This is the check by hand, giving the same answer r <delta r dot delta r>. It is certainly worth writing a program to code in the isotropy rules exemplified in this note, and recheck this hand calculation with Maxima. The program could then be used for the magnetic dipole field and so on. Gradually the program could be extended for all of electrodynamics and indeed all of physics, with angular as well as linear fluctuations. Vacuum maps or spin connections of all kinds can be computed for any problem in physics.

In a message dated 28/11/2017 10:28:13 GMT Standard Time, writes:

When setting linear, orthogonal and cross correlation to zero, and restricting to second order terms, my calculation of eq.(7) gives the result for the X component:

This is not a multiple of <delta r * delta r> because the factor 3 appears only in front of one term. Could you please check this?

Horst

Am 28.11.2017 um 10:23 schrieb EMyrone:

Thanks again for checking with computer algebra. The terms set to zero are defined by Eq. (6), which is the assumption that orthogonal correlations are not correlated in an isotropic ensemble. The cross correlation functions (see Omnia Opera) are zero, the autocorrelation functions are not zero. Agreed that there should be no factor 3, because

<delta X squared + delta Y squared + delta Z squared)> = <delta r squared>

So the factor 3 should be removed from the right hand side of Eq. (36) and the factor 9 in Eq. (37) replaced by 3. I will repost the paper to make this entirely clear.

To: EMyrone

Sent: 27/11/2017 20:05:51 GMT Standard Time

Subj: Re: 393(5): Effect of the Vacuum on the Dipole PotentialConcerning eq.(7), which terms did you set to zero? Did you neglect terms of third order in delta X ?. There are terms like

<Z*delta X*delta Z>

and

<X*Z*delta Z>.Do these terms vanish too although they are not of type <delta Z> or <delta X * delta Z> ?

The last line of the protocol is the X component of (7). I do not see a factor of 3.Horst

Am 20.11.2017 um 13:16 schrieb EMyrone:

Using the zitterbewegung theory to first order in x of note 393(4), the effect of the vacuum on the well known dipole potential of electrostatics is to change it to Eq. (8) from Eq. (9). The dipole potential actually obseved is always the dipole potential in the presence of the vacuum, Eq. (8). This is shown conclusively by the radiative corrections, which are always present, and which are accurately observable as is well known. So the entire subject of electrodynamics can now be developed correctly with consideration of the vacuum. The same is true for gravitation. fluid dynamics and indeed, all of physics and engineering, unified by ECE2 generally covariant field theory. It would be very interesting to graph and compare Eqs. (8) and (9). In the first instance the mean square displacement can be used simply as an input parameter. In future work it can be calculated or computed in various ways, as in earlier notes for UFT393. There is no reasonable doubt that the vacuum (or aether or spacetime) contains a source of inexhaustible, safe and clean energy. This source can be used in patented and replicated circuits such as those of UFT311, UFT364, UFT382, and UFT383. This has been known since the Lamb shift was discovered in the mid forties. The zitterbewegung theory used to explain the Lamb shift conserves total energy momentum, and total charge / current density. Now it is known that it must also conserve antisymmetry. All schools of thought can accept this theory. It is the simple and straightforward extension of Lamb shift theory to macroscopic electrodynamics.