Pilot-Wave Interpretation of Quantum Theory  

In General (de Broglie-Bohm) > s.a. CPT; histories and phase-space formulation; interpretations; Kemmer Equation.
* Motivation: A realistic, deterministic theory, with no measurement problem; Unjustly neglected by most authors.
* Idea: The world is described by (, X), where X are positions etc that particles actually have, and the evolution is guided by a "quantum potential" depending on through a guidance equation; A physical system follows the configuration space trajectory determined by p = S, with p the momentum and S the phase of the wave function , which evolves according to the Schrödinger equation of quantum mechanics.
* History: Has been used as motivation by Bell for his work (but also as underpinning of Sarfatti's paraphysics).
@ I: in Gardner 81; Albert SA(94)may.
@ Intros, reviews: Passon qp/06-in; Singh a0805-in; Dürr et al a0903-in; Kiessling FP-a0905.
@ General references: de Broglie CRAS(26); Bohm PR(52), PR(52), & Vigier PR(54), & Bub RMP(66), et al PRP(87); Nelson PR(66); de Broglie FP(70); Bell FP(82); Lochak FP(87); Dürr et al JSP(92)qp/03; Valentini PhD(92); Rupertsberger qp/98; Geiger et al qp/99, qp/99/PLA; Brown & Hiley qp/00; Allori & Zanghì qp/01-in, IJTP(04); Baker-Jarvis & Kabos PRA(03); Tumulka AJP(04)sep-qp [dialogue]; Passon qp/04 [addressing criticisms]; Marchildon SHPMP(06)qp/05 [compared to ether]; Struyve PhD(04)qp/05; Ord CSF(05) [and Copenhagen]; Nikolic AJP(08)feb-phy/07 [Bohr and Bohm, hypothetical]; Rusov a0804; Rusov & Vlasenko a0806; Struyve & Valentini JPA(09)-a0808 [guidance equations for arbitrary Hamiltonians]; Schmelzer a0907 [beables and decoherence].
@ Criticisms: Zeh FPL(99)qp/98; Anandan & Brown FP(99) [action and reaction]; Zirpel a0903 [contradicts quantum mechanics]; Ghose ASL(09)-a0905 [difficulties with entangled states].
@ Hamiltonian form: Holland NCB(01).
@ Books: in de Broglie 60, 63; in Bell 87; Bohm & Hiley 93; Holland 93; Cushing et al ed-96.

Special Topics > s.a. decoherence; experiments in quantum mechanics; hidden variables; measurement; photon; probabilities; realism.
* And standard quantum mechanics: Piliot wave theory predictions are equivalent to those of standard quantum mechanics, for any question or problem that is well posed in both interpretations, if one assumes that the probability density for the system is the equilibrium one, ||2.
* Trajectories: It has been proved that the motion of a vortex in the associated velocity field can induce chaos in the trajectories.
@ Same as standard quantum mechanics: Marchildon qp/00; Golshani & Akhavan qp/01; Struyve & De Baere qp/01-in; Nikolic qp/03.
@ Inequivalent to standard quantum mechanics: Schmidt & Selleri FPL(91) [triple slit]; Neumaier qp/00 [different correlations]; Ghose qp/01 [incompatible].
@ Relativistic / Lorentz invariance: Squires qp/95; Valentini PLA(97)-a0812; Dürr et al PRA(99)qp/98; Shojai & Shojai PS(01)qp [also curved spacetime]; Nikolic qp/03 [the only consistent one in first quantization], FPL(05)qp/04 [relativistic quantum mechanics], qp/05-in, qp/06 [many-fingered time], JPCS(07)ht/06-in [and quantum field theory]; Koch a0810 [from scalar gravity]; Nikolic IJQI-a0811 [and time operator]; Koch a0901 [geometrical dual].
@ Similar proposals: Deotto & Ghirardi FP(98)qp/97; Brandt et al PLA(98)qp; Potvin qp/99; Kamalov qp/02, qp/02 [and gravity]; Sutherland SHPMP(08)qp/06 [causally symmetric version, incorporating retrocausality]; Ekholdt a0906.
@ Probabilities: Bozic & Maric PLA(91) [and interferometers]; Galvan FP(07)qp/06 [vs typicality], JSP(08)-a0711 ["imprecise probabilities"]; Callender SHPMP(07) [emergence and interpretation]; Nikolic FP(08)-a0804.
@ Mixed states: Dürr et al FP(05)qp/03, Maroney FP(05)qp/03 [density matrices].
@ Trajectories: Teufel & Tumulka CMP(05)mp/04 [global existence]; Römer et al JPA(05)qp [and scattering]; Goldfarb et al qp/06 [complex action]; Matzkin & Nurock SHPMP(08)qp/06; Borondo et al a0907 [dynamical-systems approach]; > s.a. path integrals.
@ Numerical methods: Deckert et al JPCA(07)qp; Coffey et al JPA(08)-a0807 [Monte Carlo generation of trajectories]
@ Other topics: Sanz JPA(05)qp/04 [and "quantum fractals"]; Aharonov et al PS(04)qp [time vs ensemble averages]; Potvin qp/05 [and density of states]; Goldfarb et al a0706; > s.a. collapse; information; many-worlds interpretation; mind; quantum particles; superselection rules; topology.

