Sub-Quantum Theories  

The "Origin'' of Quantum Mechanics > s.a. axioms for quantum theory; generalized quantum theory; physics theories ["visions"].
* In general: The idea is that quantum mechanics is not exact, but rather a very accurate approximation to a deeper-level theory; Depending on one's motivation, one may seek a that deeper theory reconciles the deterministic and probabilistic aspects, or one that is more compatible with gravity theory.
* 't Hooft proposal: Loss of information due to dissipation in a microscopic, classical deterministic system.
* Beyond quantum mechanics: See Valentini's proposal of more general, "non-equilibrium" sub-quantum systems based on the pilot-wave approach, for which quantum mechanics emerges in a "thermal equilibrium state".
* Phenomenology: Various proposals predict violations of Born's rule.
@ General references: Clauser & Horne PRD(74) [objective local theories, and experiment]; Adler & Bassi Sci(09)jul-a0912; 't Hooft a1112 [wave function collapse and Born's rule as features pointing towards an underlying determinism]; Blood a1211 [pre-representational theory]; Kochen FP-a1306 [reconstruction from a σ-complex of extrinsic properties of a quantum system]; Ghirardi & Romano PS(14)-a1501; Oas & de Barros in(16)-a1506 [rev]; Östborn a1601, a1703 [epistemic principles].
@ From classical mechanics / logic: Orlov AP(94), qp/96; Wetterich ht/01; Aerts IJTP(95)qp/01; Bokulich & Bokulich FP(05) [Bohr's view]; Hegseth a0912 [from non-local classical mechanics]; Wetterich AP(10)-a1003 [from coarse-grained classical probabilities]; Tipler a1007 [Schrödinger equation as Hamilton-Jacobi equation with additional condition]; Bartlett et al PRA(12)-a1111 [Liouville mechanics with an epistemic restriction]; 't Hooft JPCS(12); Galgani Mecc-a1209 [Carlo Cercignani's ideas]; De Raedt et al AP(14)-a1303 [as the most robust description of reproducible experiments]; Hall et al PRX(14)-a1402 [quantum theory from universal interaction between classical worlds]; Sebens PhSc(15)-a1403 [classical, many-worlds]; Reddiger a1509 [from the Madelung equations]; Höhn & Wever a1511 [from rules on an observer's information acquisition].
@ 't Hooft proposal: 't Hooft FPL(97)qp/96, ht/01, ht/01-conf; Blasone et al BJP(05)qp-conf, AP(05) [path-integral approach].
@ Valentini proposal: Valentini pr(91), pw(09)nov-a1001; > s.a. pilot-wave interpretation.
> Related topics: see Determinism; Born Rule [violations]; hidden-variable theories; logic.

Based on Stochastic Processes / Thermodynamics > s.a. random walk; stochastic processes; stochastic quantum mechanics.
@ General references: Percival PRS(95)qp [spacetime fluctuations]; Månsson qp/05 [as spacetime statistical mechanics]; Grössing qp/05-proc [classical mechanics + coarse-grained time and zero-point fluctuations], PLA(08)-a0711, FP(11)-a0812 [non-equilibrium]; Wiesniak et al PRB(08)qp/05 [entanglement from third law of thermodynamics]; de la Peña et al FP(09), Cetto et al JPCS(12) [interaction with zero-point radiation field]; Budiyono a1012 [deviations from least-action trajectories]; Grössing et al FP(11) [sub-quantum thermodynamics]; Schwabl et al JPCS(12) [bouncer-walker model]; Acosta et al IJGMP(13)-a1206 [and irreversible Gaussian Markov processes]; Santos a1208 [and dark energy, tests of Bell's inequalities]; Khrennikov PhyA(14)-a1212, a1605 [statistical mechanics of classical fields]; Budiyono IJTP(14)-a1301 [statistical model of quantization]; Grössing IJMPB(14)-a1304-conf [rev]; Goedecke a1408, a1408; Krumm et al NJP(17)-a1608.
@ From entropic dynamics: Caticha a0907-conf, JPA(11)-a1005; Johnson PhD-a1105 [symmetries and transformations, and the measurement problem]; Johnson & Caticha a1108-conf [and the measurement problem]; Nawaz & Caticha a1108-conf [momentum and uncertainty relations]; Caticha a1403-conf; Kornyak a1507 -conf [combinatorial models of quantum evolution]; > s.a. information.
@ From irreversible thermodynamics: Fernández de Córdoba et al a1210-conf; Fernández de Córdoba et al a1311, IJGMP(14).
@ Related models: Puthoff PRD(87) [H ground state as equilibrium between acceleration radiation and vacuum fluctuations]; Smolin qp/06 [and Nelson's stochastic formulation]; Halabi a1007-wd [classical Boltzmann equation]; Frasca a1201 [as the square root of a stochastic process]; Olavo et al AP(12) [Langevin stochastic equations]; Tsekov JPCS-a1510 [stochastic dynamics of virtual particles]; Tsekov a1703 [imaginary stochastic process].

