The exclusion principle, chemistry and hidden variables

Stanley Gudder

Peter J. Hall

Paul O’Hara

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

Ishikawa, Hiroshi

Quantum trajectory theories have not fully reconciled discrete quantum jumps with continuous unitary evolution. We address this challenge by developing a hidden variable formulation that reveals hidden correlations in individual trials. We represent jump sequences as logical propositions on energy eigenstate occupations, where logical variables describe their truth values and chain operators describe their probabilities. To circumvent established no-go theorems, we introduce a proposition selection rule that requires well-defined joint probabilities for a given density operator. This rule unifies compatibility criteria for quantum and hidden variable theories, eliminating incompatible propositions that lead to value assignment paradoxes. Unlike conventional criteria mandating operator commutativity, it permits propositions that become deterministic for specific initial conditions. This framework systematically captures deterministic relations in individual trials, including the exclusivity of state occupation implied by the observed jumps. This exclusivity, distinct from the Pauli exclusion principle, enables the formalization of a quantum version of Boolean logic as laws for quantum propositions. These assumptions circumvent Bell-type inequalities by prohibiting arithmetic operations between incompatible logical variables, while enabling classical descriptions within the complementarity. The resulting theory reconciles discrete jumps with continuous evolution, providing a direct description of individual trials while preserving standard probability predictions.

Jincheng Zhang

This paper introduces the Chemical Hidden Variable Theory (CHVT), a novel approach to theoretical chemistry predicated on the belief that existing chemical theories fundamentally lack crucial variables. Drawing an analogy with the historical search for hidden variables in quantum mechanics, CHVT posits the existence of underlying, unobserved chemical variables that dictate the behavior of chemical systems. The core objective of CHVT is to identify and model these "Hidden Chemical Variables" (HCVs) to potentially revolutionize our understanding of chemical phenomena. This paper outlines the fundamental concepts, proposed methodologies, and potential implications of CHVT, focusing on the identification and mathematical representation of HCVs. The theory relies on a revised understanding of probabilistic descriptions in chemistry, suggesting that observed probabilities are not inherent but rather results of the influence of these hidden variables. The central argument is that a more complete description of chemical systems requires acknowledging and incorporating these HCVs, leading to more accurate predictions and a deeper understanding of chemical reactions and properties. The exploration of HCVs promises a shift from purely probabilistic models to a more deterministic, yet fundamentally quantum-influenced, framework for chemical theory. ---