Separation of conditions as a prerequisite for quantum theory

TL;DR

This paper introduces the concept of 'separation of conditions' for experimental data, showing it leads to the mathematical framework of quantum theory and can be used to derive key quantum phenomena and equations.

Contribution

It formalizes the notion of separating experimental conditions, demonstrating that this approach underpins the structure of quantum theory and its key equations.

Findings

Separation of conditions leads to quantum mathematical structure.

It enables construction of quantum descriptions for Stern-Gerlach and EPR-Bohm experiments.

Under restrictions, it derives the Schrödinger and von Neumann equations.

Abstract

We introduce the notion of "separation of conditions" meaning that a description of statistical data obtained from experiments, performed under a set of different conditions, allows for a decomposition such that each partial description depends on mutually exclusive subsets of these conditions. Descriptions that allow a separation of conditions are shown to entail the basic mathematical framework of quantum theory. The Stern-Gerlach and the Einstein-Podolsky-Rosen-Bohm experiment with three, respectively nine possible outcomes are used to illustrate how the separation of conditions can be used to construct their quantum theoretical descriptions. It is shown that the mathematical structure of separated descriptions implies that, under certain restrictions, the time evolution of the data can be described by the von Neumann/Schr\"odinger equation.