Resolving_the_paradox EPR_paradox

1 resolving paradox

1.1 hidden variables

1.1.1 bell s inequality


1.2 einstein s hope purely algebraic theory
1.3 acceptable theories , experiment
1.4 implications quantum mechanics

resolving paradox
hidden variables

there several ways resolve epr paradox. 1 suggested epr quantum mechanics, despite success in wide variety of experimental scenarios, incomplete theory. in other words, there yet undiscovered theory of nature quantum mechanics acts kind of statistical approximation (albeit exceedingly successful one). unlike quantum mechanics, more complete theory contains variables corresponding elements of reality . there must unknown mechanism acting on these variables give rise observed effects of non-commuting quantum observables , i.e. heisenberg uncertainty principle. such theory called hidden variable theory.

to illustrate idea, can formulate simple hidden variable theory above thought experiment. 1 supposes quantum spin-singlet states emitted source approximate descriptions true physical states possessing definite values z-spin , x-spin. in these true states, positron going bob has spin values opposite electron going alice, values otherwise random. example, first pair emitted source might (+z, −x) alice , (−z, +x) bob , next pair (−z, −x) alice , (+z, +x) bob , , forth. therefore, if bob s measurement axis aligned alice s, opposite of whatever alice gets; otherwise, + , − equal probability.

assuming restrict our measurements z- , x-axes, such hidden variable theory experimentally indistinguishable quantum mechanics. in reality, there may infinite number of axes along alice , bob can perform measurements, there have infinite number of independent hidden variables. however, not serious problem; have formulated simplistic hidden variable theory, , more sophisticated theory might able patch up. turns out there more serious challenge idea of hidden variables.

bell s inequality

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.

einstein s hope purely algebraic theory

the bohm interpretation of quantum mechanics hypothesizes state of universe evolves smoothly through time no collapsing of quantum wavefunctions. 1 problem copenhagen interpretation precisely define wavefunction collapse. einstein maintained quantum mechanics physically incomplete , logically unsatisfactory. in meaning of relativity , einstein wrote, 1 can give reasons why reality cannot @ represented continuous field. quantum phenomena appears follow certainty finite system of finite energy can described finite set of numbers (quantum numbers). not seem in accordance continuum theory , must lead attempt find purely algebraic theory representation of reality. nobody knows how find basis such theory. if time, space, , energy secondary features derived substrate below planck scale, einstein s hypothetical algebraic system might resolve epr paradox (although bell s theorem still valid). if physical reality totally finite, copenhagen interpretation might approximation information processing system below planck scale.

acceptable theories , experiment

according present view of situation, quantum mechanics flatly contradicts einstein s philosophical postulate acceptable physical theory must fulfill local realism .

in epr paper (1935), authors realised quantum mechanics inconsistent assumptions, einstein nevertheless thought quantum mechanics might augmented hidden variables (i.e., variables were, @ point, still obscure him), without other change, achieve acceptable theory. pursued these ideas on twenty years until end of life, in 1955.

in contrast, john bell, in 1964 paper, showed quantum mechanics , class of hidden variable theories einstein favored lead different experimental results: different factor of 3/2 correlations. issue of acceptability , time concerning theory, became experimentally decidable.

there many bell test experiments, e.g., of alain aspect , others. support predictions of quantum mechanics rather class of hidden variable theories supported einstein.

implications quantum mechanics

most physicists today believe quantum mechanics correct, , epr paradox paradox because classical intuitions not correspond physical reality. how epr interpreted regarding locality depends on interpretation of quantum mechanics 1 uses. in copenhagen interpretation, understood instantaneous wave function collapse occur. however, view there no causal instantaneous effect has been proposed within copenhagen interpretation: in alternate view, measurement affects our ability define (and measure) quantities in physical system, not system itself. in many-worlds interpretation, locality strictly preserved, since effects of operations such measurement affect state of particle measured. however, results of measurement not unique—every possible result obtained.

the epr paradox has deepened our understanding of quantum mechanics exposing fundamentally non-classical characteristics of measurement process. before publication of epr paper, measurement visualized physical disturbance had inflicted directly upon measured subsystem. instance, when measuring position of electron, 1 imagines shining light on it, disturbing electron , producing quantum mechanical uncertainties in position. such pat , convenient unhelpful explanations of quantum mechanics remain commonplace today, fail explain (among other things) epr paradox, shows measurement can performed on particle without disturbing directly, performing measurement on distant entangled particle. in fact, yakir aharonov , collaborators have developed whole theory of so-called weak measurement.

technologies relying on quantum entanglement being developed. in quantum cryptography, entangled particles used transmit signals cannot eavesdropped upon without leaving trace. in quantum computation, entangled quantum states used perform computations in parallel, may allow calculations performed more ever classical computers.