Quantum
Spacetime – Proposals| Quantum
Spacetime – Proposals |
Based on Math / Geometry > s.a. critical
phenomena;
differential geometry; fractals;
lattice field theory; monopoles and solitons [fuzzy].
* Abstract homotopy theory:
View points as relational, maps between spaces (Grothendieck and topology
of any category).
@ From null surfaces: Frittelli
et al CQG(97)gq/96.
@ Non-associative geometry: Nesterov & Sabinin ht/00-in,
PRD(00)ht [de Sitter],
IJGMP(06)ht/04 [FRW
models]; Sabinin IJTP(01).
@ By extension to higher dimensions: Snyder PR(47),
PR(47)
[5D de Sitter]; Honeycutt IJTP(91).
@ d-space: Gruszczak et al JMP(88),
FP(89);
Multarzynski & Heller FP(90);
Kull & Treumann IJTP(95).
@ Topology: Kaplunovski & Weinstein PRD(85)
[dynamical topology and dimension]; Zapatrin IJTP(93),
gq/95-in [finite];
Madore & Saeger CQG(98)
[undefined at lP]; Crane MPLA(05)
[relational topology].
@ Topos theory: Guts & Grinkevich gq/96;
Raptis IJTP(07)gq/05;
Crane a0706.
@ More proposals: Álvarez et al PRD(92)
[quantum metric space]; Pirogov
PAN(03)hp/01 [symplectic];
Stuckey gq/01 [Borel
set]; Porter gq/02 ['fractafolds'];
Efremov & Mitskievich gq/03, gq/03 [discrete
T0 spaces]; Crane a0804 [loop space; non-distributive
lattice].
> Other: see connections; non-commutative
geometry; world function.
Based
on Algebra / Logic
@ Algebraic: Bohm et al pr(81)qp/06;
Bannier IJTP(94);
Yurtsever CQG(94)gq/93;
Parfionov & Zapatrin
IJTP(95)gq;
Zapatrin gq/95-in;
Raptis & Zapatrin IJTP(00)
[and continuum correspondence]; Jaramillo & Aldaya JPA(99).
@ Categorical: Isham FP(05);
Crane
a0810, IJMPA(09).
@ Other logic, abstract: Wheeler in(80), in(83); Finkelstein in(68), IJTP(87);
Moore IJTP(00)
[order].
@ Self-organising info: Cahill & Klinger PLA(96)gq, gq/97,
GRG(00)gq/98;
Cahill et al ThPh(00)gq.
Based on Quantum Theory / Particle Physics > s.a. branes;
holographic field theory; non-commutative
geometry; strings.
@ Spatial manifold from quantum theory: Balachandran qp/97;
Kempf RPMP(99)ht/98;
Kryukov FP(04).
@ Branching spacetime: Belnap Syn(02)ps/03;
Kowalski & Placek IJTP(00)
[GHZ/Bell theorems]; Weiner & Belnap Syn(06);
Wronski & Placek SHPMP(09)-a0706 [Minkowskian].
@
String theory: Hata et al PLB(86);
Amati et al PLB(89);
Ellis et al PLB(92);
Bergman
ht/96, ht/96 [string-bits];
Witten PT(96)apr;
Ansoldi et al CSF(99)ht/98,
CQG(99)ht/98;
Li & Yoneya CSF(99)ht/98;
Polchinski IJMPA(99)ht/98;
Smolin NPPS(00)ht/98 [and
spin networks]; Horowitz gq/04;
Fontanini et al PLB(06)
[0-point length]; Schimmrigk a0812 [string-theoretic
modular motives].
@ More proposals: Marlow
IJTP(82), IJTP(84), IJTP(86), IJTP(88);
Müller-Hoissen AIHP(84)
[from gauge theory]; Marlow IJTP(95), IJTP(96);
Lyre qp/97 [ur-spins-tetrads-spacetime
vectors]; Ambjørn et al
NPB(98)
[c = –2]; Anandan IJTP(02)qp/00-in
[relations between states]; Yaremchuk
qp/01, qp/01 [
0 < card < 1];
Khrennikov qp/03-in, qp/03 [prespace];
Brody & Hughston PRS(05)gq/04 [higher-dimensional
quantum
spacetime]; > s.a. Higgs Mechanism [gravitational].
Other Proposals > s.a. manifolds;
quantum field theory [generalizations]; spacetime
foam; topological
field theories; twistors;
wormholes.
@ General references: Cole IJTP(68),
IJTP(69),
IJTP(69)
[causality without a metric]; Barut in(82); Banai
IJTP(84);
Prugovecki
84;
Terazawa
in(84); Ali RNC(85); Liebscher in(85); Whipple NCA(86);
Szabó JMP(86),
IJTP(87);
Chew & Stapp FP(88);
Görnitz IJTP(88),
IJTP(88);
Majid
CQG(88)
[Hopf algebra];
Görnitz & Ruhnau IJTP(89);
Szabó IJTP(89);
Stapp FP(88);
Hemion IJTP(89);
Lev JMP(89);
Prugovecki FPL(90);
Namsrai IJTP(91);
Amati in(92);
Chapline MPLA(92),
ht/98 [coherent
graviton state], MPLA(99)
[anyonic superconductivity]; Lev JMP(93);
Wetterich NPB(93)
[from general statistics]; Gibbs ht/95 [event-symmetric
physics]; Leifer qp/96 [superrelativity,
non-locality]; Mäkelä gq/07,
a0805, a0805 [graph
with black holes at vertices].
@ Károlyházy proposal: Károlyházy et al in(82);
Diósi & Lukács NCB(93)gq, PLA(93)
[excluded by phenomenology];
Ma PLA(98),
comment Diósi PLA(99);
Frenkel FP(02)qp/00;
> s.a. cosmological acceleration, quantum-gravity
phenomenology.
@ Other: Stainsby & Cahill PLA(90)
[Euclidean spacetime inside hadrons]; Stavraki TMP(90)
[discrete operator fields]; Aref'eva & Frampton MPLA(91)
[p-adic
spacetime]; Rylov JMP(91)
[generalized Lorentz manifold]; Antonuccio gq/93 [quasi-number
algebra]; Finkelstein et al CQG(97)qp/96;
Stuckey
gq/02/JPA;
Hohmann et al a0809 [quantum manifold locally isomorphic to Schwartz space].
@ Other, books: McCall 94.
@ Doubtful, bogus: Prugovecki FP(94)
["quantum frames"]; Krasnoholovets
IndJTP(00)qp/01,
S&S(00)qp/01,
IJCAS(02)qp/01, ht/02/FizB
["inertons"]; Bogdanoff & Bogdanoff
AP(02)
[KMS condition].
> Discrete-type: see discrete
spacetime; networks; regge
calculus.
Even More Speculative > see physics [higgledy-piggledy etc].
"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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oct 2009