Why the World Appears Probabilistic A Redefinition of Probability via Structural Unresolvedness, Projection, and Capacity Limits

We show that for $S=\frac{1}{2}$ the energy eigenvalues of the so-called principal type can be determined if and only if some unphysical amplitude is nonvanishing. In the conventional treatment, normalization does not lead naturally to a direct probabilistic interpretation of the amplitudes involved. We show that such an inconvenience can be removed by a "redefinition" of the amplitudes such that the unphysical amplitudes will no longer appear. Besides, the energy eigenvalue corresponding to the unphysical amplitudes also will not appear after this redefinition.We show that for $S=\frac{1}{2}$ the energy eigenvalues of the so-called principal type can be determined if and only if some unphysical amplitude is nonvanishing. In the conventional treatment, normalization does not lead naturally to a direct probabilistic interpretation of the amplitudes involved. We show that such an inconvenience can be removed by a "redefinition" of the amplitudes such that the unphysical amplitudes will no longer appear. Besides, the energy eigenvalue corresponding to the unphysical amplitudes also will not appear after this redefinition.

Physical review. B, Condensed matterDec 1, 19781 citation

Outline of a Contextual Probability Theory A Structural Description of Probability Through Contextual Wholes

Viktoras Rimsha, Laimontas Rimsha

Interpretational paradoxes of quantum mechanics may be associated with the application of the structure of classical probability theory to systems whose probabilistic organization is fundamentally contextual. In this work, we propose an outline of an alternative probability theory in which the primary object is not an elementary outcome but a contextual whole—a class of alternatives defined by a common structural property. In this approach, probability is organized on two levels. The first level describes the probabilities of contextual wholes, while the second level describes the conditional probabilities of alternatives within those wholes. Individual alternatives do not possess autonomous probabilities outside their context. Their probabilities arise only as contextual projections of a more fundamental probabilistic structure. Within this model, quantum mechanics appears as a special case of a more general theory in which contextual wholes are described by superpositions of probability amplitudes. Classical probability theory emerges as a limiting case in which all contexts are mutually compatible and can be combined into a single global description. The proposed framework provides a possible conceptual foundation for understanding quantum probability, contextuality, interference, and hybrid probability distributions within a unified structure.Interpretational paradoxes of quantum mechanics may be associated with the application of the structure of classical probability theory to systems whose probabilistic organization is fundamentally contextual. In this work, we propose an outline of an alternative probability theory in which the primary object is not an elementary outcome but a contextual whole—a class of alternatives defined by a common structural property. In this approach, probability is organized on two levels. The first level describes the probabilities of contextual wholes, while the second level describes the conditional probabilities of alternatives within those wholes. Individual alternatives do not possess autonomous probabilities outside their context. Their probabilities arise only as contextual projections of a more fundamental probabilistic structure. Within this model, quantum mechanics appears as a special case of a more general theory in which contextual wholes are described by superpositions of probability amplitudes. Classical probability theory emerges as a limiting case in which all contexts are mutually compatible and can be combined into a single global description. The proposed framework provides a possible conceptual foundation for understanding quantum probability, contextuality, interference, and hybrid probability distributions within a unified structure.

Jun 1, 20260 citations

The Emergence of Probability from Fundamental Physical Theories

Angshul Majumdar

Jan 1, 20260 citations

Spacetime Formation under Requirements: Contextual Realization and Form-Dependent Probability

Song-Ju Kim

Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different interpretation: quantum probability is the fixed-spacetime projection of contextual spacetime formation under finite-state requirements. The framework begins not with time, space, objects, or probabilities, but with requirements such as finite representational capacity, single-state semantic stability, context-sensitive intervention, avoidance of explicit context labels, coherent world-formation, and intersubjective transformability. When these requirements cannot be realized within a single global Boolean event structure, the mismatch appears, under fixed-spacetime projection, as noncommutativity, interference, and quantum-like probability. Building on prior single-state approaches to contextuality, we reinterpret classical contextual bookkeeping cost as the fixed-spacetime shadow of contextual spacetime formation. Auxiliary memory or context labels in a classical representation correspond, in this account, to holonomy-like mismatch among locally Boolean logic-worlds. The interference term is the cross term generated when locally classical realization contributions are nontrivially glued and projected back into a fixed classical spacetime form. The result is a transcendental-operational realist account: objecthood, eventhood, probability, and spacetime are treated as forms of realization under requirements, while objectivity is defined by invariants preserved across observer- and history-dependent spacetime formations.Quantum cognition often explains order effects, contextuality, and violations of the law of total probability by replacing classical probability with quantum probability on a fixed event structure. This paper proposes a different interpretation: quantum probability is the fixed-spacetime projection of contextual spacetime formation under finite-state requirements. The framework begins not with time, space, objects, or probabilities, but with requirements such as finite representational capacity, single-state semantic stability, context-sensitive intervention, avoidance of explicit context labels, coherent world-formation, and intersubjective transformability. When these requirements cannot be realized within a single global Boolean event structure, the mismatch appears, under fixed-spacetime projection, as noncommutativity, interference, and quantum-like probability. Building on prior single-state approaches to contextuality, we reinterpret classical contextual bookkeeping cost as the fixed-spacetime shadow of contextual spacetime formation. Auxiliary memory or context labels in a classical representation correspond, in this account, to holonomy-like mismatch among locally Boolean logic-worlds. The interference term is the cross term generated when locally classical realization contributions are nontrivially glued and projected back into a fixed classical spacetime form. The result is a transcendental-operational realist account: objecthood, eventhood, probability, and spacetime are treated as forms of realization under requirements, while objectivity is defined by invariants preserved across observer- and history-dependent spacetime formations.

cs.AICross-listedarXiv:2605.23943May 5, 20260 citations

The Emergence of Probability from Fundamental Physical Theories

Angshul Majumdar

Jan 1, 20260 citations

We show that for

S=\frac{1}{2}

the energy eigenvalues of the so-called principal type can be determined if and only if some unphysical amplitude is nonvanishing. In the conventional treatment, normalization does not lead naturally to a direct probabilistic interpretation of the amplitudes involved. We show that such an inconvenience can be removed by a "redefinition" of the amplitudes such that the unphysical amplitudes will no longer appear. Besides, the energy eigenvalue corresponding to the unphysical amplitudes also will not appear after this redefinition.