I got this formula from Marion and Thornton, third edition, page 567. That page gives the general formula as Eq. (D.1) and some examples with non integral n in (D.4) to (D.8). I cross checked by looking up binomial expansion with Google. The formula used by Marion and Thornton was first derived by Isaac Newton in 1665 at home in Woolsthorpe Manor when Cambridge was closed because of plague. It is an infinite term series and I used it with n = – 3/2 and n = – 5/2.

To: EMyrone@aol.com
Sent: 28/11/2017 10:14:48 GMT Standard Time
Subj: Re: Discussion of 393(3)

I guess that this formula only holds for integer exponents, but anyway, you used a power series expansion in the other notes.

Horst

Am 28.11.2017 um 09:51 schrieb EMyrone:

Welcome back! I used Eq. (D.1) of the third edition of Marion and Thornton:

(1 + x) power n = 1 + nx + n(n-1) x squared / 2! + ……..

with n = – 3/2 and n = – 5/2. I agree that angular shivering will occur in atoms and molecules as well as radial shivering, leading to many new possibilities.

To: EMyrone
Sent: 27/11/2017 16:23:48 GMT Standard Time
Subj: Re: 393(3): Zitterbewegung and Dipole Fields

The shivering is restricted to the radial coordinate in (4). An angular shivering would also be possible, it is respected in the”real” dipole (12) or (25), respectively.
The Taylor expansion of (1+x)^(-3) in eq. (7) gives according to Maxima:

and as powerseries:

which is the same result. You seem to have used different results in (7) but these are not further used.
Horst

Am 17.11.2017 um 15:16 schrieb EMyrone:

This is a first calculation of the effect of the vacuum in inducing zitterbewegung in a dipole field. The two macroscopic charges of a dipole moment shiver due to the presence of the vacuum. In the next note I will refine this first calculation by going back to the basic definition of a dipole moment in which each charge shivers, and calculating the dipole potential and field. Zitterbewegung of macroscopic charges is a completely new idea and works its way into the whole of classical electrodynamics. The overall aim here is to calculate the spin connection and to apply the conservation of antisymmetry. These ideas go far beyond the standard model. In general the dipole, quadrupole and octopole moments of a molecule all shiver in the presence of the vacuum. These effects can all be expressed in terms of spin connections (or vacuum maps). The Lamb shift shows clearly that they exist in the H atom so they exist in all material matter, namely circuits.

The equivalent of 223,553 printed pages was downloaded (815.076 megabytes) from 3,211 downloaded memory files (hits) and 633 printed pages each averaging 3.8 memory pages and 9 minutes, printed pages to hits ratio of 69.62, top referrals total 2,333,615, main spiders Baidu, Google, MSN and Yahoo. Collected ECE2 3121, Top ten 1308, Collected Evans / Morris 891(est), Collected scientometrics 580, F3(Sp) 375, Principles of ECE 286, Barddoniaeth / Collected Poetry 264, Collected Eckardt / Lindstrom 249, Autobiography volumes one and two 170, UFT88 161, Evans Equations 119, Collected Proofs 117, Engineering Model 84, CV 71, PECE 66, UFT311 61, CEFE 54, PLENR 48, UFT321 43, 83Ref 36, SCI 34, PECE2 32, Llais 29, ADD 24, UFT313 37, UFT314 38, UFT315 50, UFT316 25, UFT317 34, UFT318 39, UFT319 58, UFT320 48, UFT322 38, UFT323 39, UFT324 65, UFT325 52, UFT326 35, UFT327 44, UFT328 47, UFT329 43, UFT330 34, UFT331 50, UFT332 52, UFT333 24, UFT334 19, UFT335 41, UFT336 41, UFT337 21, UFT338 31, UFT339 33, UFT340 31, UFT341 36, UFT342 31, UFT343 34, UFT344 20, UFT345 50, UFT346 43, UFT347 40, UFT348 50, UFT349 34, UFT351 50, UFT352 42, UFT353 48, UFT354 52, UFT355 33, UFT356 34, UFT357 30, UFT358 48, UFT359 29, UFT360 22, UFT361 20, UFT362 27, UFT363 30, UTF364 39, UFT365 34, UFT366 32, UFT367 51, UFT368 29, UFT369 40, UFT370 27, UFT371 21, UTF372 24, UFT373 25, UFT374 24, UFT375 19, UFT376 19, UFT377 33, UFT378 24, UFT379 18, UFT380 27, UFT381 35, UFT382 55, UFT383 57, UFT384 30, UFT385 44, UFT386 35, UFT387 39, UFT388 36, UFT389 61, UFT390 48, UFT391 61, UFT392 51, UFT393 11 to date in November 2017. University of Quebec Trois Rivieres UFT373 – UFT393; Students Charles University Prague UFT213; University of Hawaii at Manoa AIAS Fellows; Worcester Polytechnic Institute UFT33; Izmir Institute of Technology Turkey UFT175; Physics Imperial College London UFT99; University of Southampton UFT2; University College Swansea extensive reading of historical items. Intense interest all sectors, updated usage file attached for November 2017.

