From Classical to Wave-Mechanical Dynamics

TL;DR

This paper proposes viewing wave mechanics as a causal extension of classical mechanics using exact trajectories guided by wave potentials, eliminating probabilistic interpretations and wave-packets.

Contribution

It introduces a trajectory-based framework linking classical and wave mechanics through exact ray trajectories and a wave potential, challenging traditional probabilistic views.

Findings

Wave equations are associated with exact ray trajectories.

Wave mechanics can be viewed as a causal extension of classical mechanics.

The approach avoids probabilistic interpretations of quantum phenomena.

Abstract

The time-independent Schroedinger and Klein-Gordon equations - as well as any other Helmholtz-like equation - were recently shown to be associated with exact sets of ray-trajectories (coupled by a "Wave Potential" function encoded in their structure itself) describing any kind of wave-like features, such as diffraction and interference. This property suggests to view Wave Mechanics as a direct, causal and realistic, extension of Classical Mechanics, based on exact trajectories and motion laws of point-like particles "piloted" by de Broglie's matter waves and avoiding the probabilistic content and the wave-packets both of the standard Copenhagen interpretation and of Bohm's theory.