There are plots that compare the expectation value E(a,b) of(adsbygoogle = window.adsbygoogle || []).push({});

(i) a hidden variable theory

(ii) quantum mechanics

For example here:

1. Talk given by Alain Aspect, video at 2m28s

2. PF Thread: The Unfair Sampling Assumption & Bell Tests

For the hidden variable theory the expectation value E(a,b) or E(theta) looks like aline. My question:How do you get this line?

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Let me further explain:

From what I understand the hidden variable is constructed as follows:

E(a,b) is given by:

[itex]E(\textbf{a},\textbf{b}) = \int \rho(\lambda) A(\lambda, \textbf{a}) B(\lambda,\textbf{b}) d\lambda[/itex]

(Let's call this expressionHV-Expectation)

where the vectors a and b are the directions of the polarizers.

(See Aspect talk at 0m54s)

Aspect asks us at 2m28s to construct a hidden variable and comes up with:

[itex]A(\lambda, \textbf{a}) = sign( \{cos(2(\theta_a-\lambda )\}[/itex]

[itex]B(\lambda, \textbf{b}) = sign( \{cos(2(\theta_b-\lambda )\}[/itex]

(Let's call themHV-equations)

where [itex]\theta_a[/itex] and [itex]\theta_b[/itex] are the angles of the vectors a and b with respect to some axis.

Now, I suppose that [itex]\lambda[/itex] is the angle of a vector [itex]\vec{\lambda}[/itex]. This vector [itex]\vec{\lambda}[/itex] represents the hidden variable (sort of like a classical polarization). At least that's what I understood after reading Bell's original paper, see Eq (4).

(I also don't understand why Bell introduces the vector a').

Anyways, Aspect then explains that we get thelineafter plugging theHV-equationsintoHV-Expectation.

How is the calculation done?

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# Hidden Variable - How to calculate the straight line

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