (or fluid mechanics) can be described as a self-consistentphysicaltheoryintermsofasetofdynamicalequations.Ifonetakes these equations as fundamental and applies the principles of quantum theory to them, one will certainly discover interesting new phenomena, like, for example, phonons and their interactions. However, such an approach will not lead us to the quantum structure of matter. Similarly, there is sufficient evidence to suggest that the dynamical equationsdescribing gravity (in a large class ofmodels including— but not limited to—Einstein’s theory) have the same conceptual status as the equations of elasticity or fluid mechanics. Reinterpreting gravitational field equa- tionsusingtheprinciplesofquantumtheoryisanalogoustoattemptsinwhichone is applying the quantum principles to the equations of, say, elasticity. While some interesting new results will emerge, we will not discover the quantum nature of spacetime by such an approach. Whatisrequiredistore-examinecloselythestructureofgravitationaldynamics andtrytolearnwhatittellsusaboutthemicroscopicstructureofspacetime.Sucha vii viii Supervisor’sForeword top-down approach (in length scales) is precisely what Boltzmann used, to figure out that matter is made of discrete degrees offreedom, because it exhibits thermal phenomenon. The fact that null surfaces in a spacetime appear to be hot to certain observers holds the key to the understanding of the microstructure of spacetime. Onlyaformalism which(i)recognizesthisfactupfront and(ii) canadopt itselfto an observer dependent thermodynamics of spacetime will ever have a chance of succeedingincombiningtheprinciplesofgravityandquantumtheory.Mostofthe popularmodelsofquantumgravity,whichcameandwent(orontheirway-out!)in the last five decades, did not do justice to this fact. I and my collaborators have been exploring, since 2002, several aspects of this alternative paradigm in which the thermodynamics of null surfaces plays a crucial role. SumantaChakraborty’sthesis dealtwithseveralaspects ofthisparadigmina nice and comprehensivemanner. Thefirstpart of thethesis providesthenecessary broad introduction and the remaining chapters of the thesis deal directly with several questions which are vital to the emergent paradigm of gravity. In particular, Sumanta has made a significant amount of progress in extending theemergentparadigmtoaclassofmodelscalledtheLanczos-Lovelockmodelsof gravity. These are theories of gravity in which the field equations remain second order in time but the entropy of the horizon is not proportional to its area. In the literature,oneoftenfindsveryimaginativepiecesofresearchwhich—unfortunately— are strongly linked to the idea that the entropy of a horizon is proportional to its area.TheLanczos-Lovelockmodelsofgravitytakeyououtofthecomfort-zonein whichentropyissuchanicegeometricalquantity,viz.thehorizonarea.Sotheyact as a viable test-bed for the ideas of emergent gravity. If any of the ideas or the resultswhichonecomeupwith,holdsonlyinEinstein’sGeneralRelativitybutnot in the Lanczos-Lovelock models of gravity, I would treat it with caution. It is therefore remarkable—and gratifying—that virtually every key idea within the emergent paradigm developed by our group could be extended to Lanczos-Lovelock models of gravity and Sumanta’s thesis contains several examples of this extension. In a broader context, this fact tells you that the ther- modynamic connection transcends Einstein’s theory and should be viewed as a more fundamental feature of spacetime, not too closely linked to the specific field equations describing the gravitational dynamics. IenjoyedworkingwithSumantathroughhisPh.D.phaseandIwishhimallthe bestinhisfuturecareer.IalsocongratulateSpringerforhavingthisprogramme,of bringing out good theses as books, which both provides an encouragement to the students as well as creating topical reference works for the community. Prof. Thanu Padmanabhan Thesis Advisor Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India Preface General Relativity (GR) is a very successful theory and is the best formalism we have to describe the geometrical properties of the spacetime. It has passed all the experimental and observational scrutinies so far, ranging from local tests like perihelion precession and bending of light to precision tests using pulsars. Inspiteoftheseoutstandingsuccessestherestillremainsomeunresolvedissues, suggestingthatgeneralrelativityisnotcomplete.Themostimportantreasonisthe presence of singularities in many physical situations leading to a loss of pre- dictability. Another reason has to do with the fact that the horizons in general relativity possess thermodynamic properties like temperature and entropy. Within the framework of general relativity, there is no natural explanation for this “ther- modynamic” interpretation and it provides motivation to take a fresh look at the theory. A third reason arises from the fact that all the other known interactions (electromagnetic, weak and strong) are described by quantum theories, while gravityaloneisstilldescribedbyaclassicaltheory.Thislaidthefoundationofthe belief that “quantum theory of gravity” awaits discovery. The attempts to obtain a perturbative quantum general relativity, taking a cue from the quantization of the other forces, has not succeeded. This has the unavoidable conclusion: we need to modify our understanding of quantum field theory or the understanding of general relativity or both. In this thesis, we try to understand the thermodynamic nature of general rela- tivity better by taking a closer look at the structure of general relativity and its higher curvature cousins, collectively called Lanczos-Lovelock gravity. If one can derive a result in the context of Lanczos-Lovelock gravity, the result for general relativity is encompassed by it as well. We shall analyze the geometrical structure ofLanczos-Lovelockgravity(whichhasgeneralrelativityasaspecialcase)leading to the inescapable connection between gravity and thermodynamics. We will also have occasion to talk about Virasoro algebra associated with an arbitrary null surface and associated entropy in this context. As a complementary approach towards a quantum theory of gravity, we study some aspects of quantum field theory in curved spacetime. The specific issues addressedinthis contextinclude: (a) What canwe sayaboutclassical singularities ix x Preface from the viewpoint of quantum theory? This specifically requires one to probe quantumfieldsinsidetheblackholehorizon.(b)Istheretrievalofinformationfrom an evaporating black hole possible? (We will show that distortions to the thermal spectra of a particular kind, referred to as non-vacuum distortions can be used to fully reconstruct a subspace of initial data.) (c) Can Rindler effect be present for geodesic observers? We illustrate for a specific (1+1) black hole spacetime, there aregeodesicobserverswhoareconfinedtoaflatregionofthespacetimeandhence will experience Rindler effect. Finally,inorder tocapturesome quantumgravityeffects,we haveintroduced a zeropointlengthtothespacetimeandhavediscusseditsgeometricalconsequences. In particular, we have shown that at the Planck scale the spacetime becomes essentially two-dimensional. Kolkata, India Sumanta Chakraborty
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