Constructive Foundation of Quantum Mechanics

TL;DR

This paper develops a constructive foundation for Quantum Mechanics based on discreteness and relativity principles, providing insights into measurement, wave function information, and completeness.

Contribution

It introduces a new constructive approach to Quantum Mechanics grounded in discreteness and relativity, clarifying foundational issues.

Findings

Standard axioms derived from the construction

Provides a covariant description of quantum objects

Addresses measurement and wave function questions

Abstract

I describe a constructive foundation for Quantum Mechanics, based on the discreteness of the degrees of freedom of quantum objects and on the Principle of Relativity. Taking Einstein's historical construction of Special Relativity as a model, the construction is carried out in close contact with a simple quantum mechanical Gedanken experiment. This leads to the standard axioms of Quantum Mechanics. The quantum mechanical description is identified as a tool that allows describing objects with discrete degrees of freedom in space-time covariant with respect to coordinate transformations. An inherent property of this description is a quantum mechanical interaction mechanism. The construction gives detailed answers to controversial questions, such as the measurement problem, the informational content of the wave function, and the completeness of Quantum Mechanics.