Joy Christian wrote:gill1109 wrote:The simulation program is as local as any other we have been discussing.
This is incorrect. The Gisin and Gisin model is nonlocal. They explicitly state:
"Next, we need the conditional density probability distribution of the ~λA given that an outcome is produced: ρ(~λ | outcome produced)..."
This contradicts Bell's definition of locality, according to which ρ(λ) must depend
only on the common cause λ. It must be independent, not only of the settings a and b, but also of the outcomes A and B. Thus Bell would regard the Gisin and Gisin model non-local, because their probability density ρ(λ) depends on the outcomes A.
Don't take any notice of the words they say. Read the formulas, only, Or: read the code of the simulation model. It is manifestly local.
Hidden variable: random point on the sphere, auxiliary independent uniform [0, 1] random variable, auxiliary independent coin toss.
Generate these three objects and send them all off both to Alice and to Bob's place.
Alice and Bob's measurement stations each look at the inner product of the angle between their measurement direction and the direction of the spin.
If the coin toss said heads:
Alice's station generates an outcome "sign of inner product"
Bob's station generates an outcome "sign of inner product" provided uniform is smaller than absolute value of inner product, otherwise says "no state"
If the coin said tails:
Bob's station generates an outcome "sign of inner product"
Alice's station generates an outcome "sign of inner product" provided uniform is smaller than absolute value of inner product, otherwise says "no state"
Just as in the case of Pearle's paper, one must distinguish between the model specification, and any theoretical computations which we might want to do for a given model. The model is just the recipe for the simulation program. The instructions to the programmer. They are very simple.