The relativistic reason for quantum probability amplitudes

TL;DR

This paper derives quantum probability amplitudes from relativistic invariance and natural conditions, showing they align with Feynman's path integral formulation, thus linking relativity and quantum probability.

Contribution

It introduces a derivation of quantum amplitudes based on relativistic invariance and natural conditions, connecting quantum mechanics with relativistic principles.

Findings

Quantum amplitudes can be derived from relativistic invariance and natural conditions.

The derived probability distribution matches Feynman's path integral formulation.

A single parameter characterizes the complex exponential sum in the amplitude.

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.