Logical inference approach to relativistic quantum mechanics: derivation of the Klein-Gordon equation

TL;DR

This paper derives the Klein-Gordon equation for a relativistic, spinless particle using a logical inference framework, emphasizing robustness of experimental data and classical motion consistency.

Contribution

It introduces a novel logical inference approach to derive the Klein-Gordon equation in a relativistic context, connecting experimental robustness with classical motion.

Findings

Klein-Gordon equation derived from logical inference principles

Relates experimental data robustness to relativistic quantum equations

Bridges classical and quantum descriptions in a new framework

Abstract

The logical inference approach to quantum theory, proposed earlier [Ann. Phys. 347 (2014) 45-73], is considered in a relativistic setting. It is shown that the Klein-Gordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the space-time data collected by probing the particle is obtained from the most robust experiment and that on average, the classical relativistic equation of motion of a particle holds.