Many thanks, this looks like an interesting result, the v sub r component is a component of the Kambe vector potential, so we do not expect it to be a Coulomb potential. So it look as if all is OK.

To: EMyrone@aol.com

Sent: 29/08/2016 16:26:38 GMT Daylight Time

Subj: Re: Discussion 356(4): Spacetime Velocity Field Induced by a Static Electric FieldThe radial operator nabla_r in spherical coordinates is simply

nabla_r v_r = partial / partial r v_r,

you obviously used the term from the divergence in eq. (4). After my calculation, I am obtaining a simpler result for (v*grad)v. I used the scalar product

[v_r,

v_theta, v_phi] * [nabla_r, nabla_theta, nabla_phi]with the original gradient operator of spherical coordinates. This then gives the result v_r ~ sqrt(1/r) for the potential.

Inserting the terms of the div operator gives the following result v_r for a potential having only an r component, i.e. v_r(r), v_theta=0, v_phi=0:This has two terms of order r and 1/r. Unfortunately the integration constant %c is not in front of the r term so that this result is not the Coulomb potential. Details see in the attachment, see also the calculation for note 356(5).

Horst

Am 29.08.2016 um 09:22 schrieb EMyrone:

The expression for the divergence in spherical polar coordinates is the same from this Harvard site and VAPS, so that is a useful check. so Eqs. (1) to (8) of the note have been checked as correct. This means that Eqs. (9) to (15) of the note are correct. The protocol also seems to be correct.

To: EMyrone

Sent: 28/08/2016 20:44:22 GMT Daylight Time

Subj: Re: 356(4): Spacetime Velocity Field Induced by a Static Electric FieldThe divergence and gradient terms in spherical coordinates are different, see

http://isites.harvard.edu/fs/docs/icb.topic970148.files/Spherical_coord.pdfThe (v*grad) v term then reads for two arbitrary vector functions a and b:

(a*grad) b =

The diff. eqs. with full angular dependenced are o11-o13 in the protocol. For pure r dependence, the results are o15-o17.

This gives constant solutions for v[theta] and v[phi]. These will only be different from zero if a constant background potential is considered, for example an overlay of constant aether flow.

The solution for component v[r] is o20/o21. For %c=0, this is of type 1/sqrt(r), not of 1/r as expected. This needs to be clarified.Horst

Am 27.08.2016 um 12:55 schrieb EMyrone:

In spherical polar coordinates this is found by solving Eqs. (13) to (15) simultaneously. In general, the velocity field has a very interesting structure in three dimensions. The simultaneous numerical solution of Eqs. (13) to (15) also gives the spacetime velocity field set up by a static gravitational field g (the acceleration due to gravity). This entirely original type of velocity field exists in a spacetime defined as a fluid. The spacetime can also be called an “aether”, or “vacuum”. Any boundary conditions can be used. A magnetic and gravitomagnetic field also set up aether velocity fields.