Thanks again, agreed about the typo. A check by computer algebra of this hand calculation would be essential, in my opinion, because things get complicated. If errors are fund by computer, the papers will be corrected and reposted. One of the important things to note is that the gradient operator is defined by Eq. (16) of Note 393(4). The basic axiom is that r is replaced by r + delta r in all physics. More generally, angles are also changed in the same way in all physics. However, for the Coulonb law and dipole fields it is sufficient to consider the replacement of r by r + delta r. This is the procedure used in the highly accurate Lamb shift theory.
To: EMyrone@aol.com
Sent: 27/11/2017 20:48:59 GMT Standard Time
Subj: Re: 393(6): Shivering Electric Dipole Field in the Presence of the VacuumIs there a typo in eq.(10) ? should it read <delta X^2> instead of <X^2> , etc. ?
I hast still to check the rest of the note.Horst
Am 22.11.2017 um 12:09 schrieb EMyrone:
This is Eq. (27) to first order in x of the binomial expansion of previous notes. The zitterbewegung theory results in a very rich structure and a completely new subject: the zitterbewegung or shivering theory of macroscopic electrodynamics in the presence of the vacuum. This theory is ideal for computer algebra because the calculations quickly become laborious. My hand calculations for UFT393 should be checked as usual by computer algebra, and graphed, when Horst returns from vacation. The effect of the vacuum is very intricate, and the vacuum is ubiquitous and ever present. Note carefully that this is the same theory as used to calculate the Lamb shift with great accuracy. So there is great confidence in the theory.