Specific Systems > s.a. approaches to quantum gravity; dirac fields; quantum black holes; quantum oscillators; quantum field theory.
@ Ordinary quantum mechanics: Stomphorst PLA(02) [potential wells, transmission / reflection]; Hyman et al JPA(04) [discrete operators]; Mousavi & Golshani a0804 [2-level atom in classical field]; Matzkin FP(09)-a0806 [square billiard, classical-quantum correspondence]; Timko & Vrscay FP(09) [two electrons in helium atom].
@ Solutions: Berndl et al CMP(95); Frisk PLA(97) [types]; Appleby FP(99)qp [isolated particle].
@ In curved spacetime: Squires PLA(94) [mixed states and closed timelike curves]; Tumulka a0708, a0808 [with singularities].
@ Quantum cosmology: Vink NPB(92); Horiguchi MPLA(94); Blaut & Kowalski-Glikman CQG(96)gq/95, gq/96; Shtanov PRD(96); Valentini in(96); Pinto & Santini PRD(99)gq/98, GRG(02)gq/00; Pinto-Neto FP(05)gq/04-in [rev]; Shojai & Shirinifard IJMPD(05)gq [classical limit]; Shojai & Shojai IJMPD(09)-a0708 [in lqc]; > s.a. cosmological effects of quantum gravity [inflation].

Effects > s.a. Klein Paradox; semiclassical quantum mechanics [including macroscopic objects]; quantum effects [arrival time, tunneling time].
* And experiment: It is useful to look for effects for which standard quantum mechanics makes no prediction whereas the pilot-wave theory does, such as tunneling times.
@ And non-locality: Rice AJP(97)feb; Khrennikov qp/03, Toyama & Matsuura PS(06) [correlations]; Sanz & Miret-Artes ChemPL(07)qp.
@ Approach to equilibrium probabilites: Bohm PR(53); Valentini PLA(91) [subquantum H-theorem], PLA(91); Potel et al PLA(02); Valentini & Westman PRS(05)qp/04 [simulations]; Goldstein & Struyve JSP(07)-a0705 [uniqueness of equilibrium distribution]; Bennett a0908 [Lagrangian analysis].
@ And interference: Philippidis NCB(79) [quantum potential]; Guay & Marchildon JPA(03)qp [two-particle].
@ And non-quantum systems: Valentini PLA(04) [anomalous statistical properties].
@ Chaos: Wisniacki et al EPL(03)qp [classically chaotic]; Efthymiopoulos & Contopoulos JPA(06); Efthymiopoulos et al JPA-a0709 [transition to chaos]; Efthymiopoulos et al PRE-a0903 [and critical points of quantum flow]; > s.a. chaotic systems.
@ Measurement: de Broglie et al FP(76); Zeh FP(88), Brown & Wallace FP(05) [vs many-worlds]; Stone PhSc(94)jun, discussion PhSc(95)sep; Lewis BJPS(07), PhSc(07)dec; Wiseman NJP(07), Dürr et al a0808 [weak measurement of velocity].
@ Experiments, tests: Vigier LNC(80); Bohm et al Nat(85)may [delayed choice]; Croca FP(87), et al FPL(88); Wang et al PRL(91) [against]; Utsuro & Ignatovich PLA(98) [neutron]; Smith qp/98 [for]; Golshani & Akhavan qp/00, qp/01, JPA(01)qp/01, qp/01; Ghose qp/01; Struyve & De Baere qp/01-in, reply Ghose qp/02; Brida et al JPB(02)qp [results]; d'Espagnat qp/03 [and Schrödinger's cat]; Gondran & Gondran qp/06/PRA [identical particles].
@ Effects of empty waves: Hardy PLA(92); Wechsler qp/03; Vaidman FP(05)qp/03.
@ Related topics: Brown et al PLA(99) [identical particles]; Bedard PhSc(99)jun [material objects]; Riggs JPA(99) [energy-momentum transfer]; Appleby FP(99)qp [decoherence]; Barrett qp/00-in, PhSc(00)dec [surreal trajectories]; Nogami et al PLA(00)qp [decay]; Butterfield in(04)qp/02 [Hamilton-Jacobi]; Dürr et al qp/03 [observables]; Valentini a0804, a0805 [and cosmology]; Tausk & Tumulka a0806 [can an electron reach speed c?]; Huggett & Vistarini a0905 [entanglement exchange]; Miranda PS(09) [in nuclear and particle physics]; > s.a. quantum technology [teleportation].

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