On the CHSH Form of Bell’s Inequalities

“…I agree with him that a joint probability distribution of (A, A ′ , B, B ′ ) does not exist, hence that a joint probability distribution of the 4 variables (AB, AB ′ , A ′ B, A ′ B ′ ) does not exist. In a physical setting, Justo Pastor Lambare [13] has argued that this should imply that 4 different hidden variables λ i should be chosen in the equations corresponding to (4).…”

Section: Briefly On the Literaturementioning

confidence: 99%

“…Write the group elements s −1 (g, h) as (g ′ , h ′ ), new members of groups G and H acting on θ and η, respectively. Let again E be the subgroup of G constructed as in (13), and let F be the corrsponding subgroup of H. Write X = G/E and Y = H/F . The new elements of these cosets may be defined as x ′ = t −1 x and y ′ = t −1 y, respectively.…”

Section: Definition A2mentioning

confidence: 99%

The Bell experiment and the Limitations of Actors

Helland

2022

Preprint

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The well known Bell experiment with two actors Alice and Bob is considered. First the simple deduction leading to the CHSH inequality under local realism is reviewed, and some arguments from the literature are recapitulated. Then I take up certain background themes before I enter a discussion of Alice's analysis of the situation. An important point is that her mind is limited by the fact that her Hilbert space in this context is two-dimensional. General statements about a mind's limitation during a decision process are derived from recent results on the reconstruction of quantum theory from conceptual variables. These results apply to any decision situation. Let all the data from the Bell experiment be handed over to a new actor Charlie, who performs a data analysis. But his mind is also limited: He has a four-dimensional Hilbert space in the context determined by the experiment. I show that this implies that neither Alice nor Charlie can have the argument leading to the CHSH inequality as a background for making decisions related to the experiment. Charlie may be any data analyst, and he may communicate with any person. It is argued that no rational person can be convinced by the CHSH argument when making empirical decisions on the Bell situation.

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“…Probably the most popular version is the CHSH inequality [17]. References [18][19][20][21][22] discuss the CHSH inequality correct and incorrect derivations warning against the use of counterfactual reasoning. The derivation of the Bell inequality requires only elementary mathematics and is uncontroversial from the mathematical point of view.…”

Section: Introductionmentioning

confidence: 99%

A Critical Analysis of the Quantum Nonlocality Problem

Lambare¹

2022

Preprint

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The alleged nonlocal character of quantum mechanics is inextricably related to the formulation of the Bell theorem. However, as we shall see, that relation is commonly incorrectly assessed. The departure from the clear line of reasoning that John Bell tried to convey has led to a polarization of part of the scientific community into radical irreconcilable positions. We show how the correct appreciation of Bell's work calls for reinterpreting the usual significance given to the Bell theorem yielding a more rational perspective of the problem. Given the relevance of the Bell-type inequalities in quantum information technology and quantum foundations, further clarification of their relation to the nonlocality conundrum deserves due attention. The exposition is also of didactic value. It shows the problems arising from incorrect inferences and superfluous metaphysical ideas.

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On the CHSH Form of Bell’s Inequalities

Cited by 10 publications

References 10 publications

On the Meaning of Local Realism

On the Meaning of Local Realism

The Bell experiment and the Limitations of Actors

A Critical Analysis of the Quantum Nonlocality Problem

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