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 S137 to Sn 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.

2 responses so far

2 Responses to “Greatest Lower Bound”

  1. Kevinon 23 Dec 2021 at 9:28 am

    “If ħ and c are considered more fundamental than e, the fine structure constant becomes a measure of the electronic charge. This point of view is dominant in quantum field theory where α plays a role of the coupling constant between charged matter and electromagnetic fields.” *

    Many examples are found in the physics books of the 20th Century that anticipate quantum gravity.

    * Merzbacher, Eugen, “Quantum Mechanics”, Wiley, pg. 471-472

  2. Kevinon 23 Dec 2021 at 10:26 am

    As we, in our imaginations, go further and further out into the universe, we can visualize that a true vacuum starts to become a reality. As the solar wind, or the wind of any star, becomes far less dense, and the gravitational field becomes less dense, protons and electrons may disintegrate. The proton has never been found to decay, though most of our experiments are done on the earth.

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