phy-521/presentation/sim_notes.motes
2020-12-23 16:45:08 -05:00

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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