This is very good progress, the vector antisymmetry equations have been solved to give the vector spin connection:
omega = (kappa / root2) (i bold – i j bold) exp i phi – i kappa k
I agree that this is the correct spin connection. I will rework the note with this spin connection and send the new calculations over to Horst. The final calculations can be used in Section 3 of UFT388, because UFT389 is on gravitation.
To: EMyrone@aol.com
Sent: 26/09/2017 01:34:17 GMT Daylight Time
Subj: Re: 389(5): The Spin Cyclic TheoremWhen using the computer, there seem to be some problems with antisymmetry eqs. (32-34). The derivative
partial A_y* / partial z
is not zero. Therefore omega_z cannot be zero in (38). The eq. (42) with
i kappa = kappa
means that kappa=0, not omega_z=0.
By computer, using A* = A(2) =
,
it follows that the equation set (32-34) is of rank 2. The solution is
with an unspecified constant r2. This looks a bit strange. Some tests led to the result thatomega =
solves the antisymm. eqs. (32-34). However with omega_z=0 it does definitely not.
The subsequent calculation gives for E and B (total fields):
There are some differences in signs with eq. (53). The B_Z component (which should be equal to B(3)) is imaginary.
Maxwell’s equations give div E=0 and div B=0 but non-vanishing current densities.
The Lindstrom constraint for phi = 0 gives
(should be zero). For phi* given by (62) the equation
follows.
It seems that some adjustments have still to be done for this note, or I misunderstood some parts.Horst
Am 24.09.2017 um 14:07 schrieb EMyrone:
This theorem defines the B(3) field as in Eq. (24) through the conjugate product of spin connection plane wave vectors. Symmetry shows that omega(3) = A(3) = 0. The vector antisymmetry equations (32) to (34) are obeyed, and the other two antisymmetry equations (46) and (47) are obeyed by using the procedure on pp. 8 and ff. of the Note. This is the best procedure to adapt in every application because it makes sure that the two antisymmetry equations (46) and (47) are obeyed simultaneously and self consistently. So B(3) theory rigorously conserves antisymmetry, as must all theories of physics. There is also a gravitational and fluid dynamical B(3) field. The ECE School of Thought has become independent of the standard model and is forging ahead with rapid advances.
