I have taken a digression from my sim work to think about quantization of atomic energy levels. These energy levels, to a first order in the simplest (hydrogen) atom, are defined by the Rydberg equation. The rest energy of elementary particles such as the electron is defined by E=hv, and I have posited that field twists geometrically achieve this quantization. I’ve then followed down a bunch of different paths testing this hypothesis. However, it’s not just rest mass that is quantized. The kinetic energy of electron orbitals in an atom are also quantized. In the non-relativistic case we can look at the solutions of the Schrodinger equation, although refinement of the solutions for spin and other 2nd order and quantum effects has to be applied. Ignoring the refinements, does this quantization also imply field twists?

I think so for the same reason as the E=hv rest mass case–to achieve a modulo energy value that quantizes, a geometric solution requires a twist in a background vector field state. There has to be a lowest energy state called the background state. You can imagine a plane of floating balls that each have a heavy side and a tenuous connection to adjacent balls. Most balls will tend to the heavy side down state (obviously, this is a gravitational analogy, not a real solution I am proposing). But if there is a twist in a string of balls, the local connection for this twist is stronger than the reverting tendency to the background state, and the twist becomes topologically stable. Several geometrical configurations are possible, a linear twist could model a photon, while a twist ring could model an electron. What could model the energy states of an electron around an atom?

One thing is pretty clear–the energy of the lowest state (S orbital) is about 8 orders of magnitude smaller than the rest mass energy of the electron, so there’s no way a single field twist would give that quantization. The electron twist cannot span the atom orbital–the energy level is too far off. The fact that the energy levels are defined by the Rydberg equation as 1/r^2 increments suggests either that each energy level adds a single twist that is distributed over the orbital surface (causing the effect of 1/r^2 over a unit area), or that the energy level is the result of n^2 new twists. Since I cannot imagine a situation which would enforce exactly n^2 new twists for each quantized orbital energy level, I think the former is the right answer. There is a constant energy twist being applied each time an orbital reaches another excitation level, distributed over a surface.

But what quantizes that first energy level (corresponding to the 1.2 10^-5 cm wavelength)? This cannot be related to the electron wavelength (2.8 10^-13 cm) because the S orbital is a spherical cloud that is far larger than an EM field twist solution would give. An EM twist about a charged stationary object would have about 4 times the classical radius of the electron–but the actual cloud is around 7 orders of magnitude larger. The thing that causes the atom orbital size to be so large is the strong force, which prevents the electron and the positively charged nucleus from collapsing. Trouble is, this is a complication that I don’t have any thoughts about how the Twist Field theory would work here, other than recognizing that any type of quantization requires a return to a starting state–implying a twist. DeBroglie proposed that the probability function wave has to line up, but we don’t really have a physical interpretation of a probability distribution in quantum mechanics, so what does it mean physically for that wave to line up? No such problem in Twist Field theory, and twists are so closely related to the sine waves involved (they are a reverse projection) that I don’t think it’s preposterous to propose field twists as an underlying cause.

But there’s a lot of gaping holes in that explanation that would require a lifetime of investigation.

Agemoz

Tags: 3d ring schrodinger, orbitals, quantization, Rydberg, twist ring, twists quantization, vector field

## Leave a Reply