Based on Measure / Information Theory and Similar Proposals > s.a. formulations; interpretations [stochastic].
@ General references: de la Peña & Cetto FP(75), FP(78); Davidson JMP(78), LMP(79), LMP(79)qp/01, JMP(79)qp/01 [algebra of operators]; Wallstrom FPL(89); Sanz PLA(90) [and quantum probabilities]; Olavo PRA(00); Torres & Figueiredo qp/02; Davidson AIP(07)qp/06 [assessment]; Khrennikov IJTP(08), a1204; Santos a1205.
@ From measure theory / probability: Landsberg FP(88); Youssef MPLA(91); Sorkin MPLA(94); Caticha PRA(98)qp; Chapline qp/99; Fuchs qp/02; Pitowsky qp/05-fs; 't Hooft JPCS(07)qp/06 [equivalence classes of data]; Goyal qp/07, qp/07; Rau a0706 [consistent reasoning with finite evidence]; D'Ariano a0807-in; Klein PRI(10)-a0810; Wetterich JPCS(09)-a0811, AP(10)-a0906; Isidro et al AIP(10)-a0912 [Ricci flow as coarse-grained description]; Skála et al AP(11); Reginatto & Hall a1108-conf [geometry of evolving probabilities]; Wetterich JPCS(12)-a1201 [fermions]; Kurihara a1206 [and code transfer errors]; Leifer & Spekkens PRA(13) [as a causally neutral theory of Bayesian inference]; Hofmann PRA(14)-a1306 [law of quantum ergodicity], a1405-proc, a1508 [complex-valued probabilities]; Benavoli et al a1605 [quantum mechanics as Bayesian theory in the complex numbers]; Wilce EPTCS(17)-a1701 [formally real Jordan algebras]; > s.a. axioms for quantum theory; quantum probabilities.
@ From information theory: Goyal PRA(08)-a0805, a0805, NJP(10)-a0805 [information geometry]; Lee FP(11)-a1005 [applied to a causal horizon]; Reginatto & Hall AIP(13)-a1207 [information geometry, dynamics and discrete quantum mechanics]; Chiribella et al Ent(12)-a1209-conf; Bub a1211, response Mohrhoff a1212 [Bananaworld]; Budiyono PhyA(14); Chiribella & Scandolo a1411-proc; Fields a1411 [additive Hamiltonian and Landauer's principle]; Höhn a1412; Plotnitsky a1503 [and the Dirac equation]; Chiribella et al ch(16)-a1506; Smolin a1506 [and the principle of maximal variety]; Krumm a1508-MS; Heunen & Kissinger a1604; D'Ariano et al 17; Koberinski a1707-in.
@ Models: Cufaro Petroni & Vigier IJTP(79); Harding IJTP(80) [relativistic]; Bordley PLA(95); Yeung qp/99; Kaniadakis PhyA(02)qp/01; Hall & Reginatto JPA(02) [uncertainty principle]; Ord & Mann AP(03)qp/02, PRA(03)qp/02 [entwined pair paths]; Adler ht/02; Helland qp/03, AIP(05)qp/04, qp/05-proc; Khrennikov qp/05, IJTP(08)ht/06, PLA(06), RPMP(07), FP(09), FP(10); de la Peña et al AJP(08)oct-a0712 [from oscillator vacuum energy]; Fritsche & Haugk a0912; Fu et al a1003 [classical fields modulated with pseudorandom phase sequences]; Bondar a1008; Knoll a1109-wd [Extended Charge Dynamics and the self-force problem]; Klein a1109-ch; Budiyono JPCS(12)-a1205 [à la pilot-wave theory]; Nieuwenhuizen JPCS-a1409 [subquantum arrow of time]; Frasca a1412-proc [as square root of Brownian motion]; Galehouse a1501 [Born rule from spontaneous emission during a measurement]; Roser a1507 [dynamical geometry of trajectories]; Skrebnev & Polski a1701 [subquantum processes].

