It seems to me that the issues being argued over in this thread are not as cut and dried as many would assume.
On the question of magnetic fields and superconductors.
Bolding mine. Noone has brought gravity into their explanations, so here it is.
The spontaneous exclusion of magnetic fields upon crossing Tc could not be explained in terms of the Maxwell equations and indeed turned out to be a non-classical phenomenon.
The essential new assumption H. and F. London made is that the bracket is not an arbitrary constant but is identical to zero.
It should be noted that this assumption cannot be justified within classical physics, even worse, in general it is wrong. For instance the current density in a normal metal will vanish when no electric field is applied, and whether a static magnetic field penetrates the metal is of no importance.
So the magnetic field does not stop abruptly at the superconductor surface but penetrates into the material with exponential attenuation. For typical material parameters the penetration depth is quite small, 20 – 50 nm. In the bulk of a thick superconductor there can be no magnetic field, which is just the Meissner- Ochsenfeld effect. Here it is appropriate to remark that in the BCS theory not single electrons but pairs of electrons are the carriers of the supercurrent. Their mass is mc = 2me, their charge -2e, their density nc = ns=2. Obviously the penetration depth remains unchanged when going from single electrons to Cooper pairs.
We have now convinced ourselves that the superconductor can tolerate a magnetic field
Superconductivity
Peter Schmuser
Institut fur Experimentalphysik der Universitat Hamburg
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Does A Uniformly Accelerating Charge Radiate?
One of the most familiar propositions of elementary classical electrodynamics is that "an accelerating charge radiates". In fact, the power (energy per time) of electromagnetic radiation emitted by a charged particle is often said to be strictly a function of the acceleration of that particle. However, if we accept the strong Equivalence Principle (i.e., the equivalence between gravity and acceleration), the simple idea that radiation is a function of acceleration becomes problematic, because in this context an object can be both stationary and accelerating. For example, a charged object at rest on the Earth's surface is stationary, and yet it's also subject to a (gravitational) acceleration of about 9.8 m/sec2. It seems safe to say (and it is evidently a matter of fact) that such an object does not radiate electromagnetic energy, at least from the point of view of co-stationary observers. If it did, we would have a perpetual source of free energy. Since the upward force holding the object in place at the Earth's surface does not act through any distance, the work done by this force is zero. Therefore, no energy is being put into the object, so if the object is radiating electromagnetic energy (and assuming the internal energy of the object remains constant) we have a violation of energy conservation.
Of course, we could question the claim that no work is being done by the force holding the object in place. Indeed if we imagine a capsule in freefall, and within that capsule an object being accelerated in such a way that it maintains a constant altitude relative to the outside gravitating source, we would say, inside the capsule, we had done work on the object as we increased its velocity relative to the capsule, even though from the outside standpoint of the gravitating source the object is stationary and no work has been done on it.
This is not too surprising, since work and kinetic energy are understood to be relative concepts, but it seems to lead to the puzzling conclusion that electromagnetic radiation must also be a relative concept. The familiar relativity of kinetic energy corresponds to the symmetry between different frames of reference, which is to say, we can always find a system of inertial coordinates with respect to which any given object (at a given instant) has zero kinetic energy. Our consideration of charged particles in a gravitational field seems to suggest similarly that we can always find a system of coordinates (at least locally) with respect to which a charged particle (at a given instant) does not radiate - even though the particle may be radiating at that instant with respect to some other system of coordinates.
It's also possible to question whether the equations of electrodynamics really do imply that an accelerating charge necessarily radiates. Surprisingly, this is still an open question for the classical theory. The difficulty is in knowing how to correctly account for the influence of a charged particle on itself. Remember that two electrons repel each other with a force (statically) proportional to the reciprocal of the square of the distance between them. This is traditionally understood in terms of each particle interacting with the field of the other particle. The intensity of each electron's field increases to infinity as the distance goes to zero (assuming point-like particles), so the force with which an electron is repelled increases to infinity as it approach the location of an electron - but therein lies a conceptual difficulty. According to this description, each electron is located in a place where there is an infinite force of repulsion against electrons!
