I intend to continue by using the approach used in previous UFT papers developing the fermion equation, but to explore approximations other than those used by Dirac and contemporaries. In those approximation they used E = gamma mc squared about equal to m c squared in the denominator, UFT247 to UFT253. I like this kind of work because it is so elegant and produces so much information and has so many possible variations on the theme. It is based on the Einstein energy equation, which is a retsatemtn of the realtivistic momentum p = gamma m v (see Marion and Thornton or good websites). It can be looked upon as quantization of the ECE2 Lorentz force equation. In the Einstein energy equation

E squared = c squared p squared + m squared c fourth

where p is the relativistic momentum p = gamma m v. In the Dirac type approximations p is approximated in the development by the non relativistic momentum in the numerator of

E – m c squared = p squared c squared / ( E + m c squared)

After this development I intend to go back to the earlier ECE2 equations and develop them for the spin connection. Dirac used the minimal prescription which is equivalent to adding U as shown in immediately preceding UFT papers. The approximations used by Dirac et al. are crude and rough ones which can only be justified by the agreement with experimental data, the famous half integral spin , ESR, NMR and so on. I suggest strongly that readers follow this discussion with readings of Marion and Thornton, chapter on special relativity. It is especially important to understand the Lorentz transform and the definition of the Lorentz gamma factor from the Minkowski metric. Horst’s demonstration of precession from special relativity in UFT325 is also very important. At first, special relativity can be very confusing but it is not difficult if a few rules are kept clearly in mind.

The p0 is the Newtonian momentum, so Eqs. (29) and (32) can be solved, p0 does not contain gamma but p contains gamma:

p = gamma p0 = gamma m v = h bar kappa

and
E = gamma m c squared = h bar omega

as in many previous UFT papers.

. The origin of the Lorentz factor gamma is relativistic, i. e.

c squared dtau squared = c squared dt squared – v squared dt squared

I agree with these points, for the free particle, E = T, thi sis just a matter of notation. It is clear from page 5 that the velocity appearing in gamma is the Newtonian velocity, see the steps in Eq. (38), page five. I also agree that it does not come from a classical analysis. It comes form the relativistic Minkowski metric as described for example in Marion and Thornton. So the theory is rigorously self consistent and also consistent with the lagrangian theory.

To: EMyrone@aol.com
Sent: 30/08/2015 20:56:45 GMT Daylight Time
Subj: Re: 326(5): Final Version of Note 326(4)

In eq.(15), E is obviously the total energy without rest mass, in contrast to (5).
eq.(24): hbar squared kappa squared
eq.(25): wouldn’t it be better to write mT intead of mE? E is without restmass again here.
eq. (29) allows computing the relativistic kinetic energy if the classical kinetic energy T_0 is known:

T_0 = 1/2 (1+gamma)/gamma^2 T
or
T = 2 gamma^2/(1+gamma) T_0.

However this is not a self-consistent procedure, see below:

Eq.(32) can be written with the classical momentum p_0 but this does not mean that this comes out from a non-relativistic theory. This is rather a “back-transfomation” to a non-relativistic case from a self-consistent relativistic solution of quantum or Lagrange equations. We solved them in paper 325 for example.

Considering the limit gamma –> 1 gives the correct non-relativistic limit, that is o.k.

Horst

Am 30.08.2015 um 15:07 schrieb EMyrone:

I went through my calculations again and found that the correct free particle quantization equation is Eq. (29) with gamma defined by Eq. (32) and the de Broglie wave particle dualism by Eq. (33). So these equations can be solved by computer algebra to give E in terms of p sub 0, the classical momentum, and kappa. The cross check on page (5) confirms that everything is self consistent. Having gone through this baseline calculation the particle on a ring and H atom can be defined in a relativistic context. The answer to the computer algebra must be:

E squared = (h bar kappa c) squared + m squared c fourth

so this gives a check on the results of the computer algebra. The fermion equation for the free particle is therefore Eq. (29) where gamma is given by Eq. (32). and where the de Broglie wave particle dualism is given by Eq. (33). Although these equations look like familiar special relativity they are the quantization of the ECE2 Lorentz force equation.

