Bell's Theorem and Inequalities |
In General
s.a. applications and generalizations; hidden variables;
history of quantum physics; realism [including tests].
* Bell's inequalities: Inequalities
(the original one was proposed by J Bell, others were derived later by other authors)
satisfied by correlations between measurements of observables in all local realist
theories, but not in quantum mechanics.
* Bell's theorem: No physical theory
of local hidden variables can reproduce all of the predictions of quantum mechanics.
* Rem: 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.
* And experiment: Several experimental
tests, starting with those of A Aspect et al., have confirmed the predictions of quantum
mechanics, hence falsifying local realism, and even some non-local theories have been
falsified; 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.
@ For non-specialists: Jack PW(95)apr;
Nadeau & Kafatos 00;
Avis et al IEICE(09)-a0812;
Blaylock AJP(10)jan-a0902,
reply Maudlin AJP(10)jan;
Ekert pw(09)sep;
Alford AJP(16)jun-a1506.
@ General references: Bell Phy(64);
Wigner AJP(70)aug [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);
Ballentine & Jarrett AJP(87)aug;
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)-a1802 [and Kochen-Specker];
Sudarshan & Rothman IJTP(93);
Jones & Adelberger PRL(94);
Ferrero et al AJP(90)jul;
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 PhD(07)-a0708;
Corbett & Home a0802;
Loubenets JPA(11)-a1012;
Sadiq et al PRD(13)-a1106 [the most elementary ones];
Khrennikov AIP(12)-a1108 [locality or realism?];
Abramsky & Hardy PRD(12)-a1203 [logical method];
Rudolph a1206 [from quantum steering];
Wiseman JPA(14)-a1402,
Wiseman & Rieffel IJQI-a1503 [two versions];
Rosset et al JPA(14)-a1404 [classification];
Maudlin JPA(14)-a1408
+ JPA(14)-a1408 [history and logical structure];
Vaidman a1501-in [and parallel worlds];
Żukowski a1501-conf;
Bertlmann PT(15)jul;
Ulrey a2001 [parametric and geometric perspective];
Waegell & McQueen a2003 [many worlds and locality].
@ Proofs: Herbert AJP(75)apr;
Gisin PLA(91) [non-product states];
Hess & Philipp qp/02,
qp/02,
qp/02,
qp/02,
qp/02,
AIP(05)qp/04 [critiques],
refuted by Mermin FP(05);
Ryff qp/05 [simple];
Cabello PRL(05) [2-observer];
Maccone AJP(13)nov-a1212 [simplest];
Gründler a1704 [versions and conclusions].
@ Superdeterminism: Vervoort FP(13)-a1203 [and 'supercorrelation' interpretation];
Palmer a1609 [and p-adic distance];
Bass & Le Bihan a2009 [problems with this view];
> s.a. measurement in quantum physics.
@ 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;
Nieuwenhuizen AIP(09)-a0812;
Christian a0904 [entanglement as an illusion],
a1005 [with a pair of entangled photons],
a1103-in [explicit counterexample];
Moldoveanu a1109 [disproof of Christian's counterexample];
Christian in(12)-a1110 [refutation of arguments],
refutation Gill a1203,
response a1203;
Leffler a1109 [and the space of all paths];
de Oliveira et al EPL(12)-a1208
[translation-invariant systems that do not violate Bell's inequality];
Weatherall FP(13)-a1212 [apparent counterexample];
news pw(13)apr [photons];
Coddens a1309 [geometrical];
Bierhorst a1311;
Lazarovici a1401 [time-symmetric interactions];
Larsson JPA(14)-a1407;
Romero-Rochín a1510;
Aspect Phy(15),
news PT(16)jan [on closing two loopholes at once];
Iannuzzi a1601 [questioning the experiments];
Nieuwenhuizen & Kupczynski FP(17)-a1611;
Christian a1704 [oversight by Bell];
Oaknin a1912 [no preferred absolute reference frame];
Suzuki & Mertes a1905;
Rossi et al a2006 [freedom of choice, solution];
Lambare a2008 [comment];
Kaiser a2011-ch [rev];
> s.a. pilot-wave theory phenomenology;
Retrocausation.
> Online resources:
see faacets.com;
Wikipedia page.
Related Topics
s.a. experiments in quantum theory and EPR-type;
probability in quantum theory; types
of quantum correlations.
* Implications: Loophole-free tests
of the violation of Bell's inequalities have demonstrated that at least one of
three properties of Locality, Realism or Ergodicity, is not satified in nature.
@ Conceptual, interpretations: Dotson AJP(86)mar;
Durt FP(94);
Peres FdP(00)qp/99 [Bayesian];
Dai Pra et al LMP(13)-a1301 [geometric interpretation];
Santos EJP(16)-a1410;
Kupczynski a2004.
@ Assumptions: Rothman & Sudarshan IJTP(01);
Lokajíček a1108-conf;
Żukowski & Brukner JPA(14)-a1501;
Tumulka a1501-in;
Hall a1511-fs [significance of measurement independence].
@ And entanglement: Cereceda PLA(96)qp/98,
PRA(02)qp;
Werner & Wolf QIC(01)qp [review].
@ And causality: Argaman AJP(10)oct-a0807;
Norsen FP(09)-a0808;
Robins et al SJoS(12)-a1207;
Gill StatS(14)-a1207;
Wüthrich FP(14);
Chaves et al PRL(15)-a1411 [relaxation of the causal assumptions];
Wiseman & Cavalcanti a1503-proc;
Healey a1601 [and probability];
Chaves et al Quant(17)-a1607 [multipartite];
Pearl & Cavalcanti a1909 [violations of classical causality].
@ And non-locality, indeterminism:
Stapp PRL(82);
Eberhard PRL(82);
& Aerts et al, Sassoli de Bianchi AP(14)-a1302 [models with varying parameters];
Brunner et al RMP(14)-a1303 [rev];
Budiyono IJTP(14);
Boughn a1604-conf,
FP(17)-a1703;
Hnilo a2001
[randomness test to decide which of locality, realism or ergodicity is violated];
Lambare a2102 [comment on inconsistency claims];
> s.a. determinism; locality in quantum mechanics.
@ Other topics: Berthelot NCB(80);
Harrison AJP(82)sep [correlations];
Svetlichny et al PhSc(88)sep;
Hacyan PLA(01) [invariance];
Auberson et al PLA(02) [in phase space];
Lupo et al JPA(06)qp [in the tomographic representation];
Matzkin AIP(09)-a0802,
a0808;
Junge et al PRL(10) [operator space theory];
Cavalcanti et al PRA(11)-a1012 [large violations using continuous variables];
Kupczynski a1611 [computer simulations];
Bolonek-Lasoń & Kosiński a1812 [group-theoretical approach];
> s.a. CHSH Inequality; CPT theorem;
Separability.
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