Many thanks to Doug Lindstrom. The calculation and computation just sent over by passes the Dirac delta function and calculates the vacuum correction. So this new method can be used in quantum mechanics and in NMR theory

Sent: 15/12/2017 15:17:26 GMT Standard Time
Subj: Re: Discussion of 394(7)

Mathematica gives an identical result Doug

On Dec 15, 2017, at 4:58 AM, EMyrone wrote:

Thanks, this is why the Dirac delta function is needed. Can Maxima derive the result:

del squared (1 / r) = – 4 pi delta sub D (r)

where delta sub D (r) is the Dirac delta function? There are many formulae on the net for the Dirac delta function, and in each formula r can be replaced by r plus delta r

To: EMyrone
Sent: 15/12/2017 11:21:25 GMT Standard Time
Subj: Re: 394(7): Shivering of the Contact Term

Computer algebra gives that the contact term vanishes because of

nabla^2 (1/r) = 0.

As can be seen from the protocol, all terms cancel out.

Horst

Am 14.12.2017 um 15:37 schrieb EMyrone:

The contact term in NMR is shown to have a similar structure to that of the magnetic dipole field. This is not apparent from its usual representation as a Dirac delta function, Eq. (2). The effect of the vacuum on the contact field is given by Eq. (17). This seems to be a new insight to the contact field. The vacuum will affect the hyperfine spin spin structure of NMR. There are many ways of representing the Dirac delta function in mathematics, and each method can be corrected for the vacuum shivering. That will lead to a lot of interesting graphics. Dirac’s original idea of a delta function was dismissed outright by mathematicians as complete nonsense, despite its success in physics. The mathematicians later developed theories for the Dirac delta function that showed its deeply insightful nature. As Horst and I have shown in various UFT papers on the Dirac equation, he was not bothered very much about the finer points of mathematics if the physics emerged in a way that made sense. This is OK as far as it goes, but as we have shown, Dirac missed a lot of physics and a lot of people went on missing it for almost a hundred years because they just followed Dirac.

<394(7).pdf><394(7).wxm>

verify.pdf

This is a very interesting result, and is the ensemble averaged magnetic flux density responsible for hyperfine spin spin interaction in NMR. The graphics will be very interesting. There is already a great deal of interest in UFT393 as the daily report shows.

394(8).pdf

OK thanks, I sent over the calculation of the contact term in our theory, it is much more elegant than the use of the Dirac delta function. As you infer, the vacuum results in a non zero contact term.

To: EMyrone@aol.com
Sent: 15/12/2017 12:08:35 GMT Standard Time
Subj: Re: Discussion of 394(7)

The delta function in Maxima is only known as an input function for a Laplace transformation. It cannot be used for general calculations.

Horst

Am 15.12.2017 um 12:58 schrieb EMyrone:

Thanks, this is why the Dirac delta function is needed. Can Maxima derive the result:

del squared (1 / r) = – 4 pi delta sub D (r)

where delta sub D (r) is the Dirac delta function? There are many formulae on the net for the Dirac delta function, and in each formula r can be replaced by r plus delta r

To: EMyrone
Sent: 15/12/2017 11:21:25 GMT Standard Time
Subj: Re: 394(7): Shivering of the Contact Term

Computer algebra gives that the contact term vanishes because of

nabla^2 (1/r) = 0.

As can be seen from the protocol, all terms cancel out.

Horst

Am 14.12.2017 um 15:37 schrieb EMyrone:

The contact term in NMR is shown to have a similar structure to that of the magnetic dipole field. This is not apparent from its usual representation as a Dirac delta function, Eq. (2). The effect of the vacuum on the contact field is given by Eq. (17). This seems to be a new insight to the contact field. The vacuum will affect the hyperfine spin spin structure of NMR. There are many ways of representing the Dirac delta function in mathematics, and each method can be corrected for the vacuum shivering. That will lead to a lot of interesting graphics. Dirac’s original idea of a delta function was dismissed outright by mathematicians as complete nonsense, despite its success in physics. The mathematicians later developed theories for the Dirac delta function that showed its deeply insightful nature. As Horst and I have shown in various UFT papers on the Dirac equation, he was not bothered very much about the finer points of mathematics if the physics emerged in a way that made sense. This is OK as far as it goes, but as we have shown, Dirac missed a lot of physics and a lot of people went on missing it for almost a hundred years because they just followed Dirac.

