The Transformation of the Concept of Alternatives in the Analytic Approach to Quantum Probability: From Isolated Properties to Equivalence Classes

Viktoras Rimsha, Laimontas Rimsha

Published May 22, 2026• 0 citations

Abstract

In our previous works [1], it was demonstrated that quantum probability calculus requires an analytic approach where the whole (the totality of alternatives) is primary, while the probabilities of individual alternatives are derived quantities. In this paper, we take an essential methodological step forward by clarifying and updating the very concept of an alternative. We argue that within the analytic framework, alternatives cannot be treated as isolated, atomized elements, as is done in the synthetic Kolmogorovian model. Instead, they function as elements of a mathematical equivalence class and never lose their global contextual feature. This refinement allows us to reconcile the local realization of historical events with the global preservation of quantum interference. Consequently, this opening offers a completely new perspective for quantum cosmology without relying on the hypothesis of an external observer.

DOI: 10.5281/zenodo.20347905

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