Derivation of quantum mechanics from a single fundamental modification of the relations between physical properties

TL;DR

This paper derives quantum mechanics from a single fundamental law called quantum ergodicity, which relates complex conditional probabilities and the dynamics of measurement interactions, providing a deterministic framework without traditional axioms.

Contribution

It introduces the law of quantum ergodicity, showing that quantum mechanics can be derived solely from this law combined with Bayesian probability theory, eliminating the need for axiomatic assumptions.

Findings

Quantum mechanics can be derived from the law of quantum ergodicity.

Complex phases encode the dynamical structure of property transformations.

The formalism explains quantum phenomena without state vectors or superpositions.

Abstract

Recent results obtained in quantum measurements indicate that the fundamental relations between three physical properties of a system can be represented by complex conditional probabilities. Here, it is shown that these relations provide a fully deterministic and universally valid framework on which all of quantum mechanics can be based. Specifically, quantum mechanics can be derived by combining the rules of Bayesian probability theory with only a single additional law that explains the phases of complex probabilities. This law, which I introduce here as the law of quantum ergodicity, is based on the observation that the reality of physical properties cannot be separated from the dynamics by which they emerge in measurement interactions. The complex phases are an expression of this inseparability and represent the dynamical structure of transformations between the different properties. In its quantitative form, the law of quantum ergodicity describes a fundamental relation between the ergodic probabilities obtained by dynamical averaging and the deterministic relations between three properties expressed by the complex conditional probabilities. The complete formalism of quantum mechanics can be derived from this one relation, without any axiomatic mathematical assumptions about state vectors or superpositions. It is therefore possible to explain all quantum phenomena as the consequence of a single fundamental law of physics.