Vortices and atoms in the Maxwellian era

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.

O elemento tubo na fundamentação do conceito de campo

“…Em seu artigo Über Integrale der hydrodynamischen Gleichungen [29], 15 Helmholtz introduz vórtices na investigação da dinâmica de um fluido, 16 usando analogias com fenômenos eletromagnéticos para ilustrar sua teoria hidrodinâmica. Ele apontou que as linhas de movimento do fluido eram organizadas da mesma maneira que as linhas de força magnética em torno de uma corrente elétrica fluindo ao longo do eixo do vórtice e, assim, trabalhou a partir do eletromagnetismo para desenvolver argumentos físicos e obter uma compreensão intuitiva do comportamento dos vórtices [31]. A associação feita era: o eixo de rotação dos vórtices do fluido ficava determinado pelo sentido da corrente elétrica.…”

Is electromagnetic field momentum due to the flow of field energy?

“…Since E is nonzero except when E=B=0, throughout this paper we will take definition A, V A = S/E, to be equivalent to the formula S = EV A 5. Electromagnetic formulas in this paper are taken from Griffiths[8] and Jackson[9], with translation into Heaviside-Lorentz units.…”