A computational model of Bell correlations

[Zafa Pi]

You're correct. "Such" in our sentences referred to hidden variables models, so we agree with you. No hidden variables model can be local, but other models can be.

Thanks. Do you have a simple example of one of the other models? Does MWI qualify?

 

[Zafa Pi]

##\overline{A\cap{B}}## implies ##\bar{A}\cup\bar{B}## but not ##\bar{A}\cap\bar{B}##. However, the situation here is somewhat more complex because the assumptions Bell made in his original paper do not exactly correspond to "hidden variables" and "locality"; they're closer to "the properties that a theory must have to 'complete' (in the EPR sense) QM".

@OCR at #70 is almost right. Only I don't consider what you said to be a fact.
Bell defines locality on the first page, gets (2) as a consequence, has hidden variables λ throughout his proof. Many others think he assumes hidden variables and locality.
As a simpleton, I look forward to an explanation I can understand as to why they are not assumed.

 

[OCR]

Only I don't consider what you said to be a fact.

Fixed...!

 

[Jilang]

I posted a note about this a year or so ago. Here's the summary:

• [itex]P(A | \alpha, \la

Does there exist a parameter [itex]\lambda[/itex] and amplitudes [itex]\psi(\lambda), \psi(A | \alpha, \lambda), \psi(B | \beta, \lambda)[/itex] such that:

• Let the conditional amplitudes be:
  • [itex]\psi(A | \alpha, \lambda_u) = cos(\frac{\alpha}{2})[/itex]
  • [itex]\psi(A | \alpha, \lambda_d) = sin(\frac{\alpha}{2})[/itex]
  • [itex]\psi(B | \beta, \lambda_u) = sin(\frac{\alpha}{2})[/itex]
  • [itex]\psi(B | \beta, \lambda_d) = cos(\frac{\beta}{2})[/itex]

.

Should the third one have a beta in it?

 

[Zafa Pi]

Fixed...!

So is my dog.
I agree with your edit.

 

[jk22]

Trying to reproduce the correlation we could try the following reasoning :

The model is : $$C(a,b)=\int \underbrace{A(a,x)\cdot B(b,x)}_{AB(a,b,x)}dx$$
more generally :

$$AB(a,b,x)=g(A(a,x),B(b,x))$$

numerically an exhaustive search over the functions : $$g,A,B : \{0,1\}^2->\{0,1\}$$ since a,b can take 2 values and x too for the spin 1/2 case (we could remap the names of the two angles)

The total number of functions AB is $$2^{(2^3)}=256$$

The decomposition above gave 192 functions generated.

Hence i came to the paradox : even if in this way 75% of the functions can be generated , the quantum real function shall be in the remaining.

But then this also lead to the fact that the decomposition $$AB(a,b,x)=g(h(A(a,x),B(b,x)),A'(a,x))$$
Gives 256 over 256 functions (but seems physically akward or unacceptable)?

I would like to try functions thst can take 3 values but on my pc it will last weeks...

 

[jk22]

Addendum, erratum :

In fact nonlocality is hidden here, since if the angles can take $$na,nb$$ values then the cube can be sliced in $$nb$$ functions of $$ a$$ and $$\lambda$$, hence it depends on $$a$$ and a property of b.