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].

@ __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];
Bojowald a1002-conf [and lqg, lqc];
Hedrich a1101;
Noldus a1305 [universal construction];
Bennett & Nielsen a1306-proc [need for new fundamental physics];
Svozil 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]; Wüthrich a1405-in [in lqg].

@ __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]; > s.a. emergent gravity; gravitational thermodynamics.

**Theoretical Aspects** > s.a. information and spacetime / gravity; quantum black holes.

* __Evidence__: Area of quantum
black holes, with Δ*A*_{min}
~ 4 ln2 *l*_{P}^{2};
Indications of UV cutoff from existence of fixed point for *G*;
Arguments re quantum uncertainty and black holes.

@ __Theoretical evidence__: Cacciatori et al PLB(98)ht/97 [gas
of wormholes]; Sidharth CSF(00)qp/99 [??];
Doplicher AIP(01)ht.

@ __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.

@ __Non-local correlations__: Requardt ht/02 [and
non-commutative geometry]; > s.a. locality.

@ __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].

> __Quantum-field-theory approach__:
see quantum field theory, in
curved backgrounds and phenomenology [short-distance
structure].

> __Discreteness, minimal length__: see discrete
geometries; GUP; Minimal Length; quantum-gravity and geometry; spacetime [points].

> __Related topics__: see dimensionality; Event; quantum gravity and geometry and matter; oscillators [model
for spacetime decondensation].

**Some Approaches and Issues ** > 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.

@ __Fluctuations__: Redington gq/97;
Rosales & Sánchez-Gómez
gq/97 [conformal];
Acebal et al PLB(98),
Miller JMP(99)
[stochastic]; Zizzi IJTP(99)ht/98 [and
Planck-size euclidean-black-hole foam]; Hogan PRD(08)-a0806 [based
on wave optics]; Shalyt-Margolin a1306, Ent(16)-a1603 [and minimal length].

@ __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}\(\rangle\)_{vev} ≠ 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.

"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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