Knots, Braids and Elementary Particles

For a long time, there has been a speculation in physics that knots and links are somehow related to the structure of very small physical entities such as atoms and particles. For example, Lord Kelvin (Sir William Thompson) theorized in the 19th century that atoms were knotted vortices in the luminiferous aether. (something like knotted smoke-rings) This idea of Kelvin lost favor when the aether theory was banished by special relativity, but the idea lives on in other forms. Herbert Jehle, in the 1970's suggested that elemenary particles were knotted quantized electromagnetic flux. Jehle's work was in the spirit of string theory, but knotted strings is not yet a full subject of investigation for technical reasons. In the 1980's there began an intense series of relationships between knots and physics via the advent of the Jones polynomial, state summation models for knot invariants and three-manifold invariants, and Witten's work relating these new invariants to quantum field theory. More recent work by Fadeev, Niemi and Kephart suggests that gluon flux (particles called glueballs) may have knotted states. Recent work of Sundance Bilson-Thompson, Lee Smolin, Fotini Markopoulou and the speaker suggests relationships between particles, framed braids and braided surfaces. This talk will be a survey of ideas about knots and elementary particles, from Kelvin's time to the present day.