# On the quantum mechanical description of the interaction between particle and detector

## TL;DR

This paper develops a quantum detector model to describe real position measurements involving single particles, bridging the gap between quantum interactions and classical measurement outcomes.

## Contribution

It introduces a detector model that captures the time-dependent quantum interactions and explains how real measurements yield definite results without predicting outcomes.

## Key findings

- The model describes the transition from quantum to classical behavior in detectors.
- It explains why individual measurements produce definite results.
- It accounts for the unpredictability of measurement outcomes.

## Abstract

Quantum measurements of physical quantities are usually described as ideal measurements. However, only a few measurements fulfil the conditions of ideal measurements. The aim of the present work is to describe real position measurements with detectors that are able to detect single particles. For this purpose, a detector model has been developed that can describe the time dependence of interactions between nonrelativistic particles and a detector. At the beginning of a position measurement, the detector behaves as a target consisting of a large number of quantum mechanical systems. The incident object interacts with a single atom, electron or nucleus, but not with the whole detector. This reaction is a quantum mechanical process. At the end of the measurement, the detector can be considered as a classical apparatus. A detector is neither a quantum mechanical system nor a classical apparatus. The detector model explains why one obtains a well-defined result for each individual measurement. It further explains that, in general, it is impossible to predict the outcome of the next measurement. The main advantage is that it describes real rather than only ideal measurements.