Sub-Quantum Theories| 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,
IJQF-a1703 [epistemic principles];
Boughn a1910 [what leads us to quantum mechanics?].
@ 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 FP(17)-a1509 [from the Madelung equations];
Höhn & Wever PRA(17)-a1511 [from rules on an observer's information acquisition].
@ 't Hooft proposals: 't Hooft FPL(97)qp/96,
ht/01,
ht/01-conf;
Blasone et al BJP(05)qp-conf,
AP(05) [path-integral approach];
't Hooft a2005 [Hamiltonian, with interactions];
't Hooft a2010 [from fast vacuum fluctuations].
@ 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;
Knoll FP(17)-a1804 [statistical description of classical electrodynamics];
Cetto et al a2010 [quantization from stochasticity];
Westra a2011.
@ 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. Entropic Dynamics; 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];
Nurdin a1907-en [quantum stochastic process];
Gokler a2006 [random force];
> s.a. cellular automata.
Based on Measure / Information Theory and Similar Proposals
> s.a. axioms for quantum theory; 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,
EPJD(16)-a1508 [complex-valued probabilities];
Benavoli et al PRA(16)-a1605 [quantum mechanics as Bayesian theory in the complex numbers];
Wilce EPTCS(17)-a1701 [formally real Jordan algebras];
Rundle et al PRA(19)-a1708;
Matone a1710 [ergodic average over microstates];
Skilling & Knuth a1712;
Hofer-Szabó a1906
[non-commutative representation of conditional probabilities];
Klein a1907;
Janas et al a1910;
Budiyono PRA(19)-a2005 [from epistemic restriction];
> s.a. quantum probabilities; wigner functions.
@ 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;
Szangolies FP(18)-a1805;
Felline a1806;
> s.a. quantum information.
@ 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(14)-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];
Dragan & Ekert a1910 [special relativity];
> s.a. modified quantum mechanics [pre-quantum theories].
@ From Finsler geometry: Torromé JMP(06) [Finsler version of 't Hooft proposal];
Torromé a1402 [emergence from Hamilton-Randers system].
@ From other 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];
Frederick a1601 [stochastic spacetime];
Singh IJMPD(20)-a2005-GRF
[coarse-grained matrix dynamics of general relativity and matter].
@ 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];
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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