See also the other posts in this category. Reading them in the order posted might be a good idea.
Real soon now, Archimerged is going to make that animation. But he has some puzzles first. (Ark likes puzzles).
- The total energy of the electron ought to be proportional to its rate of spin.
- What (in this model) causes interference?
- How does one photon end and another begin?
- How does a photon carry energy?
- What is the meaning of the second (ingoing) principal null congruence?
The above questions are at least partly answered today. These are not:
- Besides its literal meaning (go around twice to return to the original state), spin-half also means the angular momentum is quantized in units of half h-bar.
- What is Planck’s constant anyway?
In the process of making the animation, and solving the puzzles, Ark is doing some concrete thinking in four dimensions. The spinning metric isn’t really spinning so long as the principal null curves end up moving straight to infinity. Rather, the outgoing null curves twist round and round the spherical surface (initially, they move an infinitesimal distance outward for each turn around the sphere), until at a large distance, they began moving outward faster than around. This original metric (Ark is withholding its name because it has irrelevant connotations and also because he converts it to a photological space) is a stationary sphere with null curves wrapped around it which eventually end up proceeding in all directions out to infinity.
When many spinning particles are incorporated into a target photological space, the principal null curves of the particles (both ingoing and outgoing curves, separately) all begin and end wrapped around the spherical surface of particles. None of them ever make it to (or come from) “outer” infinity. The null curves of the target space which reach infinite distance also come from infinite distance. When a group of null curves of a pair of particles are bundled into a photon, all of them run from the source particle to the destination.
Obviously, a null curve which starts as the outgoing null of one particle becomes the trapped null curve of the photon (in a preferred frame, the principal null vector has two zero components), and when it reaches the second particle, it becomes the ingoing null curve. What about the other congruence?
Because principal null curves form a congruence (they fill four-space and never cross), at any given time and place, there is exactly one null curve (from a given principal null vector field) at that event. Ark’s animation is going to show points moving along some of these null curves in three-space. Two of these points will never end up colliding.
Since the original spinning metric isn’t really spinning, Ark is making the sphere spin on its axis so that at infinite distance (in a photological space containing nothing but the sphere), the null curves go around at a specified rate, which is the total energy of the particle.
Now Ark knows that photons of high frequency have high energy. And electrons absorb and emit photons, gaining and losing energy in the process. He is right now investigating exactly how his particles do this (if they do it). The principal null curves of a spin-half electron are arbitrarily straightened and bundled into a rope (the photon) perpendicular to the spin axis, with the north pole curve on the outside and the south pole curve at the center of the rope. The rope describes a cylinder or an elliptical cylinder as it moves above the north pole and below the south pole to permit the sphere to spin without making the rope twist. At the other end of the cylinder, there is another spinning particle where the principal null curves can unbundle and dive back into the maelstrom.
The rope must trace out the cylinder (the straight rope revolving about the cylinder axis) once for every two turns of the sphere. Obviously, the angular frequency of the photon is the angular frequency of this revolving rope. (Ark expects that actually, a photon consists on just one turn around the cylinder, after which a new photon starts, pointing usually in a different direction. If the rope goes around twice, that is two photons one after the other.)
Ark believes that his model fits very closely to Cramer’s Transactional interpretation of quantum mechanics (TIQM), which is also related to Feynman and Wheeler’s advanced and retarded absorber theory. [ref to be added]. One nice thing about this is that Cramer has already established (at least it got published in Reviews of Modern Physics) the equivalence of his interpretation with ordinary quantum mechanics, and to some extent with quantum field theory. Of course, Ark would rather use an ensemble of systems (or multiverse of universes, with each universe a fixed 4D spacetime) view in place of Cramer’s “offer wave,” but he isn’t that far into working it out.
One striking thing about TIQM is the advanced and retarded waves, and the negative and positive energy they carry. In thinking about this puzzle, Ark has decided that photons carry twist as well as having a frequency: an outgoing photon can cause an increase or decrease in spin, and the simultaneously arriving ingoing photon must exactly match this increase or decrease. Because of the spin-half pattern (the rope revolves around the cylinder once, going above the north pole and below the south pole, as the sphere rotates twice), the twist carried by the rope is precisely the change in rotational frequency of the sphere. There are always two of these ropes (which are completely oblivious to each other — they correspond to two separate null congruences), and if they didn’t both twist by exactly the same amount, a great tangle would ensue. Thus, the sphere does not go around precisely twice for one revolution of the rope, but the difference corresponds to the amount of energy delivered or removed by the advanced and retarded photons (ingoing and outgoing congruences).