Time in Quantum Gravity  

In General > s.a. 2D quantum gravity; 3D gravity; parametrized theories; quantum cosmology; time; topology change.
* The issue: Quantum gravity does not have a satisfactory interpretation (even minisuperspace models), mainly because of the difficulty of defining a measurement "made at a time t''; Time is merely an arbitrary label, only histories are meaningful; This is in addition to, and much more serious than, the problem that time measurements are subject to a quantum uncertainty; > s.a. quantum-gravity phenomenology [including minimum time].
@ Reviews: Isham in(92)gq, LNP(94)gq/93; Kuchař in(92); in Zeh 92; Macías & Quevedo gq/06-in; Anderson a1206.
@ General references: Torre PRD(92); Barbour PRD(93), CQG(94), CQG(94); Moffat FP(93); Kitada gq/94, & Fletcher Ap-gq/94; Unruh in(94)gq/93; Parentani gq/97-MG8; Shestakova & Simeone G&C(04)gq [canonical], G&C(04)gq [path integral]; Kiefer a0909-FQXi; Anderson ch(12)-a1009; Husain & Pawłowski PRL(12)-a1108, comment Świeżewski QCG(13)-a1307 [with dust and other fields, complete theory based on lqg]; Huggett et al a1207-in; Gryb & Thebault BJPS(15)-a1408 [time remains]; Małkiewicz a1601 [and quantum dynamics].
@ Time / spacetime as emergent: Singh IJMPD(10); Gomes a1706.
@ Arrow of time: Liu PhSc(93)dec; Ellis et al CSF(99)ht/98; Castagnino PRD(98)gq/96, et al CQG(02)gq [minisuperspace]; Jejjala et al Ent(12)-a1203.

After Quantization: From States > s.a. quantum cosmology.
* WKB interpretation: Assume Ψ = A exp(iS), nearly classical; From the Hamilton-Jacobi equation for S, we obtain trajectories in superspace; From these, we get a current.
* From quantum correlations: Time arises as an approximation, and the Hamiltonian formulation is appropriate for late times.
@ Quantum correlations: Wootters IJTP(84); Kiefer PRD(88).
@ Probabilistic time: Hartle in(87); Halliwell PRD(87) [correlations]; Castagnino in(88), PRD(89), in(90), & Mazzitelli PRD(90); Castagnino & Lombardo PRD(93) [and real clocks]; Abolhasani & Golshani gq/97; Khosravi & Sepangi PLB(09)-a0903.
@ Other: Bander gq/02 [vacuum expectation value of field energy]; Halliwell & Thorwart PRD(02) [and decoherent histories]; Lawrie PRD(11)-a1011.

Before Quantization: Intrinsic Time > s.a. canonical general relativity [dust as reference frame]; canonical quantum gravity [gauge fixing]; {& Ashtekar}.
* Idea: Time is a function of phase space variables (3D), so probabilities are conditional probabilities; Problems arise because the quantum mechanics analog is not viable; One needs a measure, and a definition of time such that H is linear in p0.
* Conditions: Not always possible (> see Taub-NUT); A coordinate q0 in phase space can be singled out as an intrinsic time if there is a canonical transformation such that the Hamiltonian constraint can be written as C(p, q) = p0 + h(pi, qi), with i ≠ 0.
* Variation: Consider Ψ as a single-particle state in superspace (third quantization).
@ General references: Kuchař in(81), JMP(81), JMP(82), in(90); Page & Wootters PRD(83); Hájíček PRD(86), in(86); Barbour in(86); Unruh & Wald PRD(89); Kiefer CQG(89) [continuous measurement, by fermions]; in Smolin in(91); Page in(93)gq; Doldán et al IJTP(96)ht/94; Romano gq/95; Graham & Luckock PRD(97) [cosmological, supergravity]; Pulido et al GRG(01)gq/00; Simeone 02 [path integral and canonical]; Pestov gq/03; Mercuri & Montani MPLA(04)gq/03, NCB(05)gq/04-conf [dust as frame]; Gambini et al NJP(04)gq [and decoherence].
@ Examples: McGuigan PRD(90), Gorobey & Lukyanenko CQG(93), TMP(93) [3D volume]; Smolin & Soo NPB(95)gq/94 [Chern-Simons functional]; Ashworth PRD(98)qp/97 [oscillator as clock for rest]; Cianfrani et al CQG(09)-a0807 [with perfect fluid, entropy]; Alexander et al CQG(13) [electric vector potential]; Massar et al PRA(15)-a1410 [experiments with trapped ions].
@ Problems with clock: Weinstein gq/97-MG8; Dolby gq/04 [response].
@ Specific types of spacetimes: Friedman & Higuchi PRD(90) [asymptotically flat]; Romano & Torre PRD(96)gq/95 [2 Killing vector fields].
@ From HJ formalism: Peres in(98)gq/97; Simeone JMP(99) [FLRW models].