We can try to deal with this in various ways. For example, we might simply declare that an electron does not interact with its own field, it interacts only with the fields of other particles. If we take this approach we must then explain why a charged particle resists changes in its state of motion more strongly than an uncharged particle of the same inertial mass. The traditional account of accelerated charges tell us that this "radiation reaction" force applied through the particle's motion supplies the energy that is radiated away in the form of electromagnetic waves. The origin of this force is usually taken to be the interaction of the particle with its own field. Thus if we declare that charged particles do not interact with their own fields we need a different explanation for radiation reaction. One well-known candidate is the Wheeler-Feynman absorber theory, according to which the excess resistance of a charged particle to changes in its state of motion is due to advanced waves emanating backwards in time from an all-encompassing array of absorbers in the future, whose waves are excited by the retarded waves emanating forwards in time from the particle.
We could also point out that although the force of repulsion on a charged particle from its own field is infinite, it is equally infinite in all directions, so the infinite forces cancel out, leaving no net force on the particle due to its own field - at least if the particle is in uniform motion. Then we can further suppose that the acceleration of a charged particle causes it to bias this singularity as it overtakes its own field, thereby incurring a net force. This same disturbance of the field results in radiation, so we can see the expected correlation between radiation and reaction. However, this approach leads to some highly non-intuitive conclusions. For one thing, the equation of motion based on this premise seems to imply that a uniformly accelerating charge does not radiate at all. (This is sometimes called hyperbolic motion, because the worldline of the particle is a hyperbola in spacetime, asymptotic to a particular pair of light rays.) Even more disquieting, we find that the equations of motion for a free charged particle possess "run-away" solutions, in which the particle rapidly accelerates toward the speed of light.
In effect the particle is surfing on its own field.
Whether these solutions are realistic or not is an open question, but the predicted absence of radiation for hyperbolic motion has sometimes been cited as a way of reconciling the Equivalence Principle with the fact that a charged particle held stationary in a gravitational field (and therefore undergoing constant proper acceleration) does not radiate. For example, in Feynman's "Lectures on Gravitation" he says "we have inherited a prejudice that an accelerating charge should radiate", and then he goes on to argue that the usual formula giving the power radiated by an accelerating charge as proportional to the square of the acceleration "has led us astray" because it applies only to cyclic or bounded motions.
Of course, above some frequency level, we know that the classical equations of electromagnetism are invalid, as shown by the "ultra-violet" catastrophe in cavity radiation. We must also account for the photo-electric effect and all the other familiar effects of quantum mechanics, which are incompatible with the simple wave conception of electromagnetic radiation. Nevertheless, even in the quantum theory of electrodynamics we find that the question of radiation reaction leads to difficulties, which to date have only been resolved in a somewhat ad hoc manner by means of re-normalization.
This is the basis for the claim that a uniformly accelerated charge does not radiate, because the energy of radiation presumably comes from the work done against the radiation reaction force, which is zero for motion with constant proper acceleration - at least according to the Lorentz-Dirac equation.
However, as noted previously, this equation is based on questionable assumptions, and is known to possess unphysical solutions. Perhaps the most disquieting of these are the run-away solutions.
The strangeness of these run-away solutions has led to careful re-examinations of the premises underlying the Lorentz-Dirac equation. There are subtle issues of interpretation when trying to equate the energy of radiation with the work done on a particle, not to mention the difficulty of isolating the inertial mass m from the electromagnetic mass. (For example, when asking whether a charged particle requires the same upward force to hold it stationary in a gravitational field as does an uncharged particle of the same mass, we need to carefully consider how the charge contributes to the mass of the particle.)
As a result, the Lorentz-Dirac equation does not provide a definite answer to the question of whether a uniformly accelerated charge radiates.
http://www.mathpages.com/home/kmath528/kmath528.htm
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