On observation of position in quantum theory

TL;DR

This paper unifies classical and quantum dynamics within a Hilbert space framework, revealing new insights into measurement, wave function collapse, and the classical-quantum relationship, with implications for understanding macroscopic positions.

Contribution

It introduces a dynamical mechanism explaining the Born rule and wave function collapse without special measurement assumptions, linking classical diffusion to quantum state evolution.

Findings

Relation between classical Brownian motion and quantum state diffusion

Wave function collapse explained by state diffusion, not measurement

New formula connecting probability distribution and Born rule

Abstract

Newtonian and Scrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes beyond the results provided by the Ehrenfest theorem. A formula relating the normal probability distribution and the Born rule was also found. Here the dynamical mechanism responsible for the latter formula is proposed and applied to measurements of macroscopic and microscopic systems. A relationship between the classical Brownian motion and the diffusion of state on the space of states is discovered. The role of measuring devices in quantum theory is investigated in the new framework. It is shown that the so-called collapse of the wave function is not measurement specific and does not require a "concentration" near the eigenstates of the measured observable. Instead, it is explained by the common diffusion of a state over the space of states under interaction with the apparatus and the environment. This in turn provides us with a basic reason for the definite position of macroscopic bodies in space.