The Hilbert space operator formalism within dynamical reduction models

TL;DR

This paper demonstrates how the Hilbert space operator formalism of quantum mechanics can be derived from dynamical reduction models, showing it as a convenient statistical tool rather than an ontological necessity.

Contribution

It provides a derivation of the operator formalism within dynamical reduction models, clarifying its role as a statistical framework rather than an ontological element.

Findings

The operator formalism can be derived from the evolution equations of dynamical reduction models.

Operators are shown to be a convenient representation of experimental statistics.

The formalism has no intrinsic ontological meaning within these models.

Abstract

Unlike standard quantum mechanics, dynamical reduction models assign no particular a priori status to `measurement processes', `apparata', and `observables', nor self-adjoint operators and positive operator valued measures enter the postulates defining these models. In this paper, we show why and how the Hilbert-space operator formalism, which standard quantum mechanics postulates, can be derived from the fundamental evolution equation of dynamical reduction models. Far from having any special ontological meaning, we show that within the dynamical reduction context the operator formalism is just a compact and convenient way to express the statistical properties of the outcomes of experiments.