Bell's Theorem and Inequalities  

In General blue bullet 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; Wikipedia page.

Related Topics blue bullet 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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