Hidden_variables EPR_paradox

in 1964, john bell showed predictions of quantum mechanics in epr thought experiment different predictions of particular class of hidden variable theories (the local hidden variable theories). speaking, quantum mechanics has stronger statistical correlation measurement results performed on different axes these hidden variable theories. these differences, expressed using inequality relations known bell s inequalities , in principle experimentally detectable. after publication of bell s paper, variety of experiments test bell s inequalities devised. these relied on measurement of photon polarization. experiments conducted date have found behavior in line predictions of standard quantum mechanics theory.

later work henry stapp showed key property of local hidden variable theories lead bell s inequalities counter-factual definiteness. building on stapp s observations, p.h. eberhard showed local counter-factual model results in bell s inequality without assumption of there being hidden variables unknown physics upon relevant observables depend. arthur fine subsequently showed theory satisfying inequalities can modeled local hidden variable theory. (although eberhard referred result bell s theorem without hidden variables , fine used more general definition of hidden variables includes possibility of observables being elementary.) fine went on show stochastic factorizable model leads bell s inequality. itamar pitowsky showed bell s inequality special case of inequality discovered george boole provides consistency check on whether data can represented variables on single classical probability space. interpreted indication locality assumption prevented data being represented events on such space.

as eberhard s proof made use of both locality , counter-factual definiteness assumed interpretation reject either 1 of these escape bell s inequality. violation of locality difficult reconcile special relativity, , thought incompatible principle of causality, nevertheless there renewed interest in bohm interpretation of quantum mechanics keeps counter-factual definiteness while introducing conjectured non-local mechanism in form of quantum potential defined 1 of terms of schrödinger equation. mainstream physics preferred keep locality , reject counter-factual definiteness. fine s work showed that, taking locality given, there exist scenarios in 2 statistical variables correlated in manner inconsistent counter-factual definiteness, , such scenarios no more mysterious other, despite fact inconsistency counter-factual definiteness may seem counter-intuitive .

further insights resulted work of lawrence j. landau. landau showed if assumed there single classical probability space underlying observables under consideration in epr experiment, bell s inequality result. fundamental issue quantum mechanical probabilities cannot modeled using classical (kolmogorovian) probability regardless of whether quantum mechanics considered complete description of reality or not. regarding landau s proof ray streater notes shows bohmian mechanics inconsistent quantum mechanics , succumbs bell s inequality despite claims contrary proponents. streater notes landau s proof requires assumption of single classical probability space (a condition still satisfied bohm s theory) , fact bohmian mechanics additionally postulates existence of non-local mechanism, cannot prevent bell s inequality applying it.

similar observations have been made karl hess, walter, philipp, hans de raedt , kristel michielsen, note in bell s proof, bell s assumption of space of hidden variables behaving classical probability space sufficient produce contradiction predications of quantum mechanics via consistency theorem of n. n. vorob ev, statistician had built on same work of boole used pitowsky. additional assumption of locality used bell redundant , indeed fine s work had included derivation of bell s inequality did not require assumption of locality . non-locality not sufficient escape bell s inequality, interpretation of quantum mechanics needs reject counter-factual definiteness consistent quantum mechanical predications. authors produced model of epr experiment local violates bell s inequality, demonstrating non-locality not necessary escaping bell s inequality. note loophole regarding models of epr experiments whereby counter-factual definite model can result in data violates bell s inequality if in actual experiments there time window based post-selection of results due need identify particles belonging emitted pair. robert griffiths has shown according quantum mechanical analysis, instrument settings measurement of 1 of particles in epr scenario, not influence subsequent measurement results on second, ruling out non-locality viable explanation epr correlations.

however, bell s theorem not apply possible philosophically realist theories. common misconception quantum mechanics inconsistent notions of philosophical realism. realist interpretations of quantum mechanics possible, although discussed above, such interpretations must reject counter-factual definiteness. examples of such realist interpretations consistent histories interpretation , transactional interpretation (first proposed john g. cramer in 1986). griffiths notes not local realism ruled out quantum mechanics classical realism . workers in field have attempted formulate hidden variable theories exploit loopholes in actual experiments, such assumptions made in interpreting experimental data, although no theory has been proposed can reproduce results of quantum mechanics.

alternatives still possible. recent review article based on wheeler–feynman time-symmetric theory rewrites entire theory in terms of retarded liénard–wiechert potentials only, becomes manifestly causal, and, establishes conservation law total generalized momenta held instantaneously closed system. outcome results in correlation between particles handshake principle based on variational principle applied system whole, idea non-local feature theory nonetheless in agreement essential results of quantum electrodynamics , relativistic quantum chemistry.

there individual epr-like experiments have no local hidden variables explanation. examples have been suggested david bohm , lucien hardy.