Quantum
Gravity |

**In General**

* __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) *g*_{ab} 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
quantum gravity.

__Approaches__: see conventional approaches [including algebraic, perturbative, ...], canonical, covariant, histories, and modified approaches.

**On Whether to Quantize** > s.a. emergent gravity;
general relativity;
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]; Oriti a1803-in [the Bronstein hypercube].

@ __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]; Crowther a1712 [inter-theory relationships]; > s.a. logic; Relationalism.

**Online Resources**

> __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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send feedback and suggestions to bombelli at olemiss.edu – modified 7
mar 2018