The physicist Sir William Thomson (also known as Lord Kelvin) proposed in 1867 that physical atoms were knotted vortex tubes in the then postulated all pervasive fluid called ether. The physicist Peter Guthrie Tait became so enamored with Thomson's theory that he undertook a study of the mathematical properties of knots, thus giving birth to the field of knot theory.
Although scientific evidence has since shown conclusively that physical atoms are by no means knotted vortices in the sense of Thomson, Thomson's theory has fragmented and relatively recently reemerged in many much more sophisticated forms in both classical and non-classical physics. With the work of Jones, Witten, and others, knot theory has now begun to reassociate on a serious basis with its long lost ancestor, physics.
The first section of this paper gives a brief survey of the early Thomson atomic vortex theory as it developed within the James Clerk Maxwell milieu. The paper then focuses on the modern legacies of this theory in classical electrodynamics. In particular, the second and third sections of this paper look at some of the recent developments on knotted magnetic vortices and knotted electrostatic vortices, respectively.
In summary, this paper focuses on the study
of the electromechanical behavior of knotted tubes of electrical charge
and magnetic flux. Surprisingly, even within classical physics (more specifically,
classical electrodynamics), there are many important unresolved questions
about such objects. Many of these questions are relevant to such diverse
fields as plasma physics, polymer physics, molecular biology, and, of course,
(*) Partially supported by the L-O-O-P Fund.