Stephen A. Lawrence writes > Horace Heffner wrote: There are various concepts in which charge might not be conserved.
[snip] > Since the ring is uniform, the 4-current density is not varying in time, > and we can forget about the "retarded" part. The motion of the ring > affects the spacelike parts of the integral but not the timelike part. > So, the timelike part of the 4-vector potential will be identical to the > timelike part of the 4-vector potential for a STATIONARY ring of charge. This may be adding too much complexity, but... Thinking (out loud) about "conservation of charge" and "capacitive coupling" in the context of RTSC (room temperature superconductivity) raises a nonreciprocality issue. Does the capacitive coupling from a superconductor to a normal conductor always obey all the energy conservation laws? The knee-jerk reaction is "yes, why not?"... but have all the "4-vector potentials" you mention been accounted for with RTSC as one component ? There seems to be some avenue for nonreciprocality in that instance, but it sounds like you are very much up-to-speed on these issues and may recognize why this would not work. Vortexians seem to be always looking for something new which fits into the idea of nonreciprocality : such that a source of potential energy (i.e. magnet or static field) + efficient means of modulating potential energy + nonreciprocal element = OU The "information" provided by any Maxwell's Demon type-device, of course, provides one generalized notable feature: the characteristic of classical nonreciprocality and asymmetry. Other devices like gyroscopes, Hall effect devices, Faraday effect devices, and microwave isolators are examples of classical nonreciprocality, but it has been difficult to fashion an energy device out of them, so many experimenters are thinking about the possibility of "layering" of two nonreciprocal devices. Using the magnetic vector potential may end up being one of the most inviting instance of classical nonreciprocality for the clever researcher - as it can be nonzero in regions of zero magnetic field. It may be possible to scale up this effect to a usable level by combining it with flux modulation (or flux-gating, for lack of a better term) or modulation of the capacitive coupling situation. At first glance one would say that an air coil surrounding a RTSC toroid coil which surrounds a PM magnetic core will have little interaction with either but there is such a delicate balance there that if capacitive coupling was not conserved, then any slight movement in the coil could be multiplied in two nonreciprocal ways. Either way alone might not be OU (in the sense of overcoming the parasitic losses of moving the coil (ultrasonics?), but the combination of the two might be OU (riiiiight....). ...but he beauty of the A-B effect in part of any device is that it does not depend on EM radiation, but might be able to modulate it ... or not. Jones
