Three viewpoints: realist, orthodox, agnostic



// |phi_1> |phi_2> 



For parallel detectors:

P(a,b) = -1


arbitrary orientation:

P(a,b) = -a⋅b

Our understanding of entanglement is consistent with the idea that modern local variables 



A(a,λ) = ±1.
B(b,λ) = ±1.

If detectors are aligned:

A(a,λ) = -B(b,λ).

Average of product of measurements

P(a,b) = ∫ ρ(λ) A(a,λ) B(b,λ) dλ

    but since A(a,λ) = -B(b,λ),

    P(a,b) = - ∫ ρ(λ) A(a,λ) A(b,λ) dλ

c is any other unit vector...

P(a,b) - P(a,c) = - ∫ ρ(λ) [ A(a,λ) A(b,λ) - A(a,λ) A(c,λ) ] dλ

    = - ∫ ρ(λ) [ 1 - A(a,λ) A(c,λ) ] A(a,λ) A(b,λ) dλ

Because A(a,λ) = ±1 and B(b,λ) = ±1,

    -1 ≤ [A(a,λ) A(b,λ)] ≤ +1.

ρ(λ) [1 - A(b,λ) A(c,λ)] ≥ 0, so

    │P(a,b) - P(a,c)│ ≤ ∫ ρ(λ) [1 - A(B,λ) A(c,λ)] dλ.




│P(a,b) - P(a,c)│ ≤ 1 + P(b,c)



simulation:


pion decays, leaving two particles

each particle has a spin state