* Idea: A theory describing the structure of spacetime down to subplanckian scales, and for an arbitrary number of occupied states; Often considered as a theory in which the spacetime metric is quantized (beyond quantum field theory in curved spacetime or semiclassical gravity – includes back-reaction), as well as possibly other geometrical structures – it describes gravitation as well as quantum geometry.
* Goal: We want to get a complete, consistent theory with well-defined general relativity limit.
* History: Serious work on quantum gravity began in the early 1950s; Until the 1970s only gravity was included, not matter fields.
* 2016: There is a feeling that gravitation and spacetime will be closely related to, maybe even emergent from, quantum entanglement.
* Difficulties: (1) gab is both gravitational field and metric, there is no background metric, so how to write canonical commutation relations?; (2) Perturbative non-renormalizability, which could be similar to the UV catastrophe before quantum mechanics (> see covariant quantum gravity); (3) Unbounded action; (4) Conceptual difficulty, What is time, What are the observables? (5) The need to incorporate the full diffeomorphism group as symmetry group.
* Issues: How much to retain of the classical general relativity technical and conceptual structure? How much of quantum theory? What matter to include? Which predictions do we expect to get? What is the vacuum? Is the theory unitary? CPT invariant? Is gravity geometrical at the quantum level? (There are arguments to the contrary, based on gravity-induced interference, > see wave phenomena); Must quantum gravity be background-independent? (Related to relational vs absolute spacetime debate).
* Interpretation: Within "conventional" interpretations, the many-worlds one is possible; The Copenhagen and the statistical ones require some "mental acrobacies"; & Banks; Susskind; Unruh & Wald.
Different sectors: see 2D quantum gravity; 3D
Approaches: see conventional approaches [including algebraic, perturbative, ...], canonical, covariant, histories, and modified approaches.
On Whether to Quantize > s.a. emergent gravity; general
semiclassical general relativity [problems].
* Theoretical arguments: (0) Similarity with other theories; (1) Structure of Einstein's equation, and inconsistency of a quantum field theory on a curved background, or semiclassical general relativity, with back-reaction; (2) Remove the singularities predicted by the classical theory (by, say, interference between amplitudes for various geometries, smearing of light-cones, cancellations in supergravity); (3) Understand black-hole (and horizon) thermodynamics; (4) Help us understand why the renormalization methods work and get a coherent picture of quantum field theories of all interactions (may help in unification); (5) Help solve the cosmological constant problem.
* Observational evidence: One indication may come from the analysis of cmb polarization.
* Rem: Bohr's argument for quantizing the electromagnetic field does not apply in this case [@ Baym & Ozawa PNAS(09)-a0902].
* Alternatives: The most straightforward alternative is to couple classical gravity and quantum matter according to the semiclassical Einstein equation, which leads to a non-linear so-called Schrödinger-Newton equation for matter; Some people (& Narlikar, Padmanabhan) have proposed to quantize only the conformal factor; This would be natural in the null-surface approach to general relativity, but it is not convincing; Another possibility is that gravity is emergent and does not need to be directly quantized.
@ General references: Kent in(09)gq/05 [proposed local causality test]; Wüthrich PhSc(05)dec [effective gravity as alternative]; Carlip CQG(08)-a0803-conf [not conclusive]; Wüthrich in(13)-a1207 [philosophical]; Carballo-Rubio et al a1502-conf [and relational nature of the theory]; Bahrami et al a1507 [proposed optomechanics experiment].
@ Support for quantization: Eppley & Hannah FP(77); Page & Geilker PRL(81); Adelman a1510 [modified Eppley-Hannah thought experiment]; Marletto & Vedral a1703 [including generalized quantum theory].
@ Alternatives: Hossenfelder PLB(13)-a1208 [perturbative quantization of gravity as an effective theory], a1212-FQXi [neither classical nor quantized]; Altamirano et al CQG(17)-a1605 [continuous quantum measurements and feedforward, and emergent dark energy]; > s.a. quantum theory in curved spacetimes.
@ Against need to quantize: von Borzeszkowski FP(90); Drechsler FP(93); Huggett & Callender PhSc(01)S; Mohrhoff MPLA(02)qp; de Souza gq/02; Cooperstock IJMPD(05); Albers et al PRD(08)-a0802 [justification does not follow from logical arguments alone]; Boughn FP(09)-a0809 [non-quantum]; Slavnov TMP(12).
General Features of the Theory
@ And quantum information: Schiffer GRG(93); Srednicki NPB(93); Itzhaki CQG(95)ht; Zizzi GRG(01)gq/00-conf; Lloyd qp/05/Sci; Girelli & Livine CQG(05)gq [with spin networks]; Terno JPCS(06)gq/05 [lqg and black holes]; Kempf FP(14) [simulation on a quantum computer]; Gyongyosi a1401 [information processing structure]; Bao et al a1704-GRF [locally finite-dimensional Hilbert space]; > s.a. approaches; black holes [as computers]; black-hole thermodynamics; discrete spacetime; information; quantum information.
@ And hep / strings: Maldacena IJMPA(00)hp-conf; Álvarez gq/03-conf; Bjerrum-Bohr PhD(04)ht; Berenstein AIP(10)-a1010 [from quantum field theory and AdS/cft]; Nicolai conf(14)-a1301 [particle physics perspective].
@ Statistical methods: Damgaard et al ed-90; Botelho PRD(95) [random surfaces]; Ambjørn et al 97; > s.a. geometrodynamics.
@ Related topics: Husain & Jaimungal MPLA(99)gq-proc [phase transitions]; Raptis IJTP(07)gq/06 [abstract differential geometry]; Saida JPCS(13)-a1301 [thermodynamics]; Chang et al IJMPD(13)-a1305 [as super-quantum theory]; Dittrich et al a1508 [potential problems from chaotic nature of theory].
