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arXiv:hep-th/9701089

Bell's inequality, the Pauli exclusion principle and baryonic structure

Paul O’Hara

Published Jan 18, 1997• 2 citations
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Abstract

Bell's inequality has been traditionally used to explore the relationship between hidden variables and the Copenhagen interpretation of quantum mechanics. In this paper, another use is found. Bell's inequality is used to derive a coupling principle for elementary particles and to give a deeper understanding of baryonic structure. We also give a derivation of the Pauli exclusion principle from the coupling principle. Pacs: 14.20-c, 12.90+b, 3.65.Bz, 12.40.Ee

DOI
10.48550/arxiv.hep-th/9701089

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Bell's inequality has been traditionally used to explore the relationship between hidden variables and the Copenhagen interpretation of quantum mechanics. In this paper, another use is found. Bell's inequality is used to derive a coupling principle for elementary particles and to give a deeper understanding of baryonic structure. We also give a derivation of the Pauli exclusion principle from the coupling principle. Pacs: 14.20-c, 12.90+b, 3.65.Bz, 12.40.Ee
Eight derivations of Bell’s inequality are given. First a simple and concrete derivation is given drawing on the full strength of the two hypotheses of locality and hidden variables. Two attempts at deriving Bell’s inequality without locality are made. They fail, but give valuable insight into the form which nonlocality must take in quantum physics. Arguments are given against this form of nonlocality. Ontological ideas which allow separation, realism, and locality in quantum mechanics (QM) are indicated. In the following five derivations, a number of variants of the assumption of hidden variables are tried. Among the insights which these derivations give rise to are: (1) Particles cannot be assumed to have spin or polarisation values for as much as one fixed direction. (2) The classical picture of electromagnetic radiation is incompatible with QM. (3) Heisenberg’s idea of potentiality in elementary particles is incompatible with QM. (4) There is a weakest form of hidden variables, called realisability, which is sufficient to yield Bell’s inequality. (5) Quantum states cannot be identified with physical states. The mathematical problem of the integration of quantum states into physical states is nontrivial.
Abstract Bell inequalities are consequences of local realism while violated by quantum mechanics. In particle physics, entangled high energy particles can be produced from a common source, and the decay of each particle plays the role of measurement. However, in a hidden variable theory, the decay could be determined by hidden variables. This loophole killed such approaches to Bell test in particle physics. It is a special form of measurement-setting or free-will loophole, which also exists in other systems. Using entangled baryons, we present new inequalities of local realism with the explicit assumption of the dependence of the decays on hidden variables, as well as the consideration of the statistical mixture of polarizations and the separation of local hidden variables for objects with spacelike distances. These violations closes the measurement-setting loophole once and for all. We propose to use the processes ηc→ΛΛˉ\eta _c\rightarrow \varLambda {\bar{\varLambda }}ηc​→ΛΛˉ ηc→ΛΛ¯ and χc0→ΛΛˉ\chi _{c0} \rightarrow \varLambda {\bar{\varLambda }}χc0​→ΛΛˉ χc0→ΛΛ¯ to test our inequalities, and show that their violations are likely to be observed with the data already collected in BESIII.
Abstract One of the Bell’s assumptions in the original derivation of his inequalities was the hypothesis of locality, i.e., the absence of the influence of two remote measuring instruments on one another. That is why violations of these inequalities observed in experiments are often interpreted as a manifestation of the nonlocal nature of quantum mechanics, or a refutation of a local realism. It is well known that the Bell’s inequality was derived in its traditional form, without resorting to the hypothesis of locality and without the introduction of hidden variables, the only assumption being that the probability distributions are nonnegative. This can therefore be regarded as a rigorous proof that the hypothesis of locality and the hypothesis of existence of the hidden variables not relevant to violations of Bell’s inequalities. The physical meaning of the obtained results is examined. Physical nature of the violation of the Bell inequalities is explained under new EPR-B nonlocality postulate. We show that the correlations of the observables involved in the Bohm–Bell type experiments can be expressed as correlations of classical random variables. The revisited Bell type inequality in canonical notatons reads 〈AB〉 + 〈A’B〉 + 〈AB’〉 − 〈A’B’〉 ⩽ 6.
In the early 1960s, John Bell decided to look once again at the hidden variable problem in quantum mechanics, through an examination of the A. Einstein, with B. Podolsky and N. Rosen (EPR) paradox. Proposals for proofs against the possibility of hidden variables had been advanced both before and after EPR. Bell developed both a “theorem” and an inequality, but this may be overstating the case. Most interpretations are that Bell is ruling out any “action-at-a-distance” type of interactions or variables, but would accept that such forces could violate the inequality. By triple of random variables, mentioned by A. Yu. Krennikov, one has to think once again about the experiment suggested by the Bell inequality. Bell has assumed that the set of hidden variables, and more importantly the probability function of the hidden variables, is unchanging. K. Hess and Walter Philipp began to worry about this assumption, because it has some implicit assumptions of its own.
The Bell inequality is derived under the assumption of three physical data sets, random or deterministic. The data sets represent a laboratory realization of the three probability based variables used by Bell. For physical data as can be written on paper, the derivation of the inequality results only from principles of algebra and is independent of assumptions of locality, hidden variables and even randomness. Cross correlations of thee data sets carried out as Bell correlated three random variables results in the same inequality that is identically satisfied even by deterministic data. However, to obtain three data sets on two particles destroyed by measurement, two experimental runs are required, followed by data matching to reduce four data sets to three. If quantum mechanical probabilities are used to describe the data frequencies, the Bell inequality is satisfied. The situation is analogous to performing two sets of coin flips to compare the effect of two different coin loadings on the probabilities for heads and tails.