Locality
and Localization in Quantum Mechanics| Locality
and Localization in Quantum Mechanics |
Locality > s.a. experiments; foundations and interpretations;
locality; locality and localization
in quantum field theory.
* Idea: Quantum mechanics
and relativistic causality imply non-locality.
* Non-locality: Wave-function
collapse, the Aharonov-Bohm effect, and likely effects due to small-scale spacetime
structure;
Quantum non-locality is usually tied to the celebrated no-go theorems, including
the Kochen-Specker and Bell theorems, as well as elegant refinements by Mermin,
Peres, Hardy, GHZ, and many others; Typically entanglement or carefully prepared
multipartite systems have been considered essential for violations of local
realism and for understanding quantum non-locality; However, sharp violations
of local realism arise almost everywhere without entanglement.
* And correlations: The
set of non-local correlations known as Popescu-Rohrlich
box can be seen as a unit of non-locality.
* Implementations of locality:
de Broglie-Bohm's pilot wave, or parametrized
relativistic quantum theory (> see modified quantum
mechanics).
* Ways out: Non-locality
is only an artifact of considering quantum objects and classical observers
(Tipler); Particles described by the Klein-Gordon or
Dirac equation
cannot be localized and therefore don't violate causality; See also Marolf
+ Rovelli model.
@ In general, and non-relativistic: Sorkin pr(83);
Groenewold PRP(87);
Hoekzema FP(87)
[in contextual theories]; Hajra & Bandyopadhyay PLA(91)
[and quantization procedure, quantum geometry]; Kar PRA(97)
[n spin-1/2]; Healey PhSc(97)mar
[Aharonov-Bohm effect]; Strunz et al PRL(99)
[stochastic quantum mechanics, high-T environment]; de la Madrid IJTP(07)qp/06 [and
rigged Hilbert space]; Ghirardi & Marinatto PRA(06)
[Hardy for mixed states]; De Bievre mp/06 [rev];
Laloë in(07)cm/06
[and BEC]; Nikolic qp/07 [algorithmic
definition of locality]; Chen & Zhu a0711 [vs
realism]; Griffiths a0908 [Einstein locality vs Bell inequalities].
@ Single particle: Björk et al PRA(01);
Dunningham
& Vedral PRL(07)
[realizable experiment]; > s.a particle
models and quantum
particles.
@ Relativistic: Omnès JMP(97);
Zakrzewski JPA(97);
Terno qp/02 [and
energy
density]; Barat & Kimball PLA(03);
Slavnov
TMP(08);
Albert & Galchen SA(09)mar; > s.a. relativistic
quantum mechanics, quantum
measurement [MR
model].
@ Photons:
Hardy PLA(91), PRL(94),
Drezet FPL(06)
[single];
Pryde
et
al PRL(05)qp/04 [without
entanglement].
@ Other systems: Parasuram & Ghosh a0903 [bipartite
spin systems]; Bancal et al PRL(09)-a0903 [multipartite]; > s.a. networks; quantum
systems; spin models.
Localization
* Idea: Described by the
Born localization formalism, which in the relativistic context becomes Newton-Wigner
localization), and modular localization in quantum field theory; Related to the
concepts
of
uncertainty,
entropy, phase space volume.
* Hegerfeldt theorem: A
wave function for a particle whose time evolution is determined by a positive
(or bounded from below) Hamiltonian, and initially confined to a finite volume,
will instantaneously
develop infinite tails and violate causality, even in relativistic quantum mechanics;
This paradoxical
result
arises in relativistic theories from a failure of objectivity of localization – the
so-called 'Jericho effect'.
* In solid state: Localization
of electrons is a dramatic effect of destructive interference; The phenomenon
is usually perceived as arising from extrinsic disorder that breaks the discrete
translational invariance of a perfect crystal lattice (e.g., defects or impurities
for phonons, disorder for electrons); However, intrinsic localized modes, a.k.a.
discrete breathers, are typical excitations in perfectly periodic but strongly
non-linear systems.
* In atomic physics: Non-dispersing
electron wave packets can be obtained by applying a circularly polarized microwave
field.
@ General references: Szabo ht/96 [and
path integrals]; Bracken & Melloy JPA(99)qp [of
electrons,
solution]; Nicrosini & Rimini FP(03)qp/02 [relativistic
spontaneous]; Detournay et al PRD(02)ht [generalized
commutation relations]; Dunstan qp/05 [interaction
with the environment]; Morchio & Strocchi JPA(07)qp/06-in
[consequences]; Pinamonti RVMP(07)
[intrinsic, from symmetry group]; Schroer a0711 [vs
quantum field theory]; Sträng JPA(08)-a0708 [squeezed
states]; Pennini et al PLA(08)
[and Husimi distributions, Wehrl entropy].
@ Hegerfeldt theorem: Wickramasekara & Bohm JPA(02)
[for t-semigroups];
Debs & Redhead SHPMP(03)
[relativistic, Jericho effect].
