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The relativistic reason for quantum probability amplitudes
Karol Sajnok, Kacper Dębski, Andrzej Dragan·December 11, 2025
Quantum Physicsgr-qc
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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.