Based on Field Theory or Geometry / Gravitation > s.a. quantum field theory; quantum gravity; quantum spacetime.
* Santamato's proposal: Geodesics in Weyl gravity (two degrees of freedom) give rise to paths in the pilot-wave view of quantum theory; The amplitude and phase of the wave function (two degrees of freedom) are functions of the connection; Similar to what happens in scale relativity.
@ From field theory / hep: Jones MPLA(95); Piron HPA(96)mp/02 [field theory and Noether's theorem]; Faraggi & Matone PLB(99); Krasnoholovets IJP(01)qp/99, S&S(01)qp, qp/01-conf; Svetlichny FP(00)qp/99; 't Hooft IJTP(03) [field theory with large gauge group]; Helesfai a1612 [charged particle in a random electric field]; > s.a. modified quantum mechanics [pre-quantum mechanics].
@ From geometry / gravity: Santamato PRD(84) [Weyl geometry]; Hadley qp/96-conf, IJTP(99)gq [general relativity]; Spaans gq/99 [spacetime topology]; Kamalov JRLR(01)qp/07 [background of random gravitational fields]; Hadley AIP(07)gq [non-time-orientable manifolds]; Covington a0912 [from electromagnetic force as curvature and discrete charge]; Mueller a1312-proc [matter waves and moving clocks].
@ From higher dimensions: Towe mp/05 [5D Kaluza-Klein geometry].

Other Proposals > s.a. emergence; quantum-classical mechanics relationship; schrödinger equation [derivations].
@ General references: Lee & Selby a1701 [no-go theorem for theories that decohere to quantum mechanics].
@ Chaos, complexity: Kirilyuk AFLB(96)cd/95, AFLB(96)qp/95 + 4ff; De Martino et al qp/97-wd; Hansson qp/00; McHarris qp/06; Frederick a1406.
@ From real theory: Finkelstein & Galiautdinov JMP-ht/00-conf.
@ Ur-objects: Lyre IJTP(95)qp/96; Kober a0905 [and field theory, general relativity].
@ Invariance principles: Brenig qp/06/PRL [as a relativity theory], JPA(07)gq/06 [from invariance of uncertainty]; Palmer PRS(09)-a0812 ["invariant set hypothesis"]; Moldoveanu JPCS(15)-a1303, a1407, a1505 [from invariances of the laws of nature].
@ Algebraic approaches: Garavaglia & Kauffmann IJTP(02)ht/99-conf; Wilce a1606.
@ Other types: Cetto & de la Peña-Auerbach FPL(91) [vacuum]; Granik FP(97); Wheeler MPLA(97)ht; Ono qp/99 [?]; Nicolescu qp/00-in ["levels of reality"]; Moret-Bailly S&S(01)qp ["phenomenological"]; Qi qp/02-conf, qp/02/FPL [discontinuous motion]; Bohr et al FP(04) [uncaused clicks]; Torrome JMP(06) [Finsler version of 't Hooft proposal]; Blasone et al JPCS(09)-a0901; Caravaglios IJMPA(09)-a0907; Dennis a1003 [with non-Markovian beables]; Kornyak a1010-in [from finite symmetry groups]; Singh a1006-FQXi [non-commuting matrices as degrees of freedom]; Requardt a1205 [undulatory translocal theory]; Goyal PRA(14) [from Feynman's rules]; Grinbaum FP(15)-a1501 [quantum theory as critical regime of a fundamental 'linguistic' theory].

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