What the Michelson Morley experiment really shows, and what most modern theories fail to recognise, is that empty space is incapable of supporting a wave. The fact that there is no ether means that all that is left which can support a wave is material and material, be it matter or antimatter is made of particles. In other words there is no such thing as a wave form of a particle as promulgated by the standard model and neither can there be such a thing, since it would by implication require a medium in which the wave exists – such a medium is the ether or the ether by another name – which Michelson Morley proved conclusively not to exist.
We are left with a conundrum – if there is no ether, what precisely is waving when we see a particle as a wave? The answer has to be that it is the particle itself that displays these wavelike properties. This is precisely the result that was obtained in Sampling the Hydrogen Atom, where the orbiting electron is seen to do so at constant radius and it is the motion of the electron itself, describing a circular orbit, that presents use with the wavelike properties of the electron.
In Shedding Some Light on the Nature of the Photon, it is seen that precisely the same argument applies to the photon. The photon is seen as being composed of two entities, a particle and its antiparticle equivalent, locked in mutual orbit and it is the motion of these two entities which presents itself as the wavelike properties of the photon.
This comes about because the centrifugal force, which tends to throw these particles off from their respective orbits, is seen to diminish due to the effects of relativity at orbital speeds which are close to the speed of light. It is this which leads to the hydrogen atom, and by implication other atoms, having stable states corresponding to the different energy levels of the atom and it is this which leads to a stable photon in which the constituent particles do not fly apart from one another.
This leaves open the question of the electron and other particles, which are simple isolated particles, but which also present themselves as having wavelike properties. Electrons for example can interfere with one another.
The reason that centrifugal force reduces with increasing velocity when the electron is traveling close to the speed of light is that orbital velocity is affected by relativity (see Relativity and Angular Momentum). In Sampling the Hydrogen Atom and Shedding Some Light on the Nature of the Photon we see that this also affects angular momentum in such a way that the orbiting particle is constrained to always orbit at a fixed characteristic radius related to Planck’s constant and to the inverse of its mass. Hence every particle has a characteristic orbital radius or, if we multiply by 2π, a characteristic wavelength which turns out to be the same as the Compton Wavelength.
This means if we impart even the smallest amount of energy to the electron it will follow a circular path, or if it is displaced it will follow a helical path. It is this motion which represents itself as the wave characteristics of such particles.
Michelson Morley showed that empty space is just that, a void, devoid of anything, not even the stuff that waves are made of. By introducing the idea of relativistic orbital velocity however we see that particles themselves display wavelike properties. In the limiting condition where we have a single particle in a space which is otherwise void, it is the motion of that particle itself which displays its wavelike properties. There is then nothing mysterious about the wave particle duality. It is not that particles exist in a nether state which collapses to be either a wave or a particle. It is more a case that particles have wavelike properties which are inherent because of their circular motion – it is the theory which collapses when we introduce the idea of relativistic orbital velocity.