Dopey Question about Bell's theorem.

In summary, Bell's theorem states that a hidden variable λ cannot exist, assuming that Λ (the set of all possible values of λ) is a measurable domain and that the probability function of λ can be integrated. However, there is a version of Bell's theorem that does not rely on this assumption, proposed by Pitowsky using a model based on unmeasurable sets.
  • #1
NateTG
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For context I'm looking at:
http://www.mtnmath.com/whatrh/node80.html

Bell's theorem suggests that a hidden variable λ cannot exist, but, at least the version above makes the assumption that Λ (the set of all posible values of λ ) is a measurable domain s.t.
[tex]\int_{\Lambda} f(\lambda)d\lambda[/tex]

is well-defined.

Is there a version of Bell's theorem that does not rely on the ability to integrate the probability function of λ?
 
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  • #2
Found it. Apparently Bell does assume that the hidden variable is in a measurable domain, and Pitowksy produced a model based on unmeasurable sets that avoids the issue.
 
  • #3


Yes, there are versions of Bell's theorem that do not rely on the ability to integrate the probability function of λ. These versions use different mathematical frameworks, such as operator algebras and category theory, to prove the same results as the original Bell's theorem. These alternative versions also do not require the assumption of a measurable domain for Λ. In fact, these versions often provide a more general and abstract understanding of Bell's theorem and its implications. So while the original version may be easier to understand and apply, it is important to recognize that there are other valid interpretations of Bell's theorem.
 

1. What is Bell's theorem?

Bell's theorem, also known as Bell's inequality, is a fundamental principle in quantum mechanics that states that no local hidden variable theory can reproduce all the predictions of quantum mechanics.

2. Why is Bell's theorem important?

Bell's theorem is important because it shows that quantum mechanics is fundamentally different from classical mechanics, and it has been experimentally validated through various tests, confirming the bizarre behavior of particles at the quantum level.

3. How does Bell's theorem relate to entanglement?

Bell's theorem is closely related to entanglement, which is a phenomenon in quantum mechanics where particles can become connected in such a way that the state of one particle affects the state of the other, no matter how far apart they are. Entanglement is a key component in some of the predictions of Bell's theorem.

4. Is Bell's theorem still relevant today?

Yes, Bell's theorem is still a relevant and important concept in modern physics. It continues to be tested and used in various experiments, and its implications have led to advancements in fields such as quantum computing and cryptography.

5. What are some potential applications of Bell's theorem?

Bell's theorem has potential applications in fields such as quantum information processing, quantum cryptography, and quantum teleportation. It also has implications for our understanding of the nature of reality and the relationship between quantum mechanics and classical physics.

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