Is Bell's parameter really a hidden variable ?

In summary, the conversation discusses the concept of a dummy hidden variable and its relationship to Bell's theorem. The question arises whether the variable, denoted as $$\phi$$, is truly hidden or not. However, the distinction between hidden and unhidden variables is not relevant because Bell's theorem applies to all variables. The existence of unhidden variables has already been disproven, leading to the conclusion that either they do not exist or they are hidden.
  • #1
jk22
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In the Ansatz : $$C(a,b)=\int A(a,s)B(b,s)ds$$, is $$s$$ not simply the mute summation index ? In this sense it is not hidden to the experiment.

Then what about an "dummy" hidden variable that is not integrated over :
$$C(a,b)(\phi)=\int A(a,s,\phi)B(b,s,\phi)ds$$

$$\phi$$ were tuned one and for all to match the predictions after all ?
 
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  • #2
Whether it's hidden or not is a bit of a red herring, because the logic of Bell's theorem applies to all variables, whether hidden or not. We discuss Bell's theorem in terms of hidden variables only because the other possibility (that quantum mechanical results can be explained using unhidden variables) is already falsified because we don't see any such variables - therefore either they don't exist or they are hidden.
 
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  • #3
jk22 said:
not simply the mute summation index ? In this sense it is not hidden to the experiment.
How the fact that it is a dummy summation index imply that it is not hidden?
 

1. What is Bell's parameter and how does it relate to hidden variables?

Bell's parameter, also known as the Bell-CHSH inequality, is a mathematical expression used to test the existence of hidden variables in quantum mechanics. It compares the correlation between two distant particles with the correlations predicted by hidden variable theories. If the Bell's parameter exceeds a certain value, it suggests that the particles are not governed by hidden variables.

2. Why is there a debate about whether Bell's parameter is a hidden variable?

The debate stems from the conflict between Bell's parameter and the principles of quantum mechanics. While Bell's parameter suggests the presence of hidden variables, quantum mechanics suggests that there are no hidden variables and that particles exhibit non-local or entangled behavior. Thus, the debate revolves around which theory accurately explains the behavior of particles.

3. Are there any experiments that have tested the existence of hidden variables using Bell's parameter?

Yes, there have been numerous experiments conducted to test the existence of hidden variables using Bell's parameter. These experiments involve measuring the correlations between two entangled particles and comparing them to the predictions of hidden variable theories. So far, the results of these experiments have consistently aligned with quantum mechanics, suggesting that Bell's parameter is not a hidden variable.

4. Can Bell's parameter be used to prove the existence of hidden variables?

No, Bell's parameter alone cannot be used to prove the existence of hidden variables. It can only be used to test the predictions of hidden variable theories. Even if the Bell's parameter were to exceed the maximum value, it would only suggest that the particles are not governed by hidden variables, but it cannot prove their non-existence.

5. How does the concept of non-locality relate to Bell's parameter and hidden variables?

Non-locality is a fundamental principle of quantum mechanics that suggests that particles can be entangled and exhibit instantaneous correlations, regardless of the distance between them. Bell's parameter is used to test this principle and determine whether particles are truly non-local or if their behavior can be explained by hidden variables. So far, the results of experiments have favored the non-locality principle and discredited the existence of hidden variables.

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