mirror of
https://asciireactor.com/otho/phy-521.git
synced 2024-11-21 20:25:07 +00:00
71 lines
977 B
Plaintext
71 lines
977 B
Plaintext
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
|
||
|
||
|
||
|
||
|
||
|
||
|
||
|