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

71 lines
977 B
Plaintext
Raw Blame History

This file contains ambiguous Unicode characters

This file contains Unicode characters that might be confused with other characters. If you think that this is intentional, you can safely ignore this warning. Use the Escape button to reveal them.

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