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

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.

Final version for publication in Phys. Rev. A, with changed title and additional discussions of the relation with other statistical approaches and the relevance of recent experimental developments

References in corpus (7)

• Quantum theory of successive projective measurements
• Measuring measurement--disturbance relationships with weak values
• Mutually unbiased bases, orthogonal Latin squares, and hidden-variable models
• Quantum instruments as a foundation for both states and observables
• Quantum-Bayesian Coherence
• Weak valued statistics as fundamental explanation of quantum physics
• Measurement uncertainties in the quantum formalism: quasi-realities of individual systems

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• Reasonable conditions for joint probabilities of non-commuting observables
• Contextuality of quantum fluctuations characterized by conditional weak values of entangled states
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• Quantum causality relations and the emergence of reality from coherent superpositions
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