Time
in Quantum Gravity| Time
in Quantum Gravity |
In General > s.a. 2D quantum gravity;
3D gravity; parametrized
theories; quantum
cosmology;
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 (> see quantum
gravity phenomenology for references on this).
@ Reviews: Isham in(92)gq, gq/93;
Kuchar in(92); in Zeh 92; Macías & Quevedo gq/06-in.
@ General references: Torre PRD(92);
Barbour PRD(93), CQG(94),
CQG(94);
Moffat FP(93);
Kitada gq/94, & Fletcher gq/94/Ap;
Unruh in(94)gq/93;
Parentani gq/97-in;
Shestakova & Simeone G&C(04)gq [canonical], G&C(04)gq [path
integral].
@ Arrow of time: Liu PhSc(93); Ellis et
al CSF(99)ht/98;
Castagnino PRD(98)gq/96,
et al CQG(02)gq [minisuperspace].
From States > s.a. quantum cosmology.
* WKB interpretation:
Assume 
=
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.
@ WKB/semiclassical: Banks et al NPB(85); in Unruh & Wald PRD(89);
Vilenkin PRD(89); Brout & Parentani IJMPD(99)gq/97;
Bak et al JKPS(00)gq/99;
> s.a. brans-dicke.
@ 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.
@ Other: Bander gq/02 [vev of field energy]; Halliwell & Thorwart
PRD(02) [and decoherent histories].
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 quantum mechanics analog not viable;
Need 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 as
a single-particle state in superspace (3rd quantization).
@ General references: Kuchar in(81), JMP(81), JMP(82),
in(90); Page & Wootters PRD(83);
Hájícek 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, sugra]; Pulido et al GRG(01)gq/00;
Simeone 02 [path integral and canonical]; Pestov gq/03;
Mercuri & Montani MPLA(04)gq/03, gq/04-in
[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].
@ 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 gq/97-in;
Simeone JMP(99)
[FRW].
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
dS 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
* 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-in;
Smolin in(00)gq/01 [criticism];
Gambini & Porto
PRD(01)gq [models];
Butterfield gq/01/BJPS;
Colosi & Rovelli
PRD(03)gq [model];
Gambini et al NJP(04)gq,
PRD(04)gq [and
decoherence], PRL(04)ht [and
black hole info]; Anderson CQG(07)gq/06,
CQG(07)gq/06 [relational
models and semiclassical WKB time].
@ 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 [nc
geometry];
Hitchcock qp/00 [info,
causal networks]; Roy
gq/03-in
[from discreteness].
References > s.a. discrete
spacetime; parametrized
theories [model];
geometrodynamics.
@ General: Ruelle CMP(82);
Hájícek 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;
Kheyfets et al IJMPA(96)
[constraints on exp values]; 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-in
[t-dependence of 
A
's];
Nikolic gq/03 [H =
0]; Bojowald et al PRD(04)gq [lqg];
Larsson ht/05 [from
anomalies upon quantization]; Thibeault & Simeone gq/06 [2-component
Wheeler-DeWitt equation]; Sawayama a0705;
Anderson a0709, a0711-in
["records theory"].
@ More than 1 timelike directions: & Vafa's "F theory" – NS(97)nov1;
Vongehr ht/99-in,
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-in
[reduced phase space].
Online Resources > tau, Time and Universe.
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26 jun 2008