I want to make the point in this post, that although one could easily dismiss my contention that existence of the Thomas precession along with electrostatic forces implies existence of an anti-centrifugal force that can overcome electrostatic repulsion as speculative and unproven (and you'd be right), it is a different matter so far as the existence of strong magnetic force that can do the same is concerned. Anyone with an undergraduate physics student's understanding of electrodynamics can see this for their self with a half-hour's worth of derivation.
To derive the interparticle separation, between two like charges, where the magnetic force will overcome electrostatic repulsion, while not leading to a mass for the bound composite that exceeds the proton mass, one can simply evaluate the magnetic part of the Lorentz force for a first relativistic charge moving in the magnetic field of a second relativistically-moving charge, that is also accelerating due to electrostatic forces due to the presence nearby of the first charge. Everything needed is in a standard electrodynamics textbook such as Jackson or Griffiths, and on just a couple of pages (or on wikipedia, alternatively).
First, calculate the acceleration of a charge with arbitrary rest mass in the non-radiative electric field of a second nearby charge, as a function of the separation between the charges and their velocities. This must be done using the proper relativistic forms for both the electric field, using the electric field derived from the Lienard-Wiechert potentials, and for the resulting acceleration due to the electric force, which must be based on the relativistic equivalent of Newton's law of inertia.
Next, get the magnetic part of the radiative field due to the accelerated (second) charge, again using the Lienard-Wiechert field expressions. Assume the second charge is moving at approximately (i.e., asymptotically close to) the speed of light perpendicularly to the direction of its acceleration. This is consistent with
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