There were 1,914 files downloaded or hits from 341 distinct visits or reading sessions, main spiders, baidu, google, MSN and yahoo. Collected Scientometrics 668, F3(Sp) 634, Evans / Morris papers 580 (est), Collected ECE2 papers 488, Autobiography volumes one and two 329, Barddoniaeth / Collected Poetry 310, Eckardt / Lindstrom papers 210. Principles of ECE 187, proofs that no torsion means no gravitation 181, UFT88 136, Evans Equations 123 (numerous Spanish), Llais 98, Engineering Model 96, UFT311 83, CEFE 70, UFT321 61, UFT322 56, UFT320 52, UFT318 52, UFT319 49, UFT324 42, UFT317 42, UFT313 40, UFT316 37, UFT323 37, UFT315 31, UFT314 29, UFT325 21 to date in August 2015. University of the Andes UFT139 (Sp), spidering from a private site in Germany, Istella Media Italy general; Gospel Ministry Alliance general; Izhevsk region extensive. Intense interest all sectors, updated usage file attached for August 2015

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I went through my calculations again and found that the correct free particle quantization equation is Eq. (29) with gamma defined by Eq. (32) and the de Broglie wave particle dualism by Eq. (33). So these equations can be solved by computer algebra to give E in terms of p sub 0, the classical momentum, and kappa. The cross check on page (5) confirms that everything is self consistent. Having gone through this baseline calculation the particle on a ring and H atom can be defined in a relativistic context. The answer to the computer algebra must be:

E squared = (h bar kappa c) squared + m squared c fourth

so this gives a check on the results of the computer algebra. The fermion equation for the free particle is therefore Eq. (29) where gamma is given by Eq. (32). and where the de Broglie wave particle dualism is given by Eq. (33). Although these equations look like familiar special relativity they are the quantization of the ECE2 Lorentz force equation.

a326thpapernotes5.pdf

Many thanks indeed, an exciting discovery! I will proceed immediately to developing these new solutions with Schroedinger quantization in preparation for numerical solution, then add a potential. The quantized versions may be soluble to give completely new relativistic free particle wavefunctions both for translational and rotational free particle motion. The golden age of quantum mechanics always comes up with something new, almost a hundred years after its first development. This is essentially quantization of ECE2 theory. This is of course the method we have used in many previous UFT papers, many variations on a them by Paul Dirac and contemporaries, but always based on geometry so the Dirac equation has become the fermion equation of generally covariant unified field theory (now ECE2 theory).

To: EMyrone@aol.com
Sent: 29/08/2015 11:30:00 GMT Daylight Time
Subj: Exact solution of the relativistic momentum equation

In note 326(4) eq.(33) can be solved with some effort in computeralgebra without approximation v<<c, see attached. There are 4 solutions for p^2, the results differ in signs and a summand m*H1.

Horst

Am 24.08.2015 um 15:57 schrieb EMyrone:

This note uses a Dirac type quantization to produce the equation (21), a relativistic Schroedinger equation which must be solved for the wavefunctions psi. In general this is a highly non trivial procedure which must be carried out numerically in three dimensions. However, it is straightforward to show that this type of quantization produces small shifts in the H atom energy levels given by the expectation value (28). The Thomas factor is given correctly by the Sommerfeld atom, but there is no spin orbit interaction, because the Sommerfeld atom does not contain a spin quantum number, later suggested by the Sommerfeld group itself and developed by Pauli and others. As in previous UFT papers spin orbit coupling and many new effects of development of ECE appears with the use of the SU(2) basis and Pauli matrices. It is known from UFT325 that these orbitals in two dimensions must be the result of a quantization of a two dimensional precessing ellipse, and that will be the subject of the next note. This method is much clearer than that used by Sommerfeld himself in 1913, who did not have the benefit of Schroedinger Debye quantization (circ 1923 / 1924). Sommerfeld produced orbitals in 1913 which he communicated by letter to Einstein.

