Physics Central wrote:See: Emptiness Tied in a Knot - Physics Central Physcis Buzz Blog - 1706-2017

Last month in the American Physical Society’s journal Physical Review A, a team of scientists from Leiden University in The Netherlands demonstrated just this. They used the mathematical theory of knots to explore electromagnetic fields. In doing so, they realized that some solutions to the fundamental equations of electromagnetism can be described as knotted structures.

The origin of knot theory dates back more than 125 years, to when Lord Kelvin suggested that atoms were swirling regions of the ether tied in knots (more on that here). The idea of ether was abandoned not long after, but it kicked off a field of study that has 1produced important results in many areas of physical science. About twenty years before knot theory was developed, James Clerk Maxwell developed a theory that describes how light, electricity, and magnetism behave and interact. He is the one that suggested light can be described as electromagnetic waves traveling through space. Maxwell’s groundbreaking work can be boiled down to a set of mathematically sophisticated equations—often called “Maxwell’s equations”—that are the foundation of classical electromagnetism, optics, and circuits. Recently, physicists realized that studying electromagnetic fields from a knot point-of-view leads to intriguing results. This new work focused on points in space called optical vortices, where the strength of an electromagnetic field is zero. Imagine a ray of light twisted like a corkscrew that is traveling toward the wall in front of you. The twisting causes the light to interfere in such a way that when it hits the wall, you see a ring of light surrounding a dark spot. The dark spot, where there is no light, is called an optical vortex. Like the calm in the eye of a hurricane, within that circle there is emptiness; the electromagnetic field is zero. In two dimensions, like on the wall, optical vortices are points. In three dimensions, they are lines.

This new work shows that optical vortices in real electromagnetic fields can be described as knotted electromagnetic field lines. Put another way, the researchers show that knotted structures can be exact solutions to Maxwell’s equations. In addition to this finding, the team mathematically describes how these structures emerge.

If you are interested in these knotty problems please look this paper up here at the preprint server:

Cable Knot Vortices in Electromagnetism

Albertus Johannes Jacobus Maria de Klerk, Roland Ivo van der Veen, Jan Willem Dalhuisen, Dirk Bouwmeester

(Submitted on 17 Oct 2016)

Knot-like structures, arising in several areas of physics, have received substantial interest for their topological properties over the preceding decades. In this letter we combine results from knot theory with Bateman variables for the electromagnetic Hopf field to construct a new family of finite energy null electromagnetic fields with stable optical vortices that are topologically equivalent to a given but arbitrary algebraic link. The class of algebraic links includes not only all torus knots and links thereof, but also cable knots which have thus far not been brought in connection to electromagnetism.

You may easily see by example that photon knots are also responsible for electrons... Williamson & van der Mark - Is the electron a photon with toroidal topology - 1997? First the "torus knot", then the "cable knot" views of the same "electron" which is actually a "particle".... or not.

A pair of these "knots" can be created from a pair of energetic photons nucleating electron and positrons in the process... functionally identical... matter from light virtually "ex nhilo". However this "electromagnetic smoke ring" does have a peculiar folding where the negative excursions of the field are all wrapped to the outside and all the positive excursions of the field are wrapped to the inside. The fields then become "static" and charged negative on the outside and positive on the inside... or as a connected "pair" an "electron" with a negative charge on the "outside" and a "positron" and a positive charge on the "inside".

Or even this recent development: Researchers develop magnetic switch to turn on and off a strange quantum property - Phys Org - 2505-2017 These "particles" are actually self trapping "waves" provided you have the "photonic energy" in these photons to create the electron-positron pair. It also suggests the source of the static charge in matter arising from the electric field of the "flying photon" constrained to a spherical compact knot. In that case the structure is the same as that of a Falaco Soliton but with a possible additional dimension. I would also add... subject to a "Page and Wootten" quantum time Mechanism. For details look here: Was Einstein Correct on Relativity and the Speed Of Light - John Duffield Site - 12 Jun 2017