Before Quantization: Extrinsic Time > s.a. unimodular gravity.
@ General references: Beluardi & Ferraro PRD(95)gq/94; Kauffman & Smolin gq/97, comment Kitada & Fletcher gq/97; Ferraro & Sforza PRD(99); Ferraro G&C(99); Giribet & Simeone PLA(01)gq [closed de Sitter example].
@ Spacetime volume: Henneaux & Teitelboim PLB(89); Brown & York PRD(89); Unruh & Wald PRD(89); Bombelli in(91); Bombelli et al PRD(91); Sorkin IJTP(94).

More Radical > s.a. semiclassical cosmology.
* Modify quantum mechanics: Maybe no Hilbert space, ...: & Penrose, Smolin.
* Relational time, no time needed: Quantum gravity is fine as is, time does not an essential role in its formulation; Trouble is, find observables; & Barbour, Hawking, Misner.
@ Relational: Englert PLB(89); Rovelli pr(88), in(90), PRD(90), PRD(91); Isham & Butterfield gq/99-ch; Smolin in(00)gq/01 [criticism]; Gambini & Porto PRD(01)gq [models]; Butterfield BJPS-gq/01; Colosi & Rovelli PRD(03)gq [model]; Gambini et al NJP(04)gq, PRD(04)gq [and decoherence], PRL(04)ht [and black-hole information]; Gambini et al PRD(09)-a0809 [with Dirac observables], a0903-FQXi [and free will, decidability]; Rovelli a0903-FQXi; Gryb CQG(09)-a0810; Anderson CQG(11) [relational particle model]; Kajuri a1705-GRF [conceptual issues].
@ Ehrenfest equation: Greensite NPB(90), NPB(91); Padmanabhan Pra(90); Squires PLA(91); Brotz & Kiefer NPB(96)gq.
@ Self-measurement: Mensky CQG(90); Camacho & Camacho-Galván NCB(99)gq.
@ Other approaches: Meyer GRG(93) [and quantum gravity phase transition]; Horwitz IJMPD(96)gq/95 [quantum tunneling]; Heller & Sasin PLA(98)gq/97 [non-commutative geometry]; Hitchcock qp/00 [information, causal networks]; Roy gq/03-conf [from discreteness]; Dreyer a0904-FQXi; Markopoulou a0909-FQXi [quantum gravity is spaceless, not timeless].

References > s.a. discrete spacetime; parametrized theories [model]; geometrodynamics; gravitational thermodynamics.
@ General: Ruelle CMP(82); Hájíček PRD(86); Zeh PLA(86), PLA(88); Hartle in(89), in(91); Unruh IJTP(89); Unruh & Wald PRD(89); Mensky PLA(90); Fukuyama & Kamimura MPLA(91); Menskii GRG(91); Pegg JPA(91); Smolin gq/93; Wald PRD(93)gq; Carlini & Greensite PRD(95)gq/94; Anderson & York PRL(98)gq; Biswas et al IJMPD(01)gq/99; Kheyfets & Miller IJMPA(00)gq; Tronconi et al PRD(03)gq [and inflaton]; Guendelman & Kaganovich gq/03-conf [time-dependence of \(\langle\)A\(\rangle\)s]; Bojowald et al PRD(04)gq [lqg]; Larsson ht/05 [from anomalies upon quantization]; Thibeault & Simeone IJMPD(07)gq/06 [2-component Wheeler-DeWitt equation]; Sawayama a0705; Anderson IJMPD(09)-a0709, a0711-proc ["records theory"]; Carroll a0811-FQXi; Anderson CQG(12)-a1204 [combined histories, timeless and semiclassical approach], a1306-conf [Machian approach].
@ From constraints as expectation values: Kheyfets et al IJMPA(96); Nikolić gq/03 [\(\langle\)H\(\rangle\) = 0].
@ More than one timelike directions: & Vafa's "F theory" – NS(97)nov1; Vongehr ht/99-conf, ht/99 [black holes]; Dvali et al hp/99-in.
@ Related topics: Marolf CQG(95)gq/94 [parametrized theories]; Hori PTP(98)ht [quantum black holes]; George et al gq/03-proc [reduced phase space]; Monton in(07) [presentism and quantum gravity]; Jannes FP(15)-a0904-FQXi [insights from condensed matter]; Barbour et al GRG(13)-a1301 [in a point-particle analogue model of scale-invariant gravity].

Online Resources > see tau, Time and Universe.


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