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arXiv · 2512.10497

The relativistic reason for quantum probability amplitudes

Karol Sajnok·Kacper Dębski·Andrzej Dragan
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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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Karol Sajnok, Kacper Dębski, Andrzej Dragan. 2025-12-11. The relativistic reason for quantum probability amplitudes. https://doi.org/10.1088/1367-2630%2Fae4d79

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