What is the topology of three rotating orthogonal dipoles?
- They are independent for this first thought experiment
- In reality they exert electromagnetic forces on each other.
- They rotate in the xy, xz, and yz planes with the same origin.
- Let’s say they have the same speed.
- We have two directions each can rotate in.
- What are the symmetries?
- How many configurations are there? One? More than one?
A helpful user on the PBS Space Time Discord server provided the following response which is incomprehensible to me other than I knew there would be a topological connection of NPQG to the group theory of the standard model.
In complex-coordinate math, this is known as SU(3) in the literature (the symmetry group for the color force; 3×3 complex matrix representation). Electroweak uses SU(2) [same idea, but 2×2 complex matrix representation]. The real analogs SO(3) and SO(2) of SU(3) and SU(2) are more for rigid rotations. [Jargon: SO := “special orthogonal group”, SU := “special unitary group”. It is formally meaningful to define SO for complex vector spaces, but these don’t behave nearly as much like SO over real vector spaces, as SU over complex vector spaces do.User on PBS Space Time Discord.
What is the physical basis for quantum mechanic’s ‘spin’?
How do nested dipoles implement containment of the other dipoles as well as personality charges?
- Are they planar like a solar system?
- Nature loves to regenerate patterns.
- What do the fields look like for various geometries?
- Are they orthogonal?
- Are they independent?
- Is there some formula about the energy ratio required for containment? That would determine the ‘gear ratio’ or how many times a dipole executes its wave equation for every single wave equation transit for the interior dipole.
- Consider also that the more momentum a particle has, the smaller it’s dipole radius.
- As you perform work W to accelerate a dipole, the dipole shrinks.
- Does a moving set of nested shells align so that the charges are rotating perpendicular to the line of travel? That would sort of make sense, especially as v approaches c.
Imagine structure formation in an inflating Planck plasma with energy and point charges rapidly attempting to spread out in a chaotic maelstrom. It’s a game where high energy dipoles form and can capture other dipoles and personality point charges. Capture or be captured.
It is amazing how much physicists know about the electrino, positrino, and especially the dipole without actually knowing their physical implementation, or even that they exist!
J Mark Morris : San Diego : California