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Chapter 22 The EPR paper and Bell's theorem by Steve Kurtz

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EPR Paper ● Albert Einstein, Boris Podolsky, Nathan Rosen ● “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?” -1935 ● Einstein – accepted Quantum Mechanics as a good approximation of the atom – could not accept a theory that all objects are defined by probabilities

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EPR Definitions ● Complete Theory – “there is an element corresponding to each element of reality” ● Element of Physical Reality - an element whose value can be precisely predicted without disturbing the system ● Two main assumptions – Realism - the world exists independently of our observations – Locality - objects cannot affect one another instantaneously through a distance

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Logical Argument ● “In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality.” ● If (1) is false, then (2) is false ● At least one of them must be true

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EPR Proof ● No action at a distance so once the two particles separate, they must assume definite elements of reality ● At A we can choose to observe either p1 or x1 thus forcing p2 and x2 to correspond to elements of reality. ● This means (2) is false, forcing (1) to be true thus quantum mechanics must be incomplete

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EPR Explanation ● Seemed to indicate quantum mechanics is incomplete assuming reality and locality hold ● Possible explanation is a hidden-variables theorem where certain unknown variables complete the theory of quantum mechanics ● Hidden-variables were not mentioned by EPR ● This idea was later disproved by Bell's Theorem

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Bell's Theorem ● 1965 while working at European Center for Nuclear Research (CERN) ● Assume – Objective Reality – there is truth whether or not we observe it – Results at A are independent of B ● Result – No hidden-variables theory can agree with all of quantum mechanics

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Mermin's Explanation Setup ● Imagine two detectors(A & B) and one emitter(C) – Detectors are not connected in any way – Lights can only be triggered by measurement of particle – 9 possible switch settings(11, 12, 13, 21, 22, 23, 31, 32, 33) – Timing is not important – Experiment is run millions of times

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Two Observed Cases ● Case A – (11, 22, 33) – Lights always flash same color – P(RR)=P(GG) ● Case B – (12, 13, 21, 23, 31, 32) – 25% Lights flash the same, P(RR)=P(GG) – 75% Lights flash different, P(RG)=P(GR)

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Mermin Explanation ● Each particle has three properties(speed, size, shape) each of which is measured by a particular lever setting – Particles emitted together are identical ● Creates 8 possible states(RRR, RRG, RGR, GRR, GGR, GRG, RGG, GGG) ● Predicts in case A, all results are the same ● Predicts in case B chances of same>33% ● Now we have a contradiction 33%>25%

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Mermin – EPR ● EPR only considers case A – Einstein insists color sets(RRR, etc) exist and are acceptable – Quantum Theory predicts this exact behavior – Quantum Theory insists that not all three colors can exist at once – Looks like Einstein is right

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Mermin - Bell ● Bell's genius involves noticing case B ● Demonstrates all three colors cannot exist together ● As experiments are performed, Bell and Quantum mechanics are supported – Unknown-variable theories no longer hold up – Local realism is called into question

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Jarrett's Divisions of Locality ● Jarrett Locality – outcome at A is independent of choice of variable at B – does not fail for quantum mechanics ● “Controllable Nonlocality” – violates special relativity ● Jarrett Completeness – outcome at A is independent of measurement at B – fails for quantum mechanics ● “Uncontrollable Nonlocality”

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Conclusions ● EPR Paper set out to show Quantum Mechanics is incomplete ● Bell shows that EPR thought experiment does not consider the complete picture ● Experiments support quantum mechanics ● Locality is called into question

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Sources ● Afriat and Selleri, The Einstein, Podolsky, and Rosen Paradox in Atomic, Nuclear, and Particle Physics ● Cushing, Philosophical Concepts in Physics ● Cushing, Philosophical Consequences of Quantum Theory ● www.wikipedia.org

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