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I will continue discussions of UFT393 tomorrow. The macroscopic zitterbewegung theory looks very promising.

This note applies conservation of scalar and vector antisymmetry to the shivering electric and magnetic dipole fields. In the given approximations the mean eletric dipole spin connections are given by Eqs. (16) and (17) and the mean magnetic dipole spin connections by Eqs. (34) and (35). They are both directly proportional to the mean square fluctuations in the vacuum. So there is a close similarity with Lamb shift theory.

a394thpapernotes2.pdf

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 Vacuum

Is 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.

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@aol.com
Sent: 27/11/2017 20:05:51 GMT Standard Time
Subj: Re: 393(5): Effect of the Vacuum on the Dipole Potential

Concerning 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.

393(3-6).pdf

OK thanks for checking.

To: EMyrone@aol.com
Sent: 27/11/2017 20:00:31 GMT Standard Time
Subj: Re: 393(4): Shivering Dipole Potential and Field due to the Vacuum

There seem to be typos in the second line of (7) but the result (8) is correct as are the other calculations.

Horst

Am 19.11.2017 um 11:33 schrieb EMyrone:

The basic law (11) for the effect of the vacuum on any equation of physics is applied to the well known dipole potential and field. The shivering potential in the presence of the vacuum is given by Eq. (22) and the shivering electric field strength due to the dipole is given by Eq. (24). A new fundamental law of physics is exemplified by Eq. (29), which shows that the effect of the vacuum is maximized by maximizing the ensemble averaged vector spin connection. Any measured electric field strength E in volts per metre always measures the spin connection vector according to Eq. (29), because all material matter such as a circuit is always in contact with the vacuum. Using binomial expansion teh dipole potential and field are given by Eqs. (39) and (40). In the next note these will be ensemble averaged. it becomes as clear as a diamond that thee is ubiquitous energy in the vacuum. Circuits are being developed by AIAS / UPITEC to use this energy, initiating Bannister’s second industrial revolution (Steve Bannister, Ph. D. Thesis, University of Utah, on www.aias.us). Note carefully that the fundamental law (11) is well tested in the theory of the Lamb shift in H. Now it is being applied to the whole of physics as part of ECE2 generally covariant unified field theory. The standard Maxwell Heaviside theory has no explanation for vacuum effects, and has no spin connection. So ECE2 is preferred to the standard theory on the basis of experimental data (Lamb shift and other effects listed on www.aias.us). This is an example of Baconian science.

Welcome back! I used Eq. (D.1) of the third edition of Marion and Thornton:

(1 + x) power n = 1 + nx + n(n-1) x squared / 2! + ……..

with n = – 3/2 and n = – 5/2. I agree that angular shivering will occur in atoms and molecules as well as radial shivering, leading to many new possibilities.

To: EMyrone@aol.com
Sent: 27/11/2017 16:23:48 GMT Standard Time
Subj: Re: 393(3): Zitterbewegung and Dipole Fields

The shivering is restricted to the radial coordinate in (4). An angular shivering would also be possible, it is respected in the”real” dipole (12) or (25), respectively.
The Taylor expansion of (1+x)^(-3) in eq. (7) gives according to Maxima:

and as powerseries:

which is the same result. You seem to have used different results in (7) but these are not further used.
Horst

Am 17.11.2017 um 15:16 schrieb EMyrone:

This is a first calculation of the effect of the vacuum in inducing zitterbewegung in a dipole field. The two macroscopic charges of a dipole moment shiver due to the presence of the vacuum. In the next note I will refine this first calculation by going back to the basic definition of a dipole moment in which each charge shivers, and calculating the dipole potential and field. Zitterbewegung of macroscopic charges is a completely new idea and works its way into the whole of classical electrodynamics. The overall aim here is to calculate the spin connection and to apply the conservation of antisymmetry. These ideas go far beyond the standard model. In general the dipole, quadrupole and octopole moments of a molecule all shiver in the presence of the vacuum. These effects can all be expressed in terms of spin connections (or vacuum maps). The Lamb shift shows clearly that they exist in the H atom so they exist in all material matter, namely circuits.