The effect is given by Eq. (10), whose isotopic average can be worked out to any order in x using the methods of UFT393. The isotopic average gives the contact magnetic flux density in Eq. (11), used in hyperfine spin spin splitting in NMR. in the absence of the vacuum the contact term is zero as in Eq. (2). In the standard model this result is ignored, and replaced by the Dirac delta function as in Eq. (3). This is why mathematicians contemporary to Dirac thought that the physicists were indulging in total nonsense, until a new kind of mathematics of the Dirac delta function was developed. This can become formidably abstract and complicated, things that we seek to avoid in ECE theory. There are now many theories of the Dirac delta function, but I think that our new MZ theory, in which the vacuum induces shivering of the coordinate system, is much more elegant than the use of the Dirac delta function. Thanks to Horst for suggesting the method of this note. In the standard model there is a fundamental contradiction between Eqs. (2) and (3). In ECE2 there is no contradiction.

a394thpapernotes8.pdf

This is a very good idea, and I will sketch out the calculation by hand and send over to you to use Maxima

To: EMyrone@aol.com
Sent: 15/12/2017 11:29:42 GMT Standard Time
Subj: Re: 394(7): Shivering of the Contact Term

PS: perhaps the delta r terms can give a different result for shivering.

Am 15.12.2017 um 12:19 schrieb Horst Eckardt:

Computer algebra gives that the contact term vanishes because of

nabla^2 (1/r) = 0.

As can be seen from the protocol, all terms cancel out.

Horst

Am 14.12.2017 um 15:37 schrieb EMyrone:

The contact term in NMR is shown to have a similar structure to that of the magnetic dipole field. This is not apparent from its usual representation as a Dirac delta function, Eq. (2). The effect of the vacuum on the contact field is given by Eq. (17). This seems to be a new insight to the contact field. The vacuum will affect the hyperfine spin spin structure of NMR. There are many ways of representing the Dirac delta function in mathematics, and each method can be corrected for the vacuum shivering. That will lead to a lot of interesting graphics. Dirac’s original idea of a delta function was dismissed outright by mathematicians as complete nonsense, despite its success in physics. The mathematicians later developed theories for the Dirac delta function that showed its deeply insightful nature. As Horst and I have shown in various UFT papers on the Dirac equation, he was not bothered very much about the finer points of mathematics if the physics emerged in a way that made sense. This is OK as far as it goes, but as we have shown, Dirac missed a lot of physics and a lot of people went on missing it for almost a hundred years because they just followed Dirac.

Thanks, this is why the Dirac delta function is needed. Can Maxima derive the result:

del squared (1 / r) = – 4 pi delta sub D (r)

where delta sub D (r) is the Dirac delta function? There are many formulae on the net for the Dirac delta function, and in each formula r can be replaced by r plus delta r

To: EMyrone@aol.com
Sent: 15/12/2017 11:21:25 GMT Standard Time
Subj: Re: 394(7): Shivering of the Contact Term

Computer algebra gives that the contact term vanishes because of

nabla^2 (1/r) = 0.

As can be seen from the protocol, all terms cancel out.

Horst

Am 14.12.2017 um 15:37 schrieb EMyrone:

The contact term in NMR is shown to have a similar structure to that of the magnetic dipole field. This is not apparent from its usual representation as a Dirac delta function, Eq. (2). The effect of the vacuum on the contact field is given by Eq. (17). This seems to be a new insight to the contact field. The vacuum will affect the hyperfine spin spin structure of NMR. There are many ways of representing the Dirac delta function in mathematics, and each method can be corrected for the vacuum shivering. That will lead to a lot of interesting graphics. Dirac’s original idea of a delta function was dismissed outright by mathematicians as complete nonsense, despite its success in physics. The mathematicians later developed theories for the Dirac delta function that showed its deeply insightful nature. As Horst and I have shown in various UFT papers on the Dirac equation, he was not bothered very much about the finer points of mathematics if the physics emerged in a way that made sense. This is OK as far as it goes, but as we have shown, Dirac missed a lot of physics and a lot of people went on missing it for almost a hundred years because they just followed Dirac.

394(7).pdf

Agreed, there is already a lot of interest in UFT393. It is worth graphing the results for the magnetic dipole potential in the presence of the vacuum, using as many x terms as needed. The Dirac delta function enters into the contact term, and I think it is better to directly differentiate rather than use a singularity. I plan to do this next.

To: EMyrone@aol.com
Sent: 14/12/2017 09:43:00 GMT Standard Time
Subj: Re: 394(6a): Vacuum Corrections for the Magnetic Dipole Potential and Field

The vacuum corrections of the magnetic dipole field are the same as for the electric dipole because the mathematics is the same. So the graphics of UFT 393 apply. The contact term will give new aspects.

Horst

Am 13.12.2017 um 15:17 schrieb EMyrone:

These will lead to new structure as in previous work, and using Horst’s algorithm they can be worked out to any order in x. The next and final note for UFT394 will evaluate the vacuum correction for the contact term used in hyperfine spin spin splitting theory. Therefore the effect of the vacuum is observable in theory. The general postulate is introduced that in any equation of physics the effect of the vacuum is calculated by replacing r by r + delta r.

