Quantum Spacetime  

In General > s.a. quantum gravity, canonical formulation / quantum-gravity phenomenology; spacetime [philosophical].
* Idea: Spacetime is not a manifold, but that picture enables us to talk about it without knowing what is going on; In particular, below Planck scale, events should be fuzzed out, and topology as well as other structures, can change; Beyond the first general points, there are many different approaches, differing on what structures are fundamental, how to treat their dynamics, and whether matter is to be identified with elementary objects, or built out of more fundamental stuff, etc; Events can be intersections of world-lines.
* History: Riemann had some early ideas, but the field did not start developing until the 1930s; Around the 1960s l = 10−12–10−14 cm was still considered a reasonable fundamental length! 1990s, Quantum geometry in lqg; 2000s, Structure of spacetime near singularities.
* Pregeometry: Geometry is not fundamental, but emerges at large scales; In some views, it does not really exist.
* Nature of theories: Most proposals are realistic (they assume the existence of physical entities endowed with concrete properties), and objective (they can be formulated without any reference to knowing subjects or sensorial fields); Many are also relational (spacetime is not a thing, but a complex of relations among things).
@ Reviews: Antonsen pr(94); Gibbs ht/95 [bibliography]; Kempf ht/98-proc; Markopoulou gq/02-ch; Gross et al ed-07; Ambjørn et al SA(08)jul; Ashtekar a0810-ch; news nat(13)aug [approaches]; Bahns et al a1501 [and algebraic quantum field theory, rev]; Licata ed-16 [and quantum theory]; Kiefer a2004-in.
@ General references: Wigner RMP(57); Zimmerman AJP(62)feb; Castell et al 75, 77, 79; Townsend PRD(77); Finkelstein & Rodriguez in(86); Namsrai FdP(88); Rüger HSPS(88); Anandan in(97)gq; Rovelli in(01)gq/99; Callender & Huggett ed-01; Crane a0706 [motivation, and quantum topos]; Hedrich a1101; Noldus a1305 [universal construction]; Bennett & Nielsen a1306-proc [need for new fundamental physics]; Svozil IJTP(15)-a1401 [and entanglement]; Amelino-Camelia & Astuti IJMPD(15)-a1404 [empty spacetime is not physically meaningful, Snyder space example]; Di Casola et al FP(15)-a1405 [no "mesoscopic" spacetime]; Ascárate CQG-a2012 [spacetime picture, and non-commutativity].
@ In lqg / lqc: Bojowald a1002-conf; Wüthrich in(17)-a1405; Rovelli a1802-in.
@ Pregeometry and emergence: Wheeler in(80); Stuckey in(00); Botta Cantcheff gq/04-GRF; Singh a0905 [gravity as a thermodynamic limit]; Piazza FP(10); Gao a1001-wd [gravity as fundamental]; Majid a1711-conf [from quantum Born reciprocity]; Wetterich a2101 [euclidean pregeometry]; > s.a. emergent gravity; gravitational thermodynamics.

Theoretical Approaches > s.a. information and spacetime / gravity; quantum black holes.
@ Theoretical evidence: Cacciatori et al PLB(98)ht/97 [gas of wormholes]; Sidharth CSF(00)qp/99 [??]; Doplicher AIP(01)ht; Capellmann a2006 [Max Born].
@ New Planck scale physics: Brandenberger gq/95; Jacobson PTPS(99)ht/00; Botta Cantcheff ht/00; Niemeyer & Parentani PRD(01)ap [and inflation]; Kowalski-Glikman MPLA(02)ht/01 [κ-Poincaré symmetry]; Arcioni et al JHEP(01)ht [with cosmological constant]; Adler AJP(10)sep [elementary arguments]; Bose a1011-wd [and Lorentz-invariant cutoff]; 't Hooft a1605-in; > s.a. inflation.
@ And decoherence: Ellis et al MPLA(97) [stringy fluctuations]; Zurek Nat(01)aug; Brody & Hughston qp/06-proc [emergence of classical spacetime].
@ Axioms, paradigms: Pérez Bergliaffa et al IJTP(98)gq/97 [axiomatic]; Kornai IJTP(03) [finitism].
@ Related topics: Bacry 88 [localizability and space]; Mazur & Nair GRG(89) [topological features]; Schiffer GRG(92) [horizons]; Nodland MPLA(98)ht [matter]; Sidharth CSF(00)qp/98 [time asymmetry]; Bernal et al FP(02)gq/00 [clock/rods]; Markopoulou JPCS(07)gq [collective excitations]; Bradonjić a0905, a1103/FP [spacetime geometry above the electroweak scale]; Cohen-Tannoudji a1402 [quanta of action, information and spacetime area]; Jia a1801 [null geodesics]; Capellmann a2006; Ascárate CQG(21)-a2012 [combination of approaches].
> Quantum-field-theory approach: see quantum field theory, in curved backgrounds and phenomenology [short-distance structure].
> Other approaches: see asymptotic safety [underlying geometry]; geometry [including metric fluctuations] and matter in quantum gravity.

Some Specific Aspects > s.a. models of spacetime; quantum spacetime proposals / types; semiclassical general relativity; spacetime foam.
* Idea: Quantize only part of the metric, and/or replace smooth manifolds by a slightly more general structure.
* Coordinate operators: If the spectra are Lorentz-invariant and the operators commute, we get a continuum; If they don't commute, we get the Snyder proposal; If we impose Poincaré invariance, again we get a continuum.
@ Non-local correlations: Requardt ht/02 [and non-commutative geometry]; > s.a. locality.
@ Signature dynamics: Greensite PLB(93)gq/92; Carlini & Greensite PRD(94)gq/93; Elizalde et al CQG(94)ht/93; Dzhunushaliev GRG(01)gq/99; > s.a. modified electromagnetism.
@ Metric degeneracy: Percacci in(92) [mean-field approach, \(\langle|g|^{1/2}\rangle_{\rm vev} \ne 0\)].
@ Deformed spaces: Toller PRA(99)qp/98 [quantum coordinates]; Quesne & Tkachuk PRA(10)-a0906 [composite systems]; > s.a. deformation quantization; discrete spacetime; generalized uncertainty relations; minkowski spacetime; modified lorentz symmetry; non-commutative geometry.
> Discreteness, minimal length: see discrete spacetime models; GUP; Minimal Length; quantum gravity and geometry; spacetime [points].
> Related topics: see dimensionality; Event; oscillators [model for spacetime decondensation].

"Everybody thinks spacetime should be an output rather than an input of a final theory" – Nathan Seiberg, NYT 26.06.2001.

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