Reasoning on the relativistic electric charge

In the previous post the relativistic electric charge concept was introduced, that is, the electric charge does not have an invariant fixed value and its value depends on the speed.
The speed of light is the threshold value at which the electric charge is canceled. This condition of electrical neutrality opens the possibility that at the speed of light can occur the conversion of matter to electromagnetic radiation.

We will look forward to establish the situations in which a charged particle can actually reach the speed of light in order to assess the compatibility with current knowledge and experimental evidence.

From the theoretical point of view the most simple situation to consider is the collision between an electron and a positron which are the two smallest particles having an electric charge of opposite sign.
Applying the laws of classical mechanics and taking into account the formulas which define the radiating mass and the relativistic electric charge is possible to simulate numerically the dynamic calculating position, speed, mass, electric charge and acceleration moment by moment.
This kind of approach, rough and coarse, does not allow to determine the exact value of the distance at which the speed of light is reached however, on the other hand, it allows to establish a distance of not reaching the limit, that is, values ​​of distance at which the speed of light has not yet been reached.
In case of collision between electron and positron you can find that the two particles must move closer to a minimum distance of 10-16 meters to arrive at the speed of light.
Currently the size of the electron (and the positron), while not yet been established, were estimated no more than 10-20 meters, about 10000 times smaller than the minimum distance identified by the numerical approach.
Therefore, the electron and the positron dimensions are compatible with the attainment of the speed of light, with the cancellation of the charge and therefore with the possibility of conversion to electromagnetic radiation. In fact, it is experimentally found that the collision between an electron and a positron leads to their annihilation with emission of two photons at 511keV.

A second example to be considered is constituted by the collision of an electron and a proton. Unlike the positron (and the electron), the proton is a particle with a spatial extension of the order of 10-15 meters, a value tenfold the detected distance limit (10-16 meters). This means that the electron comes in contact with the proton before reaching the speed of light. Since the electron is a much smaller particle than proton is possible that it may cross the proton without anything happening. In practice, the fact that the proton occupies a not null space (that is it has a spatial extension) distributes the electric charge and prevents the electron to be able to acquire the speed of light in case of collision.
While electron and positron have no possibility to coexist resulting in a very short time for annihilation, electron and proton can coexist indefinitely (and proof of this is given by the hydrogen atom).

A third situation is that in which a proton and an antiproton collide. In this case the exposed theory excludes the possibility that the two particles can reach the speed of light before impact giving rise to direct annihilation.
With a bit of fantasy you may provide two extreme scenarios as a result of the impact.
In the first scenario the collision could destabilize the two particles causing their decay. The decay generates smaller particles such as electrons and positrons which in turn may give rise to annihilation as already discussed above.
In the second scenario the approach of proton and positron could give rise to the formation of a stable neutral entity, formed by two particles of identical mass but opposite charge. Being a system more energetically stable than the two isolated particles, the energy balance requires the emission of energy in the form of electromagnetic radiation.

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