A local theory of Quantum Mechanics

TL;DR

This paper identifies ambiguities in standard quantum mechanics regarding entangled systems and proposes an alternative local theory with testable differences, aiming to resolve nonlocality issues and preserve action-reaction principles.

Contribution

It introduces a local, non-entangled quantum theory with a hidden label mechanism, contrasting with orthodox quantum mechanics, and suggests an experiment to test its validity.

Findings

Standard quantum mechanics shows ambiguity in predicting relative frequencies for entangled systems.

The proposed local theory predicts different observable frequencies and maintains locality.

An experiment is proposed to distinguish between the orthodox and alternative theories.

Abstract

It is shown that Quantum Mechanics is ambiguous when predicting relative frequencies for an entangled system if the measurements of both subsystems are performed in spatially separated events. This ambiguity gives way to unphysical consequences: the projection rule could be applied in one or the other temporal(?) order of measurements (being non local in any case), but symmetry of the roles of both subsystems would be broken. An alternative theory is presented in which this ambiguity does not exist. Observable relative frequencies differ from those of orthodox Quantum Mechanics, and a {\it gendaken} experiment is proposed to falsify one or the other theory. In the alternative theory, each subsystem has an individual state in its own Hilbert space, and the total system state is direct product (rank one) of both, so there is no entanglement. Correlation between subsystems appears through a hidden label that prescribes the output of arbitrary hypothetical measurements. Measurement is treated as a usual reversible interaction, and this postulate allows to determine relative frequencies when the value of a magnitude is known without in any way perturbing the system, by measurement of the correlated companion. It is predicted the existence of an accompanying system, the de Broglie wave, introduced in order to preserve the action reaction principle in indirect measurements, when there is no interaction of detector and particle. Some action on the detector, different from the one cause by a particle, should be observable.