Emergence of long-range force laws from classical particle exchange

TL;DR

This paper demonstrates how classical long-range force laws can emerge from simple particle exchange models, providing accessible simulations and analytic insights suitable for undergraduate physics education.

Contribution

It offers a quantitative analysis and simulations of a toy model illustrating the emergence of force laws from microscopic particle exchange, aimed at undergraduate students.

Findings

Force laws can be rigorously derived from microscopic models.

Simulations accessible to undergraduate physics students.

Analytic treatment clarifies different interaction regimes.

Abstract

The analogy of classical repulsive interactions emerging from the exchange of mediating particles is revisited with a quantitative approach. Simulations are presented for a particular toy model which are accessible to undergraduate students at any level in the physics curriculum. Analytic treatment of the various regimes shows rigorously how effective force laws can emerge from an underlying microscopic model and should be accessible to advanced undergraduate physics majors. The analysis presented uses the concept of emergence as motivation for students to gain experience building and testing simplified models for complex physical processes.