A reconstruction of quantum theory for nonspinning particles

TL;DR

This paper reconstructs quantum theory from a probabilistic classical mechanics framework by incorporating initial condition uncertainties, leading to a derivation of the Schrödinger equation and clarifying differences between classical and quantum physics.

Contribution

It introduces a probabilistic mechanics approach that bridges classical and quantum mechanics, providing a new derivation of the Schrödinger equation from classical principles.

Findings

Derivation of Schrödinger equation from probabilistic classical mechanics.

Clarification of structural differences between classical and quantum physics.

Resolution of contradictions in the individuality interpretation.

Abstract

Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact that a certain system which is described in CM by a finite number of degrees of freedom requires an infinite number in QT. The standard quantization method, which is conceptually closely linked to the individuality interpretation, is limited to finding structural similarities between observables and operators. The fundamental question \emph{why} one must move from a finite number to an infinite number of degrees of freedom, remains unanswered. This gap can only be closed if probabilistic aspects are already taken into account in the classical area. This may be done by taking the uncertainty in initial conditions into account. In this probabilistic version of mechanics (PM), a system is mathematically described as an ensemble, with an infinite number of degrees of freedom, thus bridging the gap mentioned above. This step then enables the reconstruction of QT, in particular the derivation of the Schr\"odinger equation, from PM. This work is the third in a series of works in which this program is carried out. The method used here differs from the previous one and allows a better understanding of the structural differences between classical physics and QT. The derivation of the Schr\"odinger equation essentially takes place in two steps: a projection from phase space to configuration space and a linearization. Some contradictions of the individuality interpretation are analyzed and eliminated from the point of view of the ensemble interpretation.