by **minkwe** » Sat Jun 14, 2014 9:56 am

Heinera,

You say you don't know how to evaluate

But you evaluate exactly like you evaluate

You integrate over all the distinct values of lambda. If there is just one value of lambda for each a,b, with probability 1 the integral simply gives you

or if you like

. Don't forget what we are calculating --- the expectation value of the result at Alice multiplied by the result at Bob, that is what E(a,b) is. If the result at Alice is A(a,b) and the result at Bob is B(a,b), then

There is nothing meaningless here.

In your non-local model, you calculate the average of A*B and equate that to E(a,b), you will do exactly the same thing whether you were dealing with a local model or any model whatsoever. A(a, lambda) is simply a function which takes two arguments and gives a result. It doesn't matter whether those arguments are local or non-local. So long as your model gives a result, your function is well defined contrary to what you are trying to argue here. In your model you have A(a, b, hv), you are arguing speciously now that lambda = hv. But I can easily rewrite your function into A(a, Lambda), where Lambda = (a,b,hv) and A(a,Lambda) will be well defined. Your earlier suggestion that if the two arguments of a function are not independent, then the function is not well defined is just silly. For example, f(a,b) = cos(a-b) is a function of 2 variables. Just because I tell you that b = g(x,a) = (2a - x)^2 does not mean that f(a,b) is not well defined. You are trying to defend the indefensible.

There is nothing in Bell's equation 2 that is specific to LHV theories. Nothing whatsoever. If you think there is, you will either explain what exactly in that expression restricts it to LHV theories, or in the alternative, tell us what exactly the expression would be for the expectation value of the paired product of outcomes at Alice and Bob, for a non-local theory. A non-local theory produces outcomes at Alice and Bob doesn't it? Those outcomes can be multiplied with each other can they not? What is the expectation value expression, please?

Maybe other Bell-believers who agree with your claims will help you to state what exactly the expression would be for the expectation value of the paired product of outcomes for non-local hidden variable theories.

Heinera,

You say you don't know how to evaluate

[tex]E(a,b) = \int A(a, \lambda(a,b)) B(b, \lambda(a,b)) \rho(\lambda(a,b)) d\lambda(a,b)[/tex]

But you evaluate exactly like you evaluate

[tex]E(a,b) = \int A(a, \lambda) B(b, \lambda) \rho(\lambda) d\lambda[/tex]

You integrate over all the distinct values of lambda. If there is just one value of lambda for each a,b, with probability 1 the integral simply gives you [tex]A(a, \lambda) B(b, \lambda)[/tex] or if you like [tex]A(a, b)B(a, b)[/tex]. Don't forget what we are calculating --- the expectation value of the result at Alice multiplied by the result at Bob, that is what E(a,b) is. If the result at Alice is A(a,b) and the result at Bob is B(a,b), then [tex]E(a,b) = \int A(a, \lambda) B(b, \lambda) \rho(\lambda) d\lambda = A(a, b)B(a, b)[/tex] There is nothing meaningless here.

In your non-local model, you calculate the average of A*B and equate that to E(a,b), you will do exactly the same thing whether you were dealing with a local model or any model whatsoever. A(a, lambda) is simply a function which takes two arguments and gives a result. It doesn't matter whether those arguments are local or non-local. So long as your model gives a result, your function is well defined contrary to what you are trying to argue here. In your model you have A(a, b, hv), you are arguing speciously now that lambda = hv. But I can easily rewrite your function into A(a, Lambda), where Lambda = (a,b,hv) and A(a,Lambda) will be well defined. Your earlier suggestion that if the two arguments of a function are not independent, then the function is not well defined is just silly. For example, f(a,b) = cos(a-b) is a function of 2 variables. Just because I tell you that b = g(x,a) = (2a - x)^2 does not mean that f(a,b) is not well defined. You are trying to defend the indefensible.

There is nothing in Bell's equation 2 that is specific to LHV theories. Nothing whatsoever. If you think there is, you will either explain what exactly in that expression restricts it to LHV theories, or in the alternative, tell us what exactly the expression would be for the expectation value of the paired product of outcomes at Alice and Bob, for a non-local theory. A non-local theory produces outcomes at Alice and Bob doesn't it? Those outcomes can be multiplied with each other can they not? What is the expectation value expression, please?

Maybe other Bell-believers who agree with your claims will help you to state what exactly the expression would be for the expectation value of the paired product of outcomes for non-local hidden variable theories.