These will lead to new structure as in previous work, and using Horst’s algorithm they can be worked out to any order in x. The next and final note for UFT394 will evaluate the vacuum correction for the contact term used in hyperfine spin spin splitting theory. Therefore the effect of the vacuum is observable in theory. The general postulate is introduced that in any equation of physics the effect of the vacuum is calculated by replacing r by r + delta r.

a394thpapernotes6a.pdf

This is very interesting. I think that the trace antisymmetry constraint in its original form must be the right one to use. So I will proceed like this.

To: EMyrone@aol.com
Sent: 11/12/2017 14:58:12 GMT Standard Time
Subj: Re: Examples

The examples were developed with the Riemannian elements Gamma^rho_mu nu (without tangent space indices). We can see later if these can be rewritten to the form Gamma^a_mu nu.

Horst

Am 11.12.2017 um 15:47 schrieb EMyrone:

These examples would be very useful. What about gamma sup a sub mu nu, do non zero diagonal elemnets exist for this? These are very interesting developments. So I will revert to the original Lindstrom constraint, which is a fundamental equation of physics and mathematics.

To: EMyrone, Sent: 11/12/2017 14:22:02 GMT Standard Time
Subj: Re: Eq. (42) of UFT298

I will give some examples for non-vanishing diagonal elements of the Christoffel connection in the text book I am preparing. I will see that I can finish the first chapter over the holidays and then will send it to you as a draft.

Horst

Am 10.12.2017 um 13:14 schrieb EMyrone:

This is where the trace antisymmetry constraint first appears, and uses the fact that the trace of an antisymmetric tensor or matrix is zero. The excellent Eckardt Lindstrom papers UFT292 – UFT299 are by now all heavily studied classics. This can be seen in the daily report I send out every morning. In the case of ECE2 field tensors each element of the trace is zero as is well known. The fundamental property of a square matrix is that it is made up of a sum of symmetric and antisymmetric square matrices. This is described by Stephenson, “Mathematical Methods for Science Students”, pp 292 ff. (fifth impression 1968). Every one of the antisymmetric matrices used by Stephenson has diagonal elements which are all zero. This was my undergraduate text book and it is signed by me with the address: “Brig y Don”, Sea View Place, Aberystwyth. I would like to ask Horst where the antisymmetric connection with non zero elements but zero trace first makes an appearance. I guess that it is the classic UFT354, but I cannot find it there. This is an interesting idea which I would like to study further. If the connection is defined by the commutator as starting point, instead of metric compatibility, the connection is antisymmetric with all diagonal elements zero, so is the curvature, so is the commutator of covariant derivatives.

The equivalent of 153,094 printed pages was downloaded (558.181 megabytes) from 3,631 memory files downloaded and 710 distinct visits each averaging 3.6 memory pages and 7 minutes, printed pages to hits ratio of 42.16, top referrals total 2,340,114, main spiders Baidu, Google, MSN and Yahoo. Collected ECE2 958, Top ten 503, Collected Evans / Morris 363(est), Collected scientometrics 225, F3(Sp) 114, MJE 101, Collected Eckardt / Lindstrom 100, Principles of ECE 91, UFT88 65, Evans Equations 49, Collected Proofs 38, Engineering Model 29, Llais 26, PECE 26, CV 20, CEFE 17, SCI 16, UFT321 16, ADD 11, PECE2 11, UFT313 13, UFT314 13, UFT315 12, UFT316 8, UFT317 9, UFT318 14, UFT319 16, UFT321 16, UFT322 13, UFT323 15, UFT324 26, UFT325 18, UFT326 7, UFT327 16, UFT328 12, UFT329 11, UFT330 14, UFT331 14, UFT332 19, UFT333 7, UFT334 5, UFT335 17, UFT336 20, UFT337 3, UFT338 9, UFT339 7, UFT340 6, UFT341 15, UFT342 8, UFT343 9, UFT344 6, UFT345 15, UFT346 10, UFT347 14, UFT348 15, UFT349 12, UFT351 14, UFT352 13, UFT353 14, UFT354 18, UFT355 13, UFT356 11, UFT357 8, UFT358 17, UFT359 11, UFT360 8, UFT361 8, UTF362 7, UFT363 12, UFT364 13, UFT365 10, UFT366 11, UFT367 18, UFT368 16, UFT369 13, UFT370 15, UFT371 14, UFT372 9, UFT373 7, UFT374 7, UFT375 5, UFT376 7, UFT377 8, UFT378 7, UFT379 5, UFT380 7, UFT381 10, UFT382 23, UFT383 21, UFT384 5, UFT385 6, UFT386 11, UFT387 11, UFT388 11, UFT389 11, UFT390 12, UFT391 10, UFT392 22, UFT393 25 to date in December 2017. City of Winnipeg UFT papers; University of Savoie general; Eotvos Lorand University Hungary general; University of Leiden UFT149; Moscow State University Institute of Physics and Technology general; Anadolu University Turkey UFT33; University of Bristol general. Intense interest all sectors, updated usage file attached for December 2017

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