Authors: Jean Louis Van Belle
Following a series of papers on geometric interpretations of the wavefunction, this paper offers an overview of all of them. If anything, it shows that classical physics goes a long way in explaining so-called quantum-mechanical phenomena. It is suggested that the fine-structure constant can be interpreted as a scaling constant in a layered model of electron motion. Hence, instead of one single wave equation explaining it all, we offer a theory of superposed motions based on the fine-structure constant, which we interpret as a scaling constant. The layers are the following: 1. To explain the electron’s rest mass, we use the Zitterbewegung model. Here, we think of the electron as a pointlike charge (no internal structure or motion) with zero rest mass, and (1) its two-dimensional oscillation, (2) the E/m = c2 = a2ω2 elasticity of spacetime and (3) Planck’s quantum of action (h) explain the rest mass: it is just the equivalent mass of the energy in the oscillation. 2. We then have the Bohr model, which shows orbitals pack the same amount of physical action (h) or a multiple of it (S = n·h). It just packs that amount in much larger loops which – of course – then also pack a different amount of energy. As it turns out, the equivalent energy (E = h·f) is equal to α2mc2. The fine-structure constant also acts as a scaling constant for all other dimensions (radii, velocities, and frequencies). 3. The difference between the energies of the Bohr orbitals is, of course, the energy of the photon when an electron makes a transition. Hence, we also offer an elegant one-cycle model of a photon and show the meaning of the fine-structure constant as a coupling constant in QED. This all leads to a much more comprehensive interpretation of the fine-structure constant as a scaling constant. As an added bonus, we argue that the fine-structure constant also introduces a form factor (the electron is now viewed as a disk-like structure), which might explain the anomalous magnetic moment. We argue that the anomalous magnetic moment may, therefore, not be anomalous at all.
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