Peter,
In regards to:
"A whole tranche of anomalies and paradoxes may be resolved by more precisely matching the mathematical description to the underlying physical 'mechanism' of Maxwell's near / far field transition (which includes deriving the 'LT' non-linearity). The SR postulates re-emerge with a more complete specification and explanation."
I do not think that any "fundamental" mathematical description of such anomalies is possible. As described in my 2012 FQXI essay, concise sets of equations are almost devoid of information. Consequently, they can never describe phenomenon that are not similarly devoid of information.
Maxwell's equations for electrodynamics, the equations of hydrodynamics, thermodynamics etc, are all secondary, rather than fundamental laws; they describe statistical behaviors of large sets of "initial conditions", too large to deal with individually at a more fundamental level. In other words, they are an amalgam of the information content of more fundamental laws, together with gross characterizations of the information content of the myriad, specific initial conditions.
For example,
I am in orbit around the sun. But Einstein's equations are never going to describe my exact orbit, to the same precision it can describe the orbit of the earth's center of mass.
The motions of waves on the surface of the ocean can be described by the equations of hydrodynamics. But near the shore, where wave height becomes comparable to water depth, non-linearities set in and the equations are no longer accurate. But this is not a failure of any fundamental law; no attempt was ever made to track the motion of each and every water molecule, much less all the atoms making up those molecules.
And when a high intensity sound wave drastically heats the air as it passes through it, and thereby changes it's propagation characteristics, again, it is not the failing of any fundamental principle, anymore than a baseball, encountering air-resistance, and thus not following a Newton's law derived parabolic path, represents a failure of Newton's law.
In all these cases, a "short-cut" was taken, to avoid the obstacles of having to deal with high-infomation-content initial-conditions. But it is not the fault of the fundamental laws, that a such a short-cut was attempted and then went astray.
Einstein said that light, traveling down an empty highway, can go at cruise-control at a constant speed. He never said it could do the same during rush-hour, with roads packed with free-electron pot-holes and deep gravitational mud covering the surface.
Rob McEachern
