The 4/3 electromagnetic mass problem is a famous issue in classical electrodynamics.
It arises when trying to compute the electromagnetic contribution to the mass of a charged particle, like an electron, modeled as a small charged sphere.
When computing the momentum of the electromagnetic field of a moving charged sphere, the result is: Pm=4/3⋅U/c2 *v, where U=mc2
This implies an electromagnetic mass of: m=4/3⋅U/c2
But this contradicts the energy-based result, So there's a factor of 4/3 discrepancy.
This problem was first discovered and explained by Max Abraham and the first attempt to solve was indirectly given by Poincare' who introduced a pressure from inside the electron facing a sort of "negative energy".
Very Recent papers from
Dr. Vladimir Onoochin (2024)
Physical meaning of electromagnetic mass and 4/3–problem
https://arxiv.org/html/2405.20781v1#bib.bib12
the one from Prof. Theodor Nieuwenhuizen Article How the vacuum rescues the Lorentz electron and imposes its ...
this paper by prof. Remo Ruffini et al.
Article On Fermi’s Resolution of the “4/3 Problem” in the Classical ...
https://homepage.villanova.edu/robert.jantzen/mg/fermi/fermi1234c/fermi_paper_110401.pdf
and the historical digression of Dr. Marco Giovannelli
Article The practice of principles: Planck’s vision of a relativisti...
in "2.7 The dynamics of the cavity radiation"
it is described how Planck treated this issue of the 4/3..
"The factor 4/3 arises from the radiation pressure p0 on the walls, which, as we have seen, is 1/3 of the energy density w0. Thus, the total energy is E0 + p0 V0 = E0 + 1/3 E0"
I think, in the 4/3 problem there is certain misunderstanding.
The masses
m = E/c^2 (E is the electrostatic energy)
and
m = (4/3)E/c^2
are calculated from different 'sources'.
The first mass is calculated as an energy of electrostatic E field of the classical electron.
The second mass is calculated from the vector product [E x B] - of the fields created by the electron whhen it begns to move (m = (4/3)E/c^2 is calculated at the limit 'velocity of the electron -> 0).
In the Maxwell-Lorentz electrodynamics, it is not necessary that one mass must be equal to the other mass. The equivalence of the masses is the requirement of the special relativity.
I wish to note too that these masses are the 'calculated qantities' - it is impossible to check experimentally if m is equal to E/c^2 or if m is equal to (4/3)E/c^2
Dear Vladimir Onoochin ,
basically E/c2 is calculated according to the energy density of the electric field integrated all over the surrounding space, when the charge is at rest in a frame of reference.
The other takes into account also the contribution of the magnetic field.
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