Discussion of Note 381(1)

Thanks again! This is true, so omega sub Z must be complex valued, its real part is given by Eq. (36), and its imaginary part by Eq. (37). The usual rule is that the physical part of omega sub Z is its real part. Alternatively one could work out the modulus of the complex spin connection omega sub Z. Similarly, the physical part of a plane wave is its real part. These remarks can go into the final Sections 1 and 2 as usual.

To: EMyrone@aol.com
Sent: 13/07/2017 20:04:43 GMT Daylight Time
Subj: The problem for plane waves (note 381(1))

The problem obviously is that with

omega_Z = 0

it follows from (36,37) that

partial A_X / partial Z = 0
partial A_Y / partial Z = 0

This is not the case with the definition of A in form of eq.(35) or
similar. The first and second antisymmetry relation is not fulfilled,
even when taking only the real parts.

Another point: if the relation (41),

bold omega = factor * bold A*

is true, the exponential factor must change sign in omega and the term
omega x A has an (imaginary) Z component. Consequently one would have
to take this expression for B to check the field equations (13-16).

I will do some more checks. There is still a change in the unit vectors
for A and omega necessary.


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