Dynamics Underlying the Gaussian Distribution of the Classical Harmonic Oscillator in Zero-Point Radiation

TL;DR

This paper uses simulations within Random Electrodynamics to explore how classical harmonic oscillators in zero-point radiation exhibit probability distributions similar to quantum ground states, shedding light on underlying dynamics.

Contribution

It demonstrates through simulation how RED reproduces quantum-like probability distributions and uncertainty relations for harmonic oscillators, providing insights into classical-quantum correspondence.

Findings

RED predicts Gaussian distribution matching quantum ground state

Simulation reveals relation between double-peak and Gaussian distributions

Supports RED's potential to replicate quantum mechanical results

Abstract

In the past decades, Random Electrodynamics (also called Stochastic Electrodynamics) has been used to study the classical harmonic oscillator immersed in the classical electromagnetic zero-point radiation. Random Electrodynamics (RED) predicts an identical probability distribution for the harmonic oscillator compared to the quantum mechanical prediction for the ground state. Moreover, the Heisenberg minimum uncertainty relation is also recovered with RED. To understand the dynamics that gives rise to this probability distribution, we perform an RED simulation and follow the motion of the oscillator. This simulation provides insight in the relation between the striking different double-peak probability distribution of the classical harmonic oscillator and the Gaussian probability distribution of the RED harmonic oscillator. A main objective for RED research is to establish to what extent the results of quantum mechanics can be obtained. The present simulation method can be applied to other physical systems, and it may assist in evaluating the validity range of RED.