Relativistic locality and the action reaction principle predict de Broglie fields

TL;DR

This paper proposes that incorporating relativistic locality and the action reaction principle into quantum mechanics predicts the existence of de Broglie fields, suggesting an extended Hilbert space formulation to address phase space incompleteness.

Contribution

It introduces a novel formulation of quantum mechanics in extended Hilbert spaces that accounts for relativistic locality and the action reaction principle, predicting de Broglie fields.

Findings

Standard quantum mechanics violates the action reaction principle.

Relativistic locality implies the existence of de Broglie fields.

Extended Hilbert space formulation distinguishes kinematic and dynamical representations.

Abstract

The action reaction principle is violated in the standard formulation of Quantum Mechanics, so that its phase space is incomplete. Moreover, projection of state of a quantum system under indirect measurement, when there are alternative virtual paths and one of them is discarded by negative detection implies, according to the action reaction principle, a reaction on the detector, although its macroscopic state does not change. If all interactions are local, mediated by fields with relativistically causal evolution, some system, different from the particle which follows another path, must locally interact with the detector. Relativistic locality and the action reaction principle predict the existence of de Broglie fields. A formulation of Quantum Mechanics in extended Hilbert spaces is presented, in which kinematic and dynamical representations of physical magnitudes are distinguished.