Vortices and atoms in the Maxwellian era

TL;DR

This paper explores the historical development of vortex theory in physics and mathematics, focusing on early British contributions, conceptual issues, and the eventual limitations of vortex models in explaining matter and forces.

Contribution

It provides a detailed analysis of the conceptual and mathematical evolution of vortex theory and its impact on early physics and topology, highlighting British scientists' efforts and shortcomings.

Findings

British vortex studies advanced hydrodynamics and topology

Vortex models faced conceptual challenges in explaining matter and forces

British efforts ultimately did not achieve their physical objectives

Abstract

The mathematical study of vortices began with Herman von Helmholtz's pioneering study in 1858. It was pursued vigorously over the next two decades, largely by British physicists and mathematicians, in two contexts: Maxwell's vortex analogy for the electromagnetic field and William Thomson's (Lord Kelvin) theory that atoms were vortex rings in an all-pervading ether. By the time of Maxwell's death in 1879, the basic laws of vortices in a perfect fluid in three-dimensional Euclidean space had been established, as had their importance to physics. Early vortex studies were embedded in a web of issues spanning the fields we now know as "mathematics" and "physics" - fields which had not yet become institutionally distinct disciplines but overlapped. This paper investigates the conceptual issues with ideas of force, matter, and space, that underlay mechanics and led to vortex models being an attractive proposition for British physicists, and how these issues played out in the mathematics of vortices, paying particular attention to problems around continuity. It concludes that while they made valuable contributions to hydrodynamics and the nascent field of topology, the British ultimately failed in their more physical objectives.