Pilot-Wave (de Broglie-Bohm) Interpretation of Quantum Theory  

In General > s.a. CPT; histories and phase-space formulation; interpretations; Kemmer Equation; phenomenology [systems and effects].
* Motivation: A realistic, deterministic theory, with no measurement problem; Has been unjustly neglected by many authors.
* Idea: The world is described by (ψ, X), where X are positions etc that particles actually have, and the evolution is guided by a "quantum potential" depending on ψ 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 ψ, or v(x) = m–1 Im( lnψ), which evolves according to the Schrödinger equation of quantum mechanics.
* Versions: In de Broglie's original formulation, the particle dynamics is given by a first-order differential equation; In Bohm's reformulation, it is given by Newton's law of motion with an extra potential that depends on the wave function, the quantum potential, together with a constraint on the possible velocities.
* Rem: According to most of these models, the wave influences the behavior of the particle but the particle has no influence on the wave, so energy is not conserved and these theories cannot be written in Lagrangian form.
* History: It 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-conf; Singh a0805-ch; Dürr et al a0903-en; Kiessling FP(10)-a0905; Goldstein et al a0912-in; Bernstein AJP(11)jun [pedagogical]; Tumulka a1704-ch; Sanz a1707.
@ 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-proc, 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]; Nikolić AJP(08)feb-phy/07 [Bohr and Bohm, hypothetical]; Rusov a0804; Rusov & Vlasenko a0806; Schmelzer a0907 [beables and decoherence]; Kastner FS(12)-a1107; Hiley a1303 [Bohm's 'unbroken wholeness']; Solé SHPMP(13), Esfeld et al a1406 [and wave function ontology]; Sanz JPCS(14)-a1402; Norsen et al Synth-a1410 [single-particle wave functions in physical space]; Solé et al a1610-in [emergence of uncertainty].
@ 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]; Grössing et al QSMF(15)-a1412 ["deeper level" explanation]; Boström a1503 [response to criticism].
@ Formulations: Harvey PR(66) [as a quantum-mechanical Navier-Stokes equation]; Holland NCB(01) [Hamiltonian]; Holland CP(11)-a1409 [re de Broglie and Bohm versions]; Shanahan a1503; Avanzini et al FP(16)-a1503 [with a single Bohmian trajectory]; Vassallo SHPMP(15)-a1509 [and background independence]; Sutherland FP(16)-a1509 [Lagrangian form of the Bohm model]; Vassallo & Ip FP(16)-a1602 [relational]; in de Gosson 17 [geometric]; Colin et al a1703 [de Broglie's double solution program]; > s.a. formulations of quantum theory [hydrodynamical].
@ Books: in de Broglie 60, 63; in Bell 87; Bohm & Hiley 93; Holland 93; Cushing et al ed-96; Oriols & Mompart 12, in(12)-a1206.
> Online resources: see Wikipedia pages on the Bohm interpretation and pilot-wave interpretation.

Relationship with Standard Quantum Mechanics, Variations > s.a. Born Rule [dynamical origin, as equilibrium]; geometric formulations.
* Idea: Pilot-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, |ψ|2.
* Beyond quantum theory: As emphasized by Valentini, in de Broglie's theory quantum theory emerges as a special subset of a wider physics, which allows non-local signals and violation of the uncertainty principle; Standard quantum mechanics and the Born rule arise as equilibrium situations upon quantum relaxation in de Broglie's first-order dynamics for pilot-wave theory, but in general not in Bohm's second-order dynamics, and may be unstable at the Planck scale.
@ Same as standard quantum mechanics: Marchildon qp/00; Golshani & Akhavan qp/01; Struyve & De Baere qp/01-proc; Nikolić qp/03.
@ Inequivalent to standard quantum mechanics: Schmidt & Selleri FPL(91) [triple slit]; Neumaier qp/00 [different correlations]; Ghose Pra(02)qp/01 [incompatible]; Kiukas & Werner JMP(10), comment Dürr et al a1408; Szczepański a1002 ["quantum autoscattering"]; Nauenberg a1404 [in the momentum representation].
@ 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]; Atiq et al FP(09)-a1311 [extension, non-Bohmian quantum potentials]; Ekholdt a0906; Poirier ChemPh(10) [Bohmian mechanics without pilot waves]; Nikolić a1010 [almost-local].
@ Beyond quantum theory: Valentini PLA(04) [anomalous statistical properties]; Struyve & Valentini JPA(09)-a0808 [guidance equations for arbitrary Hamiltonians]; Valentini pw-a1001 [rev]; Bacciagaluppi JPCS(12) [non-equilibrium particle distribution, and Nelson's stochastic mechanics]; Colin & Valentini PRS(14)-a1306 [instability of quantum equilibrium in Bohm's dynamics]; Valentini a1409 [instability of quantum equilibrium]; > s.a. phenomenology.

Special Topics > s.a. Beables; classical limit; decoherence; hidden variables; realism.
* Trajectories: It has been proved that the motion of a vortex in the associated velocity field can induce chaos in the trajectories.
@ Relativistic / Lorentz invariance: Squires qp/95; Valentini PLA(97)-a0812; Dürr et al PRA(99)qp/98; Nikolić qp/03 [the only consistent one in first quantization], FPL(05)qp/04, AIP(05)qp, qp/06 [many-fingered time]; Koch a0810 [from scalar gravity]; Nikolić IJQI(09)-a0811 [and time operator]; Hernández-Zapata a1003 [for a spinning particle]; Hernández-Zapata & Hernández-Zapata FP(10)-a1006 [classical and non-relativistic limits]; Nikolić a1205; Dürr et al PRS(14)-a1307 [with foliation determined by the wave function]; Struyve & Tumulka JGP(14)-a1311 [time foliation with kinks]; Dürr & Lienert PRS(14)-a1403 [description of subsystems]; Khodagholizadeh et al a1405; Galvan JSP(15)-a1509 [without a preferred foliation]; Harder a1605, a1610 [emergence of material particles]; > s.a. systems [quantum field theories].
@ In curved spacetime: Shojai & Shojai PS(01)qp; Rahmani & Golshani a1706 [and geodesic deviation].
@ Probabilities: Božić & Marić PLA(91) [and interferometers]; Galvan FP(07)qp/06 [vs typicality], JSP(08)-a0711 ["imprecise probabilities"]; Callender SHPMP(07) [emergence and interpretation]; Nikolić 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 JChemP(07)qp/06 [complex action]; Matzkin & Nurock SHPMP(08)qp/06; Borondo et al JPA(09)-a0907 [dynamical-systems approach]; Gruebl & Penz a1011-ch [non-differentiable]; Contopoulos et al a1203 [ordered, zero Lyapunov characteristic numbers]; Naaman-Marom et al AP(12)-a1207 [position measurements and 'surrealistic trajectories']; de Gosson & Hiley AJP(13)may-a1304, PLA(13) [and short-time propagator]; Dey & Fring PRA(13) [from coherent states]; Chen & Kleinert a1308 [approximate nature of particle trajectories]; Cesa et al a1603 [chaotic Bohmian trajectories for stationary states]; de Gosson et al AP(16)-a1606; > s.a. Airy Packets; path integrals; Raychaudhuri Equation.
@ 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; Sanz & Miret-Artés AJP(12)-a1205 [and the quantum phase]; Orefice et al a1310 [physical reality of the waves]; Sudbery a1409-conf [logic of the future]; Dennis et al PLA(15)-a1412 [Bohm's quantum potential as an internal energy]; > s.a. Individuality; information; many-worlds interpretation; mind; photon; probabilities; quantum particles; superselection rules; topology; wave-function collapse.

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