Dirac derived the existence of the electron spin from his relativistic equation. But, actually, does nonrelativistic quantum mechanics already imply the existence of the spin?
The electron has an electric field. If we would know that the field does not rotate, that would probably break an uncertainty principle of the rotation of an object.
That is, there has to exist a spin for all objects which have some kind of spatial extension, small and large. The spin is not constrained to elementary particles.
The electron is a point particle. One might conjecture that it cannot rotate, because it is a point. However, the electric field of the electron is not a point, and has an orientation in space. When we measure the electron spin, we measure the rotation state of its electric field.
https://aapt.scitation.org/doi/10.1119/1.11806
David Hestenes has a similar idea in his 1979 paper.
The rotation axis is confined to the surface of a unit sphere. Does the spin 1/2 correspond to half a wave circling the sphere? That might explain the strange 720 degree rotation symmetry of the spin.
Is there a way to make the electron electric field rotate more rapidly? The spin 1/2 may correspond just to the lowest rotation energy state.
In an electric potential, the electric field of the electron may have much more energy than 511 keV, and it would be natural if new rotation states appear.
What about the spin of the muon? The muon is 200 times heavier than the electron. Could we make the muon to spin more rapidly?
What is the spectrum of hydrogen like under an electric potential?
https://en.m.wikipedia.org/wiki/Aharonov–Bohm_effect
The Aharonov-Bohm effect for an electric potential has not been measured yet.
But, according to our new energy-momentum relation as well as the old one, a constant electric potential changes the inertial mass of the electron. It should be easy to measure under a potential of, say, a few kilovolts.
https://en.m.wikipedia.org/wiki/Stark_effect
In the Stark effect, the spectrum of an atom is affected by a static non-zero electric field. What about a constant potential? Our Nov 15, 2018 post studies this question.
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