Electron mass derivation, and maintenance of a locality consistent with Bell's Theorem
v. 3 n. 5
This brief derivation of electron mass is somewhat repetitive but mentioned again now because of its close relationship to the previous article on Bell's Theorem about distant objects being closely related. * A brief video by Dr. Alexander Unzicker (unknowingly) provides a three minute introduction on problems with theoretical particle mass calculations: (369) Unsolved Mysteries: The Nature of Mass - YouTube. He is particularly concerned about the units of mass, kilograms, which are not ordinarily available in a particle context, nor is the gravitational constant, G. ** According to Bell's Theorem the search for these items at the micro scale could be profitable "non-locally," at the macro scale.
Conventionally, elementary particle masses are free parameters, subject to measurement but not theory. Regarding electron mass, it has been shown that
m/r^2 = A/G
where the left side is a mass to radius ratio of the local galactic supercluster and the right is the ratio of the acceleration of this supercluster, ～ 6 x 10^-13 m/s^2, to the gravitational constant; this relation was shown to be applicable regardless of scale (scale-invariant). ? ?? Let?m?in this relation be electron mass and?r?the classical electron radius,?ke^2/mc^2, which is commonly derived by noting the coulomb energy necessary to hold two point charges, each equivalent to electron charge,?e, this distance,?r,?apart; then
m^3 = k^2(A/G)(e/c)^4.
Notably, this particle mass is a consequence of large-scale considerations, suggesting locality and a "hidden variable," but consistent with the experimentally verified Bell's Theorem if particles are gravitational sinks, a falsifiable hypothesis. * Ordinarily Bell's Theorem (reality is non-local) and hidden variables are mutually exclusive when, conventionally, particles are assumed to be sources. If particles are sinks, it might not be necessary to dispense with the bedrock principle of locality (direct contact or identifiable connections among objects).
This electron above, and superimposed on the cover image background, is a gravitational?sink, where renormalization would not be necessary, i.e., the electron gravitational field?originating in the ambient gravitational field near and far cancels?at the focus of the particle, yet is present, at large, apart from the focus. This recalls Mach's Principle, where inertia on the small scale is a consequence of large-scale considerations. ???
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Cover image background credit: John Bell, less mass equation. nature.com