R. F\"urth's 1933 paper "On certain relations between classical Statistics and Quantum Mechanics" ["\"Uber einige Beziehungen zwischen klassischer Statistik und Quantenmechanik", \textit{Zeitschrift f\"ur Physik,} \textbf{81} 143-162]

TL;DR

This paper highlights a deep analogy between quantum fluctuations and Brownian motion, laying groundwork for stochastic quantization methods developed decades later.

Contribution

It introduces a fundamental analogy between quantum mechanics and classical stochastic processes, influencing future stochastic quantization approaches.

Findings

Identifies a profound analogy between quantum fluctuations and Brownian motion

Influences the development of stochastic methods in quantum mechanics

Provides a conceptual foundation for stochastic quantization

Abstract

We present a translation of the 1933 paper by R. F\"urth in which a profound analogy between quantum fluctuations and Brownian motion is pointed out. This paper opened in some sense the way to the stochastic methods of quantization developed almost 30 years later by Edward Nelson and others.