Quantum Spacetime  

General Issues > 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-in; Markopoulou gq/02-in; Gross et al ed-07; Ambjørn et al SA(08)jul; Ashtekar a0810-in.
@ General references: Wigner RMP(57); Zimmerman AJP(62)feb; Castell et al 75–79; Townsend PRD(77); Finkelstein & Rodriguez in(86); Namsrai FdP(88); Rüger HSPS(88); Anandan gq/97-in; Rovelli gq/99-in; Callender & Huggett ed-01; Crane a0706 [motivation, and quantum topos].
@ Pregeometry and emergence: Wheeler in(80); Stuckey in(00); Botta Cantcheff gq/04-GRF; Singh a0905 [gravity as a thermodynamic limit].

Theoretical Aspects > s.a. discrete geometries; information; quantum black holes.
* Evidence: Area of quantum black holes, with Amin 4 ln2 lP2; 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 ht/01-in.
@ 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 [-Poincaré symmetry]; Arcioni et al JHEP(01)ht [with cosmological constant]; > 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-in [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]; Bradonjic a0905 [spacetime geometry above the electroweak scale].
> Quantum-field-theory approach: see quantum field theory, in curved backgrounds and phenomenology [short-distance structure].
> Related topics: see Event; quantum-gravity phenomenology and matter; oscillators [model for spacetime decondensation].

Approaches > s.a. models of spacetime; quantum spacetime proposals; kaluza-klein theory; semiclassical general relativity.
* 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.
* Dimension: From a quantum field theory point of view, the fractal (Hausdorff) dimension of spacetime is determined by the exponential falloff of the 2-point function with geodesic distance; From it one can extract critical behavior; Based on the anomalous dimension of Newton's constant and the spectral dimension, at sub-Planckian distances spacetime is a fractal with effective dimension 2.
@ 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].
@ 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, |g|1/2vev 0].
@ Deformed spaces: Toller PRA(99)qp/98 [quantum coordinates]; Quesne & Tkachuk a0906 [composite systems]; > s.a. deformation quantization; discrete spacetime; generalized uncertainty relations; modified lorentz symmetry; non-commutative geometry.
@ Dimension: Horiguchi et al PLB(95)ht/94 [small-scale 3D structure]; Khorrami et al gq/95; Antoniadis et al PLB(98)ht [Hausdorff, from quantum field theory]; Mansouri & Nasseri PRD(99)gq [variable]; Castro CSF(00)ht [infinite-dimensional]; Kobelev phy/00, phy/00 [fractal, and modified Lorentz group]; Lauscher & Reuter JHEP(05)ht [fractal, dmicro = 2]; Rama PLB(07)ht/06 [string theory]; Sakellariadou ht/07-in [Kaluza-Klein theory and large extra dimensions]; Maziashvili IJMPA(08)-a0709 [operational definition]; Horava PRL(09)-a0902 [spectral dimension at a Lifshitz Point]; Maziashvili a0905-GRF [running]; Carlip a0909-in [spontaneous dimensional reduction at small scales]; > s.a. fractals in physics, inflationary scenarios.

"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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