the magnetic field around any particle is actually comprised of virtual photons, which do not obey planck time. the further you get from them, the weaker the photon force is, which is also what explains the attraction and repulsion of charged particles.
anyway, with respect to the OP, this is an area i know a lot about so let me try to help.
special relativity has two postulates for its foundation. 1) all the laws of physics have the same form in all inertial reference frames and 2) the speed of light in a vacuum has the same value in all inertial frames, regardless of the velocity of the observer or the velocity of the source emitting the light.
based on this, we can conclude the following. from postulate 1, we can assert that all laws of physics (elecricity and magnetism, thermodynamics, optics, etc.) will have the same mathematical form or are covariant in all coordinate frames moving with constant velocity relative to one another. this, experimentally and theoretically, also shows that no absolute reference frame can be determined.
from postulate 2, the principle of the constancy of the speed of light, is consistent with postulate 1. if the speed of light was variant depending on your frame of reference, it would be possible to establish a single, preferred, absolute frame of reference, which would be in contradiction to postulate 1.
now, based on that, you must conclude that there is no absolute length or time in relativity. it is all a function of the reference frame. also, simultaneity and the relativity of time will influence how you preceive a magnetic field to be affecting something in another frame. like i mentioned before, charged particles are actually playing catch with virtual photons, and because virtual photons do not obey the uncertainty principle or planck time, they only exist in less than h-bar/2 time, so the force and acceleration felt by objects in their frame of reference is immediate but dependant upon the relative velocity.
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