DeltaV wrote:Johan, I and other engineers wish you full success in all of your research efforts. The potential applications are tantalizing.
Thank you for your support.
In what (major) points does your theory agree/disagree with the hypothesis that electrons and protons are actually closed-loop photon "knots"?
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I am still working on this problem: It is my hope that I will be able to derive a differential wave equation for a free electron from Maxwell's equations for light waves.
At present, I am working from the postulate that an electron is a (type of?) light wave which is stationary within its own inertial reference frame (I will call this inertial reference frame the rest-frame for the electron). In contrast a free light wave has no mass energy since it cannot be stationary within any inertial reference frame: However, light energy can be trapped within a black box cavity to form stationary standing waves; and these waves are then also stationary within the inertial reference frame within which the black-box cavity is stationary.
This is how Max Planck modelled black-body radiation: He assumed standing waves but added the condition that a standing light-wave with frequency (nu) cannot have less energy than an amount h*(nu); nor can it increase its energy by less than h*(nu). Thus standing (stationary) light waves which follow Boltzmann’s statistics, model black-body radiation perfectly. There is no need for “light-particles” which flit around with the speed of light c within the black box and follow Bose statistics. In other words, standing light waves and Boltzmann’s statistics work just fine when assuming that each quantum of energy h*(nu) is a “sub”-wave, emitted from the wall of the cavity and which then entangles with an existing standing wave having the same frequency, or which forms a new standing wave with that frequency. The concept that the quantum of wave-energy is a photon-"particle" only came into vogue after Einstein derived his equation for the photo-electric-effect. And Einstein regretted this until the day he died! In fact, it is possible to derive the photo-electric equation by using the assumption that a light wave and an electron wave can merge their energies by entangling with each other. There is no “collision between two particles” involved whatsoever.
The important point to notice is that where-as a free light-wave moving with speed c has no mass-energy, because it can never be stationary within any inertial reference frame, the standing light waves in the black-body cavity are not moving with a speed c. They are stationary and therefore their energies are now purely mass-energy. For this reason I believe that an electron-wave is a light-wave which is stationary within its own inertial reference frame. A free matter wave thus only has a speed within those inertial reference frames which are moving relative to the matter wave’s rest-frame.
Thus in order to solve for an electron wave, one must have a differential wave-equation which gives a suitable solution for a standing light wave within a rest-frame; and the energy of this wave must be the rest mass energy of the electron. Schroedinger’s wave equation uses the rest mass as an input, instead of obtaining the rest mass as the solution of the energy of a free electron. This is why Schroedinger’s equation (and Dirac’s equation) cannot model a free electron. It is, however, a good approximation to obtain the waves for bound electrons around the nucleus of an atom.
Now why will a electron-wave be stationary within its own inertial reference frame (its rest frame)? There must be a “potential” keeping it in equilibrium at its rest position. This means that if one wants to move the electron, there must be a restring force that opposes this attempt to move it. Thus the electron wave at rest must be the lowest energy state of a harmonic oscillator. To make a long story short, when following this route, one also obtains a causal reason why an electron aligns itself “spin-up” or “spin-down” when applying a magnetic field. This has NOTHING to do with any charge spinning and also NOTHING to do with a spin probability wave.
It also explains why an electron radiates dipole EM radiation when it is being accelerated since the restoring force relates to a positive charge that is situated along a fourth space dimension. When not accelerating there is no “vibration” between the negative charge of the electron within our three-dimensional space; but when accelerating there is vibration and the positive charge thus reveals its presence.
I discuss these concepts in more detail within my book.