The equivalent of 102,329 printed pages was downloaded (373.093 megabytes) from 2,635 downloaded memory files (hits) and 566 distinct visits each averaging 3.2 memory pages and 6 minutes, printed pages to hits ratio of 38.83, top referrals total 2,333,397, main spiders Baidu, Google, MSN and Yahoo. Collected ECE2 2671, Top ten 1275, Collected Evans / Morris 858(est), Collected scientometrics 555, F3(Sp) 364, Principles of ECE 276, Collected Eckardt / Lindstrom 234, Barddoniaeth / Collected poetry 212, Autobiography volumes one and two 167, UFT88 145, Collected Proofs 114, Evans Equations 111, Engineering Model 82, PECE 61, UFT311 59, CEFE 53, PLENR 46, UFT321 41, 83Ref 35, SCI 33, PECE2 32, Llais 28, ADD 23, UFT313 36, UFT314 36, UFT315 45, UFT316 22, UFT317 34, UFT318 38, UFT319 56, UFT320 46, UFT322 37, UFT323 35, UFT324 64, UFT325 51, UFT326 32, UFT327 43, UFT328 44, UFT329 41, UFT330 34, UFT331 49, UFT332 50, UFT333 24, UFT334 19, UFT335 40, UFT336 38, UFT337 21, UFT338 31, UFT339 32, UFT340 31, UFT341 35, UFT342 29, UFT343 31, UFT344 20, UFT345 49, UFT346 42, UFT347 38, UFT348 48, UFT349 33, UFT351 50, UFT352 41, UFT353 47, UFT354 49, UFT355 33, UFT356 34, UFT357 29, UFT358 47, UFT359 28, UFT360 22, UFT361 19, UFT362 27, UFT363 29, UFT364 38, UFT365 34, UFT366 32, UFT367 49, UFT368 27, UFT369 40, UFT370 27, UFT371 21, UFT372 24, UFT373 22, UFT374 22, UFT375 17, UFT376 17, UFT377 29, UFT378 20, UFT379 16, UFT380 25, UFT381 33, UFT382 53, UFT383 55, UFT384 27, UFT385 42, UFT386 33, UFT387 36, UFT388 34, UFT389 59, UFT390 44, UFT391 58, UFT392 49, UFT393 8 to date in November 2017. Swiss Federal Institute Zuerich (ETH) Diplomatic Objection to ‘t Hooft; University of Regensburg Diplomatic Objection to ‘t Hooft; Edu system Pakistan general; University of Edinburgh UFT177. Intense interest all sectors, updated usage file attached for November 2017.

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The equivalent of 196,009 printed pages was downloaded (714.647 megabytes) from 3,200 downloaded memory files (hits) and 618 distinct visits each averaging 4.2 memory pages and 8 minutes, printed pages to hits ratio of 61.25, main spiders Baidu, Google, MSN and Yahoo. Collected ECE2 2775, Top ten 1311, Collected Evans / Morris 825(est); Collected scientometrics 542, F3(Sp) 355, Principles of ECE 269, Barddoniaeth / Collected Poetry 260; Collected Eckardt / Lindstrom 228, Autobiography volumes one and two 164, UFT88 140, Collected Proofs 112, Evans Equations 110, Engineering Model 79, MJE 70, CV 67, PECE 60, UFT311 59, PECE 60, CEFE 52, PLENR 46, UFT321 40, 83Ref 34, PECE2 31, Llais 27, ADD 23, UFT313 36, UFT314 35, UFT315 45, UFT316 22, UFT317 34, UFT318 38, UFT319 56, UFT320 46, UFT322 37, UFT323 33, UFT324 63, UFT325 53, UFT326 32, UFT327 42, UFT328 44, UFT329 51, UFT330 34, UFT331 49, UFT332 50, UFT333 24, UFT334 19, UFT335 40, UFT336 38, UFT337 21, UFT338 31, UFT339 32, UFT340 31, UFT341 34, UFT342 29, UFT343 31, UFT344 31, UFT345 49, UFT346 43, UFT347 37, UFT348 47, UFT349 33, UFT351 49, UFT352 41, UFT353 46, UFT354 48, UFT355 33, UFT356 34, UFT357 29, UFT358 47, UFT359 28, UFT360 22, UFT361 19, UFT362 27, UFT363 29, UFT364 37, UFT365 31, UFT366 31, UFT367 48, UFT368 27, UFT369 40, UFT370 27, UFT371 21, UFT372 24, UFT373 22, UFT374 22, UFT375 17, UFT376 17, UFT377 29, UFT378 20, UFT379 16, UFT380 25, UFT381 32, UFT382 52, UFT383 54, UFT384 26, UFT385 42, UFT386 33, UFT387 36, UFT388 34, UFT389 58, UFT390 44, UFT391 57, UFT392 47, UFT393 7 to date in November 2017. Borromaeum University of Basel general; University of Stirling Etherington Report. Intense interest all sectors, updated usage file attached for November 2017.

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