Quantum Spacetime – Proposals  

Based on Math / Geometry > s.a. critical phenomena; differential geometry; lattice field theory; spacetime structure [generalizations].
* 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.
@ 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); Multarzyński & Heller FP(90); Kull & Treumann IJTP(95).
@ Topology: Kaplunovski & Weinstein PRD(85) [dynamical topology and dimension]; Zapatrin IJTP(93), gq/95-conf [finite]; Madore & Saeger CQG(98) [undefined at lP]; Crane MPLA(05) [relational topology]; Spaans IJMPD(13) [quantum foam of mini-black-holes and prime 3-manifolds].
@ Topos theory: Guts & Grinkevich gq/96; Raptis IJTP(07)gq/05; Crane a0706.
@ More proposals: Aref'eva & Frampton MPLA(91) [p-adic spacetime]; 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-GRF [loop space; non-distributive lattice]; Dahm PAN(12)-a1102-conf [from groups/Lie algebras].
> Related topics: see connections; fractals in physics [including multifractal spacetime]; monopoles and solitons [fuzzy]; Non-Associative Geometry; 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-conf; Raptis & Zapatrin IJTP(00) [and continuum correspondence]; Jaramillo & Aldaya JPA(99); Freidel et al a1606 [Heisenberg algebra polarization and modular spaces].
@ 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 information: Cahill & Klinger PLA(96)gq, PiP(05)gq/97, GRG(00)gq/98; Cahill et al ThPh(00)gq.

Based on Quantum Theory / Other Physics > s.a. branes; emergence [including entanglement]; holographic field theory; non-commutative geometry; strings.
@ Spatial manifold from quantum theory: Balachandran qp/97; Kempf RPMP(99)ht/98; Kryukov FP(04); Chew et al a1603 [quantum space]; Freidel et al PRD(16)-a1609 [Euclidean quantum space as a choice of polarization for the Heisenberg algebra of quantum theory].
@ Branching spacetime: Belnap Syn(02)ps/03; Kowalski & Placek IJTP(00) [GHZ/Bell theorems]; Weiner & Belnap Syn(06); Wroński & 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 NJP(05)-gq/04; Fontanini et al PLB(06) [0-point length]; Schimmrigk CMP(11)-a0812 [string-theoretic modular motives]; West JHEP(14)-a1403 [and gauge transformations].
@ Condensed-matter ideas: Lobo et al PRD(15)-a1412 [microscopic defects and effective metric-affine geometry]; Tenev & Horstemeyer a1603 [mechanics of the cosmic fabric]; > s.a. defects; emergent gravity.
@ 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/IJTP [ur-spins-tetrads-spacetime vectors]; Ambjørn et al NPB(98) [c = −2]; Anandan IJTP(02)qp/00-conf [relations between states]; Yaremchuk qp/01, qp/01 [ℵ0 < card < ℵ1]; Khrennikov qp/03-conf, qp/03 [prespace]; Brody & Hughston PRS(05)gq/04 [higher-dimensional quantum spacetime]; Raussendorf et al a1108 [measurement-based quantum computation]; Dvali & Gómez JCAP(14) [spacetime as composite of soft gravitons]; Steinacker a1911 [higher-spin theory]; > s.a. higgs mechanism [gravitational].

Other Proposals > s.a. Accelerated Fields; manifolds; quantum field theory [generalizations]; spacetime foam.
@ General references: Cole IJTP(68), IJTP(69), IJTP(69) [causality without a metric]; Barut in(82); Banai IJTP(84); Prugovečki 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); Prugovečki 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]; Rylov JMP(91) [generalized Lorentz manifold]; Antonuccio gq/93 [quasi-number algebra]; McCall 94; Prugovečki FP(94) ["quantum frames"]; Finkelstein et al CQG(97)qp/96; Stuckey gq/02/JPA; Hohmann et al a0809 [quantum manifold locally isomorphic to Schwartz space]; de la Torre a1705 [spacetime fabric model].
@ Doubtful, bogus: Krasnoholovets IndJTP(00)qp/01, S&S(00)qp/01, IJCAS(02)qp/01, ht/02/FizB ["inertons"]; Bogdanoff & Bogdanoff AP(02) [KMS condition].
> Related topics: see discrete geometries [time]; discrete spacetime models; geometrodynamics [including generalized space of spaces]; information and spacetime / gravity; networks; regge calculus; topological field theories; twistors; wormholes.

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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