Without the Born Rule

TL;DR

This paper proposes a formulation of quantum mechanics that eliminates the need for the Born rule by introducing probability through probability current, enabling consistent single-trial solutions and resolving key paradoxes.

Contribution

It introduces a new approach to quantum mechanics that removes the Born rule, allowing for single-trial solutions and addressing paradoxes like Schrödinger's cat and many-worlds.

Findings

Provides a consistent single-trial quantum framework

Resolves Schrödinger's cat paradox

Eliminates the need for the many-worlds interpretation

Abstract

The auxiliary rules of quantum mechanics have always included the Born rule that connects probability with square modulus. This need not be the case, for it is possible to introduce probability into the theory through probability current alone. When this is done, other rules can provide for stochastically triggered measurements within a system of any size, microscopic or macroscopic; and solutions to the Schrodinger equation can be consistently applied to individual trials, not just to ensembles of trials. Other advantages appear. The rules can then resolve the paradox associated with the Schrodinger cat experiment, and remove the possibility of the many world thesis of Everett. As a result, the system can accommodate any conscious observer, including the principal investigator who cannot otherwise be included in a quantum mechanical system.