Nov 14 2021

## Greatest Lower Bound

One would guess that the particle physicists and quantum field theorists may like a 1.3335 x 10^{-15} m diameter of a free electron, because it is closer to a point particle than many estimates of the diameter. It is possible that 1.3335 x 10^{-15} m is also the limit inferior of the sequence S_{137} to S_{n} in an atomic orbital.

The maximum diameter, on the other hand, will depend on the element and on the orbital. At a spin flip, electrons in all orbitals may reduce to 1.3335 x 10^{-15} m, before taking off on a new trajectory and increasing in diameter again. We cannot speak of a limit superior of the sequence of diameters of the electron in an atomic orbital nevertheless. That will depend on the direction of electron travel, and on whether the atom is at the surface of the earth, or at some other planet. For the latter, it depends on the density of the gravitational field.

We may also ask whether 1.3335 x 10^{-15} m is the greatest lower bound at all locations in the universe. This raises the question of whether the fine structure constant is a universal constant, or whether or not the Coulomb gauge is the same everywhere.