Thanks as usual for going through this note. The questions are answered as follows.
1) The complex circular basis was used:
e(1) x e(2) = ie(3)*
et cyclicum
so
e(3)* = e(3) = k = -i e(1) x e(2)
and – i appears. In eq. (1) the notation indicates any basis (Cartesian, cylindrical polar, and so on).
2) Yes A(3) is assumed to be:
A(3) = A(3)* = – i A(1) x A(2) / A(0) = A(0) k = constant
3) Yes agreed.
So the B(3) field comes out of ECE theory and this could be written up in the new textbook. Doug asked me to prepare a section on the B(3) field.
In a message dated 29/12/2013 19:14:05 GMT Standard Time, writes:
I have some points I do not understand in the note, probably due to unsufficient knowledge of B(3) theroy:
1. How did you derive the expressions in the parenthesis in eq.(12)? According to (1), these are the factors omega x A, but without an imaginary unit i, and all with equal sign. From the terms in parenthesis the conjugate complex has to be taken. This is different from multiplying by i.
2. Why is
nabla x A(3)* = 0
in eq. (13)? is A(3) assumed constant?3. in (14) it has obviously been assumed
A(1) = A(0) e(1),
A(2) = A(0) e(2).Horst
Am 25.12.2013 12:14, schrieb EMyrone
This note can be used to introduce the B(3) field in the new monograph with Doug and Horst. It shows that the B(3) field concept is rigorously self consistent, and also rigorously consistent inter alia with ECE theory. The unit vectors of the plane wave frame of reference are, self consistently, spin connections. The theory is shown to be rigorously consistent with the Cartan identity in vector format of UFT254. The frame of reference is a cyclic relation between vector spin connections, so electromagnetism is a theory of general relativity, part of the ECE unified field theory. Gravitation can be described in exactly the same way.