326(4).pdf

Thanks again for going through 326(4). Agreed with the first two points, I thing that the factor 2 is alright because 1 + gamma is approximately 1 + 1 – v squared / (2 c squared).

To: EMyrone@aol.com
Sent: 29/08/2015 11:20:02 GMT Daylight Time
Subj: Re: 326(2): Quantization of the Sommerfeld Hamiltonian

In eq.(39) it should read at the RHS:

hbar^2 / 2 m^2 c^2

(with m squared). In eq.(46) the factor E seems to be missing. Should there be a “3” instead of “2” because of 1+gamma in eq. (30)?

Horst

Am 24.08.2015 um 15:57 schrieb EMyrone:

This note uses a Dirac type quantization to produce the equation (21), a relativistic Schroedinger equation which must be solved for the wavefunctions psi. In general this is a highly non trivial procedure which must be carried out numerically in three dimensions. However, it is straightforward to show that this type of quantization produces small shifts in the H atom energy levels given by the expectation value (28). The Thomas factor is given correctly by the Sommerfeld atom, but there is no spin orbit interaction, because the Sommerfeld atom does not contain a spin quantum number, later suggested by the Sommerfeld group itself and developed by Pauli and others. As in previous UFT papers spin orbit coupling and many new effects of development of ECE appears with the use of the SU(2) basis and Pauli matrices. It is known from UFT325 that these orbitals in two dimensions must be the result of a quantization of a two dimensional precessing ellipse, and that will be the subject of the next note. This method is much clearer than that used by Sommerfeld himself in 1913, who did not have the benefit of Schroedinger Debye quantization (circ 1923 / 1924). Sommerfeld produced orbitals in 1913 which he communicated by letter to Einstein.

This vastly influential book was published by Abramis in 2007 as a softback, but by far its major impact has been open source on www.aias.us, www.atomicprecision.com and www.upitec.org. The impact of the book is miniscule in comparison with the websites, but still good. This is typical of the open source revolution in education. It was written by Laurence Felker, an engineer residing in Nevada and a lecturer in the Nevada / California region of the western United States. It was translated into Spanish by Alex Hill, (www.et3m.net), a leading industrialist. The Spanish version is in the Spanish section of www.aias.us divided into fifteen chapters, and the English version is UFT302. In August 2015 to date the Spanish version has been read 960 times, and the English version 118 times. This is 14,053 readings a year. The book first began to be posted in 2005, so over a decade it has accumulated at least 140,000 readings from www.aias.us alone, probably much more. Adjusting for all three ECE sites by a factor of 60% gives 224,000 readings. This is a “best reader” by any standards. There are eight times more readings in Spanish than English, suggesting that the book is well known throughout the Spanish speaking world, as well as the English speaking world. It is also read throughout the Portuguese and Italian speaking world, and this readership has been sustained for a decade and is already of historic importance. The distribution of the Spanish readership, chapter by chapter, for August 2015 is as follows.

1) Introduction 61
2) General Relativity 25
3) Quantum Theory 621
4) Geometry 28
5) Well Known Equations 37
6) Evans Field equation 21
7) Evans Wave equation 17
8) Implications 14
9) Dirac, Klein Gordon and Evans Wave Equations 25
10) Replacement of the Heisenberg Principle 20
11) The B(3) Spin Field 11
12) Electroweak Theory 17
13) Aharonov Bohm Effect 33
14) Geometrical Concepts 22
15)Unified Viewpoint 8

