Quantum interference will redirect particle paths due to wave interference effects, so it seems reasonable to assume that quantum interference could form an orbiting pair of group wave particles. It is fairly easy to show that a pair of oscillating wave sources will generate an interference pattern such that if the sources follow the pattern peak amplitude path, the paths will orbit each other (see several recent previous posts on this topic).
However, in real life, there are only a very limited set of wavelengths that could produce actual particles–electrons, for example, could be the results of such orbiting internal wave structures, but why do rest-frame electrons have precisely the wavelength they have, and no other? We know that geometry alone cannot form any specific wavelength soliton solution, because geometry by itself is scaleless–there is nothing in geometry that specifies that an orbiting pair of particles has to have a specific size. The only fixed constants we have that could form solitons are the constants of physics–speed of light c, charge q, Planck’s constant, and so on.
I’ve thought for years about what could constrain the geometry to a single soliton size, and so have many others, including DeBroglie, Compton, and others who generally tried to use the obvious candidate–charge attraction. But since EM fields are central force fields and produce unstable solutions involving infinities, no one accepts that approach anymore.
I think I have an answer. It comes from quantum interference, speed c, and Planck’s constant–let’s see if you agree or think this is just another futile exercise in numerology or wishful thinking.
We will assume that on some tiny scale, electrons consist of a dual pair of oscillating wave peaks (see image). Quantum interference determines that the peaks will orbit with a radius proportionate to the wavelength. So far, there is nothing that constrains how big this orbit is–the larger the wavelength, assuming they all move at speed c, the longer the path time, which corresponds to the longer wavelength. There are no unique solutions here. We need to determine what could constrain this orbit radius.
We know that wave particle momentum is inversely proportionate to wavelength, but directly proportionate to orbit size. In other words, the smaller the wavelength, the smaller the orbit–but conversely, the smaller the wavelength, the higher the momentum, and consequently, the larger the orbit. There is only one wavelength where the orbit is the same for both.
I computed it this way. Radius r of an orbit is equal to mass * velocity^2 divided by the force Fn (reference centripetal force) applied normal to the orbit path. This is the quantum interference force and is independent of r (quantum interference does not obey the central force derivation used for charge or gravity, reference the Aspect experiment and similar). Now, the wavelength must also define the radius; here, the radius r is equal to the wavelength wrapped around the orbit, that is, lambda/2 Pi. We assume the velocity of the waves is always c, so for non-relativistic particles, E = m c^2 = hv. Substituting into the first equation for r and using v = 2 Pi f, we obtain h c/(Fn lambda) = lambda / 2 Pi.
Therefore, there is only one wave solution for a dual pole orbit (yes, I did unit checking to make sure I didn’t goof something up on this):
lambda = Sqrt( 2 Pi h c / Fn)
Other wave peak geometries in R3 will produce similar solutions. It’s not clear what Fn would be yet–more work to do here, but one thing is for sure–such a construct will only produce one solution. The proposed soliton only works if Fn is independent of dipole spacing. This works if we use the proposed idea that poles are Fourier sums of waves (see previous posts and this paper: group_wave_constant_speed). Quantum interference alters the wave sum to guide the poles. No actual force is needed (the big drawback of the guiding pilot wave used in the Bohm quantum interpretation is the need for a new force not shown by experimental observation).
I will investigate further for specific particles such as an electron, and report back.
Agemoz
dipole structure
Tags: physics, quantum, quantum interference, quantum theory
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