Many thanks. The computer algebra and discussions for this note were very useful. Conservation of antisymmetry in ECE2 magnetostatics implies the vacuum current density:
J (vac) = curl (omega x A) / mu0
The material current density is
J = curl (curl A) / mu0
and both exist on the ECE2 level. A two dimensional analysis can always be made. So I will proceed to writing up Sections 1 and 2 of UFT386.
To: EMyrone@aol.com
Sent: 29/08/2017 17:48:24 GMT Daylight Time
Subj: Re: 386(9): Rigorous General Solution for ECE2 MagnetostaticsThis is a very clear description of the general implications of antisymmetry. We can comment that the general solution (4-6) requires all components of A to be different from zero. In our examples this is not the case, therefore we had to make special assumptions on omega x A.
The special example 3 for A which I found (constant field B=B0) is of the general form. The total charge density nabla x B is zero, but the constitutents from nabla x A and omega x A are not. This is an example for the vacuum current density. To my understanding it is counter-acted by a “real” charge density. So the total charge density is always a sum of both terms. Can we conclude this in general?Horst
Am 29.08.2017 um 15:13 schrieb EMyrone:
This procedure uses the unique solution (4) to (6) of the vector antisymmetry equations (1) to (3). This is an exactly determined problem. The solution (4) to (6) was found by co author Horst Eckardt using computer algebra. If more equations are added to the set of three equations (1) to (3) there is no solution because the problem becomes over determined. Horst and I discussed this point and are agreed. The ECE2 equations of magnetostatics are eqs. (7) to (10). So the well known material vector potential A may be found for any material current density using Eq. (10). In general this must be done by computer, but there are well known analytical solutions such as the circular current loop and magnetized sphere. Having found A, the vector spin connection is found from Eqs. (4) to (6), so omega x A can be calculated for any material J. Conservation of antisymmetry combined with del B = 0 implies that there exists a spacetime, vacuum or aether current density J(vac) defined by Eq. (17). So J(vac) can be computed from Eq. (17). The vacuum current density contributes to the total magnetic flux density B through Eq. (14), so a magnetic flux density is induced in material matter by spacetime, Q. E. D. Similarly, an electric field strength is induced by spacetime in the patented and replicated Ide circuit and the new circuits of UFT382 and UFT383 (UFT311, UFT321, UFT364, UFT382, UFT383), QED. I will now write up UFT386. In the standard model the spin connection does not exist and there is no vacuum current density, contrary to observation. Therefore given any material current density, the vacuum current density can be computed. The latter induces an extra magnetic flux density not present in the standard model (Maxwell Heaviside theory). A similar theory can be developed for ECE2 electrostatics as in immediately preceding UFT papers and notes. From Eq. (17) the vector spin connection is the link between the material vector potential A and the vacuum current density.