Bell's
Theorem and Inequalities| Bell's
Theorem and Inequalities |
In General > s.a. hidden
variables; locality;
realism.
* Idea: Bell's theorem
and inequalities are the formal counterpart of the EPR paradox, and strengthen
Einstein's argument by showing that either reality or locality must not hold
("Quantum mechanics is correct; Quantum mechanics is crazy; So nature
is crazy");
Quantum mechanics predicts that "properties
one cannot know anything about" (e.g.,
the value of spin along different directions) do not exist; Shown using entangled
states.
* Bell's theorem: No
physical theory of local hidden variables can reproduce all of the predictions
of quantum mechanics.
* Bell inequalities: Inequalities
(the orginal one by Bell and others derived later) among correlations between
different quantum observables, that can be violated if quantum mechanics (as
opposed to theories with local hidden variables) is correct.
* Consequences: Clauser
et al proved that experiments on Bell's inequalities rule out all interpretations
which assume locality, time-forwards causality
and the existence of an objective real world.
@ Non-technical references: Jack PW(95)apr;
Nadeau & Kafatos
00.
@ General references: Bell Physics(64);
Wigner AJP(70)
[simplification]; de Broglie CRAS(74); Lochak
FP(76)
[criticism]; Eberhard NCB(77), NCB(78);
Clauser & Shimony RPP(78);
Feingold & Peres JPA(80);
Fine PRL(82)
[hidden variables and probabilities], PRL(82);
Stapp PRL(82),
Eberhard PRL(82)
[and determinism, locality]; Ballentine & Jarrett AJP(87);
Fine FP(89);
Bertlmann FP(90);
issues FP(90)#10, FP(90)#11,
FP(90)#12,
FP(91)#1,
FP(91)#2,
FP(91)#3;
Home & Selleri RNC(91);
Santos PRL(91);
Stapp FP(91);
Elby BJPS(93);
Mermin RMP(93)
[and Kochen-Specker]; Sudarshan & Rothman IJTP(93);
Jones & Adelberger PRL(94);
Ferrero et al AJP(90);
Ardehali qp/98;
Aspect in(02)qp/04;
Rosinger qp/04 [and
George Boole]; Hess & Philipp FP(05)qp [Bass
theorem]; Marlow qp/06 [and
relationism]; Paterek a0708-PhD;
Corbett & Home a0802.
@ Proofs: Herbert AJP(75);
Gisin PLA(91)
[non-product states]; Hess & Philipp qp/02, qp/02, qp/02, qp/02, qp/02, qp/04 [critiques],
refuted by Mermin FP(05);
Ryff qp/05 [simple];
Cabello PRL(05)
[2-observer]; Argaman a0807 [and causality].
@ Loopholes: Brans IJTP(88);
Werbos & Dolmatova qp/00 [backwards-time
interpretation]; Volovich qp/00;
Vaidman PLA(01)qp;
Clover qp/05;
Christian qp/07,
qp/07,
a0707 [failure
for Clifford-algebra-valued local variables], Grangier a0707,
Tung a0712 [criticisms];
Morgan a0801 [coincidence
time]; LiMing & Tang a0807.
> Online resources: Wikipedia page.
Related Topics > s.a. collapse [gravity-induced]; EPR
paradox and experiments; probability
in physics [and
quantum measure].
@ And entanglement: Cereceda PLA(96)qp/98, PRA(02)qp;
Werner & Wolf QIC(01)qp [review].
@ Bounds on violations: Cabello PRL(02)
[beyond Cirel'son]; Filipp & Svozil qp/04-in
[method]; > s.a. correlations.
@ Applications: Benatti & Floreanini hp/97 [correlated K's];
O'Hara ht/97 [particle
couplings]; Campo & Parentani PRD(06)ap/05 [inflationary
spectra].
@ And covariance: Stapp AJP(01)qp/00 [acausal
propagation]; Kim & Noz qp/06-in
[simultaneity].
@ Conceptual, interpretations: Dotson AJP(86);
Durt FP(94);
Peres FdP(00)qp/99 [Bayesian].
@ Classical models: Barut & Meystre PLA(82);
Palmer PRS(95)
[spin]; Morgan JPA(06)cm/04 [random
fields]; Matzkin JPA(08)-a0709,
PRA(08) [classical violation from random interactions]; Willeboordse a0804.
@ Other topics: Berthelot NCB(80); Harrison AJP(82)
[correlations]; Svetlichny et al PhSc(88);
Hacyan PLA(01)
[invariance]; Rothman & Sudarshan IJTP(01)
[assumptions]; Auberson et al PLA(02)
[in phase space]; Lupo et al JPA(06)qp [in
tomographic representation]; Matzkin JPA(08)qp/07 [classical
distributions that violate
the inequalities], a0802;
Flitney et al a0803 [and
game theory]; > s.a. CPT, optics, spin [classical
models].
Generalizations > s.a. Penrose
Dodecahedron; relativistic quantum mechanics.
@ Single particle: Tan et al PRL(91), Hardy PRL(94) [photon]; Basu et
al PLA(01) [spin-1/2].
@ More than two particles: Mermin PRL(90)
[3-particle]; Cabello PRA(02)
[n spin-s particles]; Laskowski et al qp/03 [multipartite].
@ For mixed states: Popescu PRL(95).
@ Entropic Bell inequalities: Cerf & Adami PRA(97)qp/96;
Durham qp/07-in, a0801.
@ Without inequalities: Cabello PRL(01), PRL(03)qp,
PRL(03)qp,
comment Marinatto
PRL(03)qp,
comment Cabello PRL(04)qp;
Cabello FP(05)qp/04;
Greenberger et al qp/05 [GHZ-type,
using
inefficient detectors]; Broadbent et al NJP(06)qp/05 [logical
structure]; Ghirardi & Marinatto a0711-PLA.
@ Related topics: Braunstein & Caves PRL(88), AP(90)
[information-theoretic]; Franson PRL(89);
Stapp PRA(94);
Peres FP(99)qp/98;
Razmi & Golshani
qp/98;
Vervoort qp/00/EPL
[non-linear systems]; Collins et al PRL(02)qp/01 [high
dimensionality]; Reid
qp/01, qp/01 [continuous
outcomes]; Larsson PRA(04)qp/03 [position];
Clover qp/04 [time
ordering of measurements]; Pankovic qp/05 [general
relativistic]; Lapiedra & Socolovsky a0806 [arrow
of time and Leggett inequalities]; Christian a0806 [macroscopic domain].
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Send feedback and suggestions to bombelli at olemiss.edu – Modified
5 jul 2008