Quantum mechanics as a statistical theory: a short history and a worked example

TL;DR

This paper reviews the historical development of the statistical interpretation of quantum mechanics and demonstrates how a Kolmogorov equation can model quantum randomness in a two-level atom system, capturing phenomena like Rabi oscillations and photon emission.

Contribution

It introduces a kinetic-like Kolmogorov equation approach to model quantum randomness, providing a clear example with photon emission intervals in a two-level atom.

Findings

Kolmogorov equation models quantum jump processes.

Reproduces Rabi oscillations and photon emission statistics.

Provides probability distribution for photon emission intervals.

Abstract

A major question in our understanding of the fabric of the world is where the randomness of some quantum phenomena comes from and how to represent it in a rational theory. The statistical interpretation of quantum mechanics made its way progressively since the early days of the theory. We summarize the main historical steps and then we outline how the randomness gains to be depicted by using tools adapted to Markov processes. We consider a model system corresponding to experimental situations, namely a single two-level atom submitted to a monochromatic light triggering transitions from the ground to the excited state. After a short summary of present quantum approaches, we explain how a general "kinetic-like" Kolmogorov equation yields the statistical properties of the fluorescent light radiated by the atom which makes at once Rabi oscillations between the two states, and random quantum jumps with photo-emission. As an exemple we give the probability distribution of the time intervals between two successive emitted photons by using the Kolmogorov equation.