Download Kurtz on EPR and Bell`s Theorem

Chapter 22
The EPR paper and Bell's theorem
by Steve Kurtz
EPR Paper
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Albert Einstein, Boris Podolsky, Nathan Rosen
“Can Quantum-Mechanical Description of
Physical Reality Be Considered Complete?” -1935
Einstein
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accepted Quantum Mechanics as a good approximation
of the atom
could not accept a theory that all objects are defined by
probabilities
EPR Definitions
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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
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Realism - the world exists independently of our
observations
Locality - objects cannot affect one another
instantaneously through a distance
Logical Argument
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“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
EPR Proof
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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
EPR Explanation
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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
Bell's Theorem
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1965 while working at European Center for
Nuclear Research (CERN)
Assume
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Objective Reality – there is truth whether or not we
observe it
Results at A are independent of B
Result
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No hidden-variables theory can agree with all of
quantum mechanics
Mermin's Explanation
Setup
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Imagine two detectors(A & B) and one emitter(C)
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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
Two Observed Cases
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Case A
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(11, 22, 33)
Lights always flash
same color
P(RR)=P(GG)
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Case B
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(12, 13, 21, 23, 31, 32)
25% Lights flash the
same, P(RR)=P(GG)
75% Lights flash
different,
P(RG)=P(GR)
Mermin Explanation
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Each particle has three properties(speed, size,
shape) each of which is measured by a particular
lever setting
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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%
Mermin – EPR
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EPR only considers case A
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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
Mermin - Bell
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Bell's genius involves noticing case B
Demonstrates all three colors cannot exist together
As experiments are performed, Bell and Quantum
mechanics are supported
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Unknown-variable theories no longer hold up
Local realism is called into question
Jarrett's Divisions of Locality
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Jarrett Locality
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outcome at A is
independent of choice
of variable at B
does not fail for
quantum mechanics
“Controllable
Nonlocality”
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violates special
relativity
Jarrett Completeness
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outcome at A is
independent of
measurement at B
fails for quantum
mechanics
“Uncontrollable
Nonlocality”
Conclusions
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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
Sources
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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
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