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].
main page – abbreviations – journals – comments – other
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send feedback and suggestions to bombelli at olemiss.edu – modified 11
nov 2009