> Main aspects: see effective action; quantum spacetime; semiclassical theory [including stability, ground state]; spacetime structure [emergent].
> Formalism and techniques: see computational physics [s.a. Stephen Braham's 1995 page]; differential geometry; renormalization.
> And other field theories: see anomaly; Correspondence Principle; quantum fields in curved spacetime.
> Phenomenology: see in general, and cosmology, matter, photons; collapse; inflation; quantum cosmology.
> Related issues: see Covariance; CP violation; CPT symmetry; symmetry breaking; time; vacuum.
References > s.a. anthropic principle;
history of physics.
@ I / II: Ashtekar Rech(84); Gibbons NS(85); Sánchez 87; Isham in(89); PW(90)mar; Renteln AS(91); Au gq/95; Hawking & Penrose SA(96)jul; Norbury EJP(98)phy; Smolin pw(99)dec; Amelino-Camelia Nat(00)gq; Smolin 00; Chalmers pw(03)nov + issue; Hammond 08; Bojowald 10; Rovelli 16.
@ Reviews: Isham in(75), in(81), in(86), pr(91), CQG(96); Ashtekar ht/94-conf; Shiekh gq/96-conf; Rovelli gq/98-GR15; Wallace gq/00; Horowitz gq/00-MG9; Kiefer LNP(03); Smolin ht/03; Álvarez LNP(05)gq/04; Ashtekar NJP(05)gq/04; Kiefer AdP(06)gq/05; Rovelli in(09)gq/06; Markopoulou in(09)gq/07 [background-independent]; Booß-Bavnbek et al Sigma(07)-a0708, LNP(10)-a0911; DeWitt & Esposito IJGMP(08)-a0711-ln; Woodard RPP(09)-a0907; Esposito a1108-en; Paszko a1205-talk [intro]; Vaid a1402 ["for dummies"]; Lukierski a1404-ch, Ashtekar et al a1408-in [overviews of approaches]; Schulz a1409; Carlip et al IJMPD(15)-a1507-in.
@ Texts: Narlikar & Padmanabhan 87; von Borzeszkowski & Treder 88; Prugovečki 92, 95; Pavšič 01; Rovelli 04; Kiefer 12; Rovelli & Vidotto 14 [intro]; Manoukian 16.
@ Collections: Isham et al 75; Isham et al 81; Duff & Isham 82; Christensen 84; Markov et al 85, 88; Gibbons & Hawking 93 [euclidean]; Rickles et al ed-06 [structural, r CQG(07), SHPMP(09)]; Fauser et al ed-07 [techniques]; Oriti ed-09; Barrett et al ed PoS(11) [Zakopane 2011]; Murugan et al ed-12; Calcagni et al ed-13.
@ General: Rosenfeld AdP(30); Bronstein PZS(36); Misner RMP(57); Arnowitt & Deser PR(59); Bergmann & Komar in(62); DeWitt in(62), in(63); Bergmann pr(69); Komar IJTP(69); DeWitt GRG(70); Bergmann GRG(71); Ashtekar & Geroch RPP(74); DeWitt in(79); Ashtekar CS(80); Padmanabhan IJMPA(89); Prugovečki FP(92); Penrose in(88); Álvarez RMP(89), in(92); DeWitt GRG(09)-ln, err GRG(09); Ziaeepour JPCS(09)-a0901; Strominger NPPS(09)-a0906 [five open problems]; Dvali & Gómez a1005 [scale and self-completeness]; Álvarez JPCS(11)-a1011 [lessons from the standard model]; Heller et al FP(11) [fundamental problems]; Kitamoto & Kitazawa NPB(13)-a1211 [quantization-scheme dependence of IR effects]; Smolin a1610 [four principles]; in Manoukian 16; Smolin a1705 [reflections].
@ Conflicts between quantum theory and gravity: Isham gq/95-GR14 [structural issues]; Padmanabhan in(99)ht/98; 't Hooft SHPMP(01); Padmanabhan CQG(02)gq/01-conf; Greenberger a1011-conf; Singh a1703-fs.
@ Other difficulties: von Borzeszkowski & Treder GRG(93) [from the equivalence principle].
@ Features of the theory: Isham LNP(94)gq/93 [prima facie questions]; Sudarsky IJMPD(08)-a0712-in [unspeakables].
@ Other conceptual: Butterfield & Isham in(01)gq/99; Rovelli JMP(00)gq/99; Aerts IJTP(96); Cao SHPMP(01) [ontological synthesis]; Carlip RPP(01)gq [rev]; Rovelli IJMPD(03)ht [and strings, dialog]; Smolin ht/05 [background independence]; Stachel gq/05-in, gq/06; Rickles SHPMP(05) [interpretation]; Rosinger qp/05 [questions]; Rosen FP(08); Hedrich a0908; Koch AIP(10)-a1004 [geometry as more fundamental]; Zeh EPJH(11) [and Feynman's interpretation of quantum theory]; Lindesay 13; Stachel & Bradonjić SHPMP(14)-a1302 [meaning and measurement, ecumenical approach]; Döring a1306 [realist vs instrumentalist interpretations]; Holman SHPMP(14)-a1308 [empirical principles]; Kiefer ISRN(13)-a1401; Kober a1510-PhD; Gomes a1603 [defining superpositions of causal structures]; Susskind a1708 [thoughts]; > s.a. logic; Relationalism.
> Websites: see Qgravity.org site; Quantum Spacetime and Fields site; Cambridge University quantum gravity site; Quantum Tetrahedron site.
> Pages and articles: see John Baez's seminar; Seth Major's page; John Barrett's page; Scholarpedia article and category; Wikipedia page; Answers.com page; Ken Koehler's site; Stephen Wolfram's page.
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