in the first 28 days of August 2015 in the middle of the summer vacation, a quiet time in academia. It is seen that the Spanish version is dominated completely by chapter three on quantum theory, so this is an important area of ECE, the first theory to unify quantum mechanics with general relativity and to definitively disprove the Heisenberg Uncertainty Principle in UFT175. The Croca group in Lisbon has refuted it many times in many ways experimentally.
The book covers the initial, explosive, impact of ECE theory, since then there has been tremendous progress in many directions and the massive initial impact of ECE has been sustained, so it is already historic – a permanent and internationally famous new school of thought. This means that the standard model of physics has lost all credibility, and Governments are drastically curtailing its funding, not before time. The meteoric impact of ECE in 2003 to 2005 is clear from UFT307 (available ion softback from New Generation, London), the scientometrics, currently being read 8,173 times a year off www.aias.us. It is also known that the loonie fringe of standard physics tried to misrepresent, defame and severely distort both my work and career on wikipedia using trolling methods. Obviously there should be a Government investigation of Wikipedia. This disgusting calumny hastened the demise of standard physics funding. Trolls are of course criminals and have been reduced to historical, hysterical rubble.

cc Prime Minister’s Office.
M. P. Gower

There were 2,693 files downloaded from 417 distinct visits or reading sessions, main spiders baidu, MSN, google and yahoo. Collected Scientometrics 627, F3(Sp) 621, Evans / Morris papers 560 (estimated), ECE2 papers 484, Autobiography volumes one and two 315, Barddoniaeth / Poetry 299, Eckart / Lindstrom papers 209, Principles of ECE 184, proofs that no torsion means no gravitation 177, UFT88 136, Evans Equations 118 (numerous Spanish), Llais ( “Voice”, translation of article in Welsh by Dewi Lewis) 96, Engineering Model 95, UFT311 79, CEFE 68, UFT321 61, UFT322 55, UFT318 52, UFT320 52, UFT319 49, UFT317 42, UFT324 39, UFT314 38, UFT323 36, UFT316 36, UFT313 36, UFT315 31, UFT325 18 to date in August 2005. Bank of America UFT175; Woorank web ranking extensive; Physics University of Mainz UFT157(Sp); extensive spidering private site in Germany; Indian Institute of Technology Delhi Two Schools of Thought, overview of ECE, advantages of ECE; Istella media Italy “Diplomatic Objection to ‘t Hooft” by AIAS Co President Gareth Evans; Materials Research Institute National Autonomous University of Mexico F3(Sp) on ECE Quantum Mechanics; Protagonist Web Hosting Netherlands general; Izhevsk Region Russia extensive; Alter Vista Web Hosting Italy general; Updated usage file attached for August 2015.

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This would be very important in my opinion, a very good model for this type of book is Laurence Felker’s chapter three as just posted. I set out in 2003 to remove the mystery from quantum mechanics, and to unify electromagnetism with gravitation, using geometry. I also unified quantum mechanics and general relativity. Douglas Lindstrom, Horet Eckardt and Laurence Felker have an in depth scholarly knowledge of ECE and have pushed the subject forward a long way. Kerry Pendergast gives a very good description for the general reader in “The Life of Myron Evans” available form Cambridge International Science Publishing. The definitive monograph is “Principles of ECE Theory”, being read several times a year open source (UFT281 to UFT288, to be published by “New Generation Publishing” in London. Felker’s chapter three stars with a quote from Feynman, who laconically admitted that all he was doing was hocus pocus. I fully agree. QED and QCD have been shredded by ECE and ECE2, notably UFT85. Its claim to accuracy is as described by Feynman, hocus pocus.

Horst:

I just about have my main computer up and running again. I am studying the Fenics project-non-linear finite element method.

Have you worked with this compilation of packages before?

I am still plugging away, a little at a time, at the beginner level “armchair guide to ECE electromagnetism” to be a companion to the video material that is supposed to put out by the conference people in Idaho early in September. I don’t think that this will be ready by that time, so will get released lated in the fall.

Take care

Doug