Examine a single point charge and we see that the spherical scalar potential emission, expands with r = @t, where @ is the universal constant speed of potential fields. This is the most fundamental linkage of time and space.
The spatial position when v = 0 is a link to Euclidean time and space. In other words there really is an absolute frame where a unit potential has no velocity. This is presumably a rarely transited state. Still it is an essential concept towards understanding nature. It is a natural frame of reference.
Let’s examine the cases.
v = 0. This is electrostatics. The charge is not moving relative to its path history. This is a very unphysical and highly unlikely to achieve true v = 0, but given the speed @, even low velocity behaves essentially like v = 0 in terms of experimental observation.
There is an absolute reference frame relative to each unit potential. If its true velocity were 0 meaning 0 relative to the absolute frame, then the unit potential would present no second gradient to the potential field and therefore no magnetism. This is because with velocity = 0, the unit potential is not a current. With v > 0 there is a current and therefore a magnetic field.
v < @. The point charge never encounters its own Dirac spheres. It stays within those bubbles.
v = @. This is the symmetry breaking point. Is it possible to hold a point charge at v = @ due to action from other point charges? Is it a chaos generator? Does no self action take place when r = 0? I don’t know. I wonder if the middle point charge in a Noether core is somehow balanced near v = @, but that may be imagination over-reach.
v > @. This is the case where the point charge is outside its newly generated Dirac spheres. The point charge is exploring it’s Dirac sphere history at this velocity. Since like charges repel, it would seem that this would cause the point charge to be accelerated away from its own historical path if it were in isolation. However, it is not in isolation, as there are other point charges, including the ones that performed work to cause velocity to exceed @.
Truly this appears to be an unexplored dynamical geometry. A blank canvas. A new way to imagine nature as networks of electrino and positrino unit potentials. Thought experiment, geometry, and simulation are essential.
J Mark Morris : Boston : Massachusetts