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71 lines
977 B
Plaintext
71 lines
977 B
Plaintext
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Three viewpoints: realist, orthodox, agnostic
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// |phi_1> |phi_2>
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For parallel detectors:
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P(a,b) = -1
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arbitrary orientation:
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P(a,b) = -a⋅b
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Our understanding of entanglement is consistent with the idea that modern local variables
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A(a,λ) = ±1.
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B(b,λ) = ±1.
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If detectors are aligned:
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A(a,λ) = -B(b,λ).
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Average of product of measurements
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P(a,b) = ∫ ρ(λ) A(a,λ) B(b,λ) dλ
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but since A(a,λ) = -B(b,λ),
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P(a,b) = - ∫ ρ(λ) A(a,λ) A(b,λ) dλ
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c is any other unit vector...
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P(a,b) - P(a,c) = - ∫ ρ(λ) [ A(a,λ) A(b,λ) - A(a,λ) A(c,λ) ] dλ
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= - ∫ ρ(λ) [ 1 - A(a,λ) A(c,λ) ] A(a,λ) A(b,λ) dλ
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Because A(a,λ) = ±1 and B(b,λ) = ±1,
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-1 ≤ [A(a,λ) A(b,λ)] ≤ +1.
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ρ(λ) [1 - A(b,λ) A(c,λ)] ≥ 0, so
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│P(a,b) - P(a,c)│ ≤ ∫ ρ(λ) [1 - A(B,λ) A(c,λ)] dλ.
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│P(a,b) - P(a,c)│ ≤ 1 + P(b,c)
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simulation:
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pion decays, leaving two particles
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each particle has a spin state
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