A lot of research has led me to several conclusions that have changed the course of my thinking. First, I have finally abandoned the dipole twist solution for the electron, at least on a scale larger than the Planck length. It’s so tempting because a lot of interesting things come out of that approach (see all the previous posts on the subject here), but all the reading and research I have done seems to instead confirm the point size of the electron. I’m still a believer in the quantum interference approach, that is, quantum interference is involved in a lot more than just adjusting space-time locations of quantum decoherence.
So, to make a long story short, I now accept the point particle nature of electrons and quarks. I still believe that special relativity must arise if all particles are solely comprised of waves (see paper:https://agemozphysics.com/wp-content/uploads/2020/12/group_wave_constant_speed-1.pdf). I suspect that two additional principles are also true but I don’t have proof: that E=hv implies quantized twists in R3 from a background state vector I normal to R3, and that particles exist where quantum interference of waves sum to a peak value (see previous posts on this subject). This peak value moves according to how waves interfere over time.
Having abandoned attempts to solve for an internal electron wave dipole structure, I turned my attention to quarks, a substantially more complex particle set. I noted that there is only one stable way in an EM field to physically align three point particles where one particle has 1/2 the negative charge of the other two particles (a u,u,d proton configuration) such that there is no net force on any of the particles–in a straight line with the negatively charged particle is in the center. There are analogous solutions with a center negatively charged particle surrounded by n equally spaced positive charges in any of the polygon or Platonic polyhedra configurations. Also note the vice versa solutions where charge polarity is reversed.
Note that this discovery reinforced the thought that the electron cannot be a +,- charged dipole–such a configuration can never statically exist, it will always collapse. As far as I can determine, there no other statically stable particle configurations.
So, I decided to attempt a Schroedinger wave solution of the u,u,d solution. Since now the potential V is dependent not just on r (the case of the hydrogen atom), cylindrical coordinates are required where the radial eigenstates are independent but the x and y displacements will have composite eigenstates. All the tricks we use to solve for the hydrogen atom won’t work here. However, it’s clear that this Hamiltonian is closely related to the hydrogen atom–it’s clearly bounded even though there’s a pole at the third particle (when solving for the first particle). If it is bounded, there has to be fixed energy eigenstates. I am now in the process of trying to find out what they are–I’m pretty sure the ground state has to be the in-line solution that is statically stable. One way or the other, the u,u,d case definitely has a quantum well (see image) and thus should have time independent quantum eigenstates. This is a complex problem that is taking all my research time right now.
I also noted that the d,d,u configuration does not have a statically stable state, but if you assume a quantum linear combination of two symmetric isosceles triangles, I do see a statically stable configuration–maybe. If I make any progress on the u,u,d case, I’ll apply the same approach to the d,d,u Schroedinger.
If I do end up finding eigenstates, that’s just the beginning–what confines these quarks to a “bag” and why is the rest mass of the proton so much greater than the electron? How do gluons derive from this Schroedinger equation and why do they carry mass given that emission from quarks would not conserve mass (and hence energy)? If they are virtual, how does that factor in a Schroedinger model?
Agemoz
Tags: physics, quantum, quantum theory, special relativity
Agemoz's Physics Blog 
Leave a comment