Quantum
Spacetime| 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|1/2
vev 
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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send feedback and suggestions to bombelli at olemiss.edu – modified 21
sep 2009