Description_of_the_paradox EPR_paradox

1 description of paradox

1.1 epr paper
1.2 measurements on entangled state
1.3 locality in epr experiment

description of paradox

the original epr paradox challenges prediction of quantum mechanics impossible know both position , momentum of quantum particle. challenge can extended other pairs of physical properties.

epr paper

the original paper purports describe must happen 2 systems , ii, permit interact ... , and, after time, suppose there no longer interaction between 2 parts. explained manjit kumar (2009), epr description involves 2 particles, , b, [which] interact briefly , move off in opposite directions. according heisenberg s uncertainty principle, impossible measure both momentum , position of particle b exactly. however, possible measure exact position of particle a. calculation, therefore, exact position of particle known, exact position of particle b can known. alternatively, exact momentum of particle can measured, exact momentum of particle b can worked out. kumar writes: epr argued had proved ... [particle] b can have simultaneously exact values of position , momentum. ... particle b has position real , momentum real.

epr appeared have contrived means establish exact values of either momentum or position of b due measurements made on particle a, without slightest possibility of particle b being physically disturbed.

epr tried set paradox question range of true application of quantum mechanics: quantum theory predicts both values cannot known particle, , yet epr thought experiment purports show must have determinate values. epr paper says: forced conclude quantum-mechanical description of physical reality given wave functions not complete.

the epr paper ends saying:

while have shown wave function not provide complete description of physical reality, left open question of whether or not such description exists. believe, however, such theory possible.

measurements on entangled state

we have source emits electron–positron pairs, electron sent destination a, there observer named alice, , positron sent destination b, there observer named bob. according quantum mechanics, can arrange our source each emitted pair occupies quantum state called spin singlet. particles said entangled. can viewed quantum superposition of 2 states, call state , state ii. in state i, electron has spin pointing upward along z-axis (+z) , positron has spin pointing downward along z-axis (−z). in state ii, electron has spin −z , positron has spin +z. because in superposition of states impossible without measuring know definite state of spin of either particle in spin singlet.

the epr thought experiment, performed electron–positron pairs. source (center) sends particles toward 2 observers, electrons alice (left) , positrons bob (right), can perform spin measurements.

alice measures spin along z-axis. can obtain 1 of 2 possible outcomes: +z or −z. suppose gets +z. according copenhagen interpretation of quantum mechanics, quantum state of system collapses state i. quantum state determines probable outcomes of measurement performed on system. in case, if bob subsequently measures spin along z-axis, there 100% probability obtain −z. similarly, if alice gets −z, bob +z.

there is, of course, nothing special choosing z-axis: according quantum mechanics spin singlet state may equally expressed superposition of spin states pointing in x direction. suppose alice , bob had decided measure spin along x-axis. ll call these states ia , iia. in state ia, alice s electron has spin +x , bob s positron has spin −x. in state iia, alice s electron has spin −x , bob s positron has spin +x. therefore, if alice measures +x, system collapses state ia, , bob −x. if alice measures −x, system collapses state iia, , bob +x.

whatever axis spins measured along, found opposite. can explained if particles linked in way. either created definite (opposite) spin every axis—a hidden variable argument—or linked 1 electron feels axis other having spin measured along, , becomes opposite 1 axis—an entanglement argument. moreover, if 2 particles have spins measured different axes, once electron s spin has been measured x-axis (and positron s spin x-axis deduced), positron s spin z-axis no longer certain, if (a) knows measurement has taken place, or (b) has definite spin already, second axis—a hidden variable. however, turns out predictions of quantum mechanics, have been confirmed experiment, cannot explained local hidden variable theory. demonstrated in bell s theorem.

in quantum mechanics, x-spin , z-spin incompatible observables , meaning heisenberg uncertainty principle applies alternating measurements of them: quantum state cannot possess definite value both of these variables. suppose alice measures z-spin , obtains +z, quantum state collapses state i. now, instead of measuring z-spin well, bob measures x-spin. according quantum mechanics, when system in state i, bob s x-spin measurement have 50% probability of producing +x , 50% probability of -x. impossible predict outcome appear until bob performs measurement.

here crux of matter:

you might imagine that, when bob measures x-spin of positron, answer absolute certainty, since prior hasn t disturbed particle @ all. turns out bob s positron has 50% probability of producing +x , 50% probability of −x, meaning outcome not certain. s if bob s positron knows alice has measured z-spin of electron, , hence positron s own z-spin must set, x-spin remains uncertain.

put way, how bob s positron know way point if alice decides (based on information unavailable bob) measure x (i.e., opposite of alice s electron s spin x-axis) , how point if alice measures z, since supposed know 1 thing @ time? copenhagen interpretation rules wave function collapses @ time of measurement, there must action @ distance (entanglement) or positron must know more s supposed know (hidden variables).

here paradox summed up:

it 1 thing physical measurement of first particle s momentum affects uncertainty in own position, measuring first particle s momentum affects uncertainty in position of other thing altogether. einstein, podolsky , rosen asked how can second particle know have precisely defined momentum uncertain position? since implies 1 particle communicating other instantaneously across space, i.e., faster light, paradox .

incidentally, bell used spin example, many types of physical quantities—referred observables in quantum mechanics—can used. epr paper used momentum observable. experimental realisations of epr scenario use photon polarization, because polarized photons easy prepare , measure.

locality in epr experiment

the principle of locality states physical processes occurring @ 1 place should have no immediate effect on elements of reality @ location. @ first sight, appears reasonable assumption make, seems consequence of special relativity, states information can never transmitted faster speed of light without violating causality. believed theory violates causality internally inconsistent, , useless.

it turns out usual rules combining quantum mechanical , classical descriptions violate principle of locality without violating causality. causality preserved because there no way alice transmit messages (i.e., information) bob manipulating measurement axis. whichever axis uses, has 50% probability of obtaining + , 50% probability of obtaining − , @ random; according quantum mechanics, fundamentally impossible influence result gets. furthermore, bob able perform measurement once: there fundamental property of quantum mechanics, known no cloning theorem , makes impossible him make million copies of electron receives, perform spin measurement on each, , @ statistical distribution of results. therefore, in 1 measurement allowed make, there 50% probability of getting + , 50% of getting − , regardless of whether or not axis aligned alice s.

however, principle of locality appeals powerfully physical intuition, , einstein, podolsky , rosen unwilling abandon it. einstein derided quantum mechanical predictions spooky action @ distance . conclusion drew quantum mechanics not complete theory.

in recent years, however, doubt has been cast on epr s conclusion due developments in understanding locality , quantum decoherence. word locality has several different meanings in physics. example, in quantum field theory locality means quantum fields @ different points of space not interact 1 another. however, quantum field theories local in sense appear violate principle of locality defined epr, nevertheless not violate locality in more general sense. wavefunction collapse can viewed epiphenomenon of quantum decoherence, in turn nothing more effect of underlying local time evolution of wavefunction of system , of environment. since underlying behaviour doesn t violate local causality, follows neither additional effect of wavefunction collapse, whether real or apparent. therefore, outlined in example above, neither epr experiment nor quantum experiment demonstrates faster-than-light signaling possible.