@ Measurement-induced: Irby PRA(03)qp/02 [gamma-rays];
Cable et al PRA(05)qp/04 [relational
degrees of freedom].
@ In condensed matter, mesoscopic physics: Janssen 01 [fluctuations
and localization]; > s.a. Anderson
Localization [random media].
@ In atomic physics: Maeda et al PRL(09)
and Stroud Phy(09)
[non-dispersing electron wave packets].
Other References > s.a. particle
statistics; quantum
technology; realism;
time in quantum theory; wave-function
collapse.
@ I, II: Nadeau & Kafatos 00; Jacobs & Wiseman AJP(05)oct
[short story].
@ Non-locality: Bohm & Hiley FP(75);
Brody & de la Peña-Auerbach NCB(79);
Stapp AJP(85)apr, FP(88);
Ne'eman FP(86)-in(88)
[and
gauge theory]; Clifton FPL(89);
Aerts & Reignier HPA(91);
Elitzur et al PLA(92);
Popescu PRL(94);
Rosen AJP(94)feb;
Rohrlich & Popescu qp/95;
Nogueira et al PS(96);
Popescu & Rohrlich qp/97-in;
Stapp AJP(97)apr,
comment Finkelstein qp/98,
Mashkevich qp/98,
Shimony & Stein AJP(01)aug;
Mermin AJP(98)oct-qp/97,
qp/97;
Tittel et al EPL(97)qp [experiment
with photons]; Unruh PRA(99)qp/97,
comment Stapp qp/98,
PRA(99)qp/98;
Hegerfeldt
qp/98-in,
AdP(98)qp-in;
Pati qp/98-in;
Sidharth qp/98;
Choy & Ziegeler qp/99/AJP;
Stapp
qp/00;
Dieks PRA(02)qp [inequalities];
Jones et al PRA(05)qp/04 [multi-particle];
Wiseman CP(06)qp/05 [history,
Einstein]; Ghirardi & Marinatto JOB-qp/05-in
[without inequalities]; Unruh IJQI(06);
Scarani PRA(08)-a0712 [Elitzur-Popescu-Rohrlich
approach]; Dukaric & Wolf a0808 [non-locality
distillation]; Almeida et al a0911 [multipartite].
@ Proof: Hardy PRL(93)
[two particles]; Boschi et al PRL(97);
Hardy in(97) [spin-1/2]; Cabello PRA(98)
[ladder, spin-1].
@ And correlations: Clifton
et al BJPS(90);
Tittel et al
PRA(98)qp/97 [> 10
km]; Mermin FP(99)qp/98;
Unnikrishnan qp/00;
Barrett & Pironio PRL(05)qp [as
non-locality units]; Buchholz & Summers PLA(05); Suarez
a0902 [why not
maximally non-local?]; > s.a. EPR
correlations.
@ And entanglement: Bennett et
al PRA(99)qp/98;
Unnikrishnan qp/00-in;
Brunner et al NJP(05)qp/04;
Malley & Fine PLA(05)qp.
@ And information processing: Forster et al PRL(09)
[distilling nonlocality in generalized non-signaling theories].
@ And causality: Ruijsenaars AP(81),
Bruß et al PRA(00)qp [superluminal
propagation]; Mashkevich qp/98;
Busch JPA(99)
[unsharp localization]; Buscemi & Compagno JPB(06)qp.
@ And Bell's inequality: Jarrett Noûs(84);
Stapp qp/99;
Pitowsky & Svozil PRA(01);
Socolovsky PLA(03)qp;
Rizzi qp/03;
Hemmick qp/04 [hidden
variables]; Cavalcanti a0911.
@ Quantum mechanics is local: de Muynck
et al FP(94),
comment Stapp FP(94);
De Baere et al FP(99);
Bene qp/00-in;
Tommasini JHEP(02)ht;
Unnikrishnan FPL(02)qp, qp/02-in
[wave-function collapse]; Clover qp/03;
De Baere FP(05)qp;
Filk IJTP(06)qp;
Weinstein FP(09)-a0812 [model].
@ In many-worlds interpretation: Sakaguchi qp/96; Tipler qp/00; Rubin
FP(02)qp.
@ And hidden-variable interpretations:
Teufel et al PRA(97); > s.a. pilot-wave
theory.
@ Recovery of locality in classical limit: Pagonis et al PLA(91); Gisin
et al qp/96-in;
't Hooft ht/00-in.
@ Related topics: Aharonov & Vaidman qp/99 [fermions
vs bosons]; Sant'Anna qp/00 [and
quasi-set theory]; Melloy FP(02)
[formalism]; Kafatos et al qp/02 [and
sheaf cohomology]; van Dam et
al IEEE(05)qp/03 [strength
of proofs]; Assar & Putz mp/05 [massless,
momentum]; Slavnov a0903.
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nov
2009