The relativistic reason for quantum probability amplitudes

• URL: http://arxiv.org/abs/2512.10497v1
• Date: Thu, 11 Dec 2025 10:18:27 GMT
• Title: The relativistic reason for quantum probability amplitudes
• Authors: Karol Sajnok, Kacper Dębski, Andrzej Dragan,
• Abstract summary: We show that the quantum-mechanical probability distribution involving complex probability amplitudes can be derived from three natural conditions.<n>Conditions are: (i) pairwise Kolmogorov additivity, (ii) time symmetry, and (iii) Bayes' rule.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We show that the quantum-mechanical probability distribution involving complex probability amplitudes can be derived from three natural conditions imposed on a relativistically invariant probability function describing the motion of a particle that can take multiple paths simultaneously. The conditions are: (i) pairwise Kolmogorov additivity, (ii) time symmetry, and (iii) Bayes' rule. The resulting solution, parameterized by a single constant, is the squared modulus of a sum of complex exponentials of the relativistic action, thereby recovering the Feynman path-integral formulation of quantum mechanics.

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