Building a bridge between Classical and Quantum Mechanics

TL;DR

This paper proposes a framework that generalizes classical mechanics to quantum mechanics, connecting the two by extending point-like objects to quantum states and measurement apparatuses within a unified theory.

Contribution

It introduces a novel approach to derive quantum mechanics from classical mechanics by generalizing objects and measurement processes, providing a conceptual bridge between the two.

Findings

Quantum state vectors emerge naturally from the generalization process.

Measurement apparatuses are shown to be special cases of quantum objects.

An example of an intermediate-sized measurement apparatus illustrates the theory.

Abstract

The way Quantum Mechanics (QM) is introduced to people used to Classical Mechanics (CM) is by a complete change of the general methodology) despite QM historically stemming from CM as a means to explain experimental results. Therefore, it is desirable to build a bridge from CM to QM. This paper presents a generalization of CM to QM. It starts from the generalization of a point-like object and naturally arrives at the quantum state vector of quantum systems in the complex valued Hilbert space, its time evolution and quantum representation of a measurement apparatus of any size. Each time, when generalization is performed, there is a possibility to develop new theory giving up most simple generalizations. It is shown that a measurement apparatus is a special case of a general quantum object. An example of a measurement apparatus of an intermediate size is considered in the end.