Using the hydrogen simulation I wrote that generates fractured (fractal) electron orbits in hydrogen, I attained the following quantum jump:

http://sb635.mystarband.net/kerr2_n2.pdf

The n = 1 shell is created first, then the electron jumped to the n = 2 shell. The simulation stops before the end of the creation of the n = 2 shell. (It gives it an "incomplete Death Star look" to n = 2.) This was a jump the electron made "on its own," I did not program in any purposeful quantization anywhere in the mathematics. Let me stress this, I had no information about the n = 2 shell in this simulation. For the n = 1 shell, the vast majority of computer runs result in a stable ending, with the electron staying in the n = 1 shell, but infrequently, a quantum jump is made like the above. This could be nothing more than simulation effects, but likely not because it's probably physically driven that it jumped to the n = 2 shell, there probably being a strong attractor there. All of this occurs with a deterministic integrating of the electron's Kerr continuous equations of motion. (If you don't like this Kerr implementation, just think I'm moving the electron in a Coulomb field with magnetism.) As I mentioned, I've implemented a kind of "stochastic geodesic motion." After a deterministic step of the Kerr equations, a random out-of-plane perturbation of the resultant velocity vector is imposed. In a statistical theory sense, the output from the deterministic integrator produces a population mean of a velocity pdf, around which are actualized perturbed velocities and then added to the mean. In a Newtonian-type field, this does not change the acceleration the electron is subjected to, it being a function of only the un-perturbed position, but it does in a differential geometry representation of the proton's Coulomb field. As the velocity gets perturbed, so does the acceleration imposed on the electron. The Kerr metric itself does not "jink," it is a static field, so I would not say "space is stochastic," but the geodesic upon which the electron coasts is jinking, and quite a lot for a fractured orbit. The time delta in between these velocity perturbations is on the order of 10^-20 sec. I assume the energy of these various delta-v's come from some source outside the atom (or inside, if from the zero-point energy background, if you believe in such a thing.). Also, during the electron's motion, it is not only subjected to just a specially relativistic time dilation proportional to (1 - v^2/c^2), but is instead fully time dilated according to how a Kerr differential geometry dilates time. Also, since velocity is jinking in direction, so is the electron's Kerr time dilation. At the scale that unifies gravity and electricity, these "fully relativistic" quantized effects are subtle, but may be just what's needed to somehow drive these quantum jumps.

The next plot shows the n = 2 shell completed, with the n = 1 shell nested within:

http://sb635.mystarband.net/kerr1_n2.pdf

For these runs, I did not perturb radius. This is why there are such strong attractors to the initial beginning radial distance. I have programmed the radial perturbations, and tested this, and only very small perturbations can be tolerated before the atom falls apart. I at first gave the radius a pdf in width like the classic radial pdf of QM, and of course, the atom falls apart. I knew this would happen, from an orbital standpoint it is simply not a tenable postulate that the electron's radius shows such wide variation. And I mean ridiculously wide is the QM result, imo. The needed variance in the electron's radial value is so small, that leaving it perfect is ok with me. There are also theoretical reasons to do so. The beginning "perfect" radial distance is what the closed system is started with, and according to Planck's laws, it can't change in radius accept to another integral multiple, like the jump to n = 2. In the simulation, the electron actually does not make an instantaneous jump, there is some travel from n = 1 to n = 2, and when it hits n = 2's distance, it locks in a strong attractor there and fills in the shell. I really don't think the electron's radius is truthfully perfect like this, I do think there is some "slop," but very, very small, so leaving it alone is fine. The hydrogen atom is much more of a little deterministic machine than what QM states. Chaotic, but on the small level of an atom, bound and strongly attracted to specific radial distances.

These fractured electron orbitals have interesting characteristics. One is that an electron can stay in a patch "on the attractor (shell)" for many orbital "periods". It's as if over a time of many "periods," the electron can "paint in" a local part of the shell, and still remain in a nearly-conserved energetic condition for the shell. Even still, the actual period between a "shell filling" and another is extremely small. The classic n = 1 period is about 10^-16 sec, so thousands of periods still take less than 10^-12 sec. If this is indeed how an electron moves in an orbital, these computer results give insight as to how an atom can appear to be solid. I also think that the degree of "fracturing" I can numerically impose with stability on my home computer is probably far greater than the real world, which I think is fractured on a much smaller level. I think with infinite fracture, the electron just sits there in space and doesn't move. That obviously doesn't happen, so the "jitter" in the background acceleration field can't be nearly infinitely strong, but probably is fractured on the Planck scale, unbelievably small but finite. But I think the essence of the effects of a good degree of fracturing of the electron's orbit, like I can attain, is producing some interesting results. I would have never thought a basically deterministic orbit program with a small amount of velocity perturbations imposed, would show such strong chaotic-quantized-attractor behavior. It's as if the fracturing is causing the quantization of the shells.

It is also interesting to note that I can essentially completely "tame down" the level of fracture of the orbits by introducing strong electronic Kerr frame dragging effects (magnetism). Even keeping the same degree of orbit fracture in the above plot, I can make them significantly more "normal" looking, going around the proton on a normal-looking orbit instead of the zig-zag by increasing the Kerr frame dragging effects. In terms of Dr. Cahill's fluid vorticity explanation of frame dragging, it would be that strong geomagnetic fields could "smooth out" the quantum foam.

Steve Bell