Many thanks to Alex Hill for all his key work on translation. This has succeeded to such an extent that our work is read across the whole of Central and South America, and also of course in Spain and Portugal, a population of several hundred million people. The scientometics show that wikipedia is completely ineffective, and its readership is declining (see internet), because the younger generation probably find it boring and use small screen computers that make wikipedia difficult to read (article on the internet). Students are not allowed to cite it. The instigators of the trouble in the nineties have all faded into obscurity. There is just the detritus on google caches which have no effect. It is well known that these people tried to destroy ECE theory, and before that tried to destroy B(3) theory. They were also responsible for destroying my career at UNCC, which has been severely condemned internationally, and implicitly condemned by the award of a Civil List Pension, akin to Order of Merit or Pour le Merite (Blue Max). They attacked my first wife, greatly harming her. This is the worst thing they did by far to both of us. Those responsible were Buckingham, Barron, Lakhtakia, Bruhn, Rodrigues, and to a lesser extent one or two others like Jadzcyk. Hehl’s article was ineffective and has been forgotten. A hate blog was set up in 2016, this is also completely ineffective as semrush shows. It is run by a nutter who has been biling for eighteen years, and who is completely ignored. This is a criminal site, and in my opinion so is the Wikipedia site (Malicious Communications Act). Ioan Richard, former Mayor of Swansea, used the hate blog to try to organize attacks on me locally. He and his local friends are regarded as lower than vermin by the profession, and he has recently retired into oblivion. I have never met these local nutters, with the exception of Ioan Richard. I intend to keep completely away from Santilli, whose quarrels with Fucilla were so stupidly vulgar and disruptive. Rodrigues seems to have vanished, and Bruhn vanished in about 2008 after years of illegal harassment (a criminal activity). Apparently he collapsed under the pressure of my counter arguments. He made himself look stupid by attacking the British Head of State.and the Welsh Assembly, causing great anger. Most people also regard wikipedia’s attacks on ECE and myself as lower than vermin (in the words of Aneurin Bevan in describing the tories). I made several complaints against Ioan Richard, which hopefully gave him the message that he should go. In my opinion all these people should be behind bars. Rodrigues and Fucilla were involved with Albert Reda, who was given a prison sentence for wire fraud. None of these people have ever made a scientific statement, none have ever refuted Cartan geometry. I use the same geometry as Sean Carroll and everyone else. That is enough to refute wikipedia and it can be forgotten. It is well known that the EGR and standard model mafia are totally dishonest, they ignore refutations to protect their funding, so Government should stop their funding.. Albert Reda was not far away from the real mafia, neither are Fucilla and Santilli. There have been local attacks on me such as damage to my car, prolonged verbal attacks and threats in the road, and so on. The local police are completely ineffective, they are more or less in league with the criminals to protect themselves, and are increasingly ineffective in society in general. In the past few months my wife Larisa has been receiving effective and extensive preventative treatment designed to stop the onset of a heart attack or stroke, so obviously I have been helping her. Very thorough treatment was carried out in a medical institute in Krasnodar, and she is now feeling better. We both keep away entirely from the local vermin, and keep to our local friends. Larisa has been here for fifteen years, bu the vermin still describe her as "that Russian", or similar, some of them having been year just a couple of years. She is a British permanent resident and recently became a Russian citizen having been held stateless by Latvia for thirty years. An attack on he at Riga airport catalyzed very high blood pressure and almost catalyzed a stroke after she buried her first husband who treated her very badly. She is a fine lady in all respects and was born in the Ukraine. Larisa’s grandmother was departed to Siberia as an enemy of the people and lost ten out of thirteen children on the journey. She left each behind at a station on the long journey into exile. This was due to Jo Stalin, a psychopath lower than vermin. Very soon I will be arrested and exiled for trying to speak Welsh. The local medical profession is ineffective, and almost neglected Larisa’s condition to the point where she could have had a stroke. The local hate bloggers include two near neighbours, both of them are nasty expletives who have admitted reading and greatly enjoying the hate blog – imported bigots. It is seen how psychopathic hatred propagates over the internet like bubonic plague or amplified and vicious gossip. Teachers are also subjected to hate blogging and false accusation by children as young as about ten years old, and the police are also subjected to hate blogging, being deeply hated as loathsome hypocrites. In towering contrast, the international AIAS / UPITEC group goes from strength to strength, and has made its indelible mark on history. It has taken the intellectual high ground and is unassailable. Wikipedia and the hate nutters are disturbed criminals who lurk in the gutter, a dirty feather to an elephant. There has been a complete deterioration of society, and a complete moral degeneration. Obviously my first concern is to protect my wife Larisa. If she were attacked they could easily kill her by catalyzing a stroke. In this respect I have been greatly helped by Steve Dewitt (computer systems) and Ashley Jones (CCTV systems and general maintenance).The judge in the recent land case was effectively an idiot who knew nothing about Wales. I won my objections, proved that Ellis Williams did not own the land. These objections were made to try to reform the adverse possession law – legalized theft of land under Anglo Norman law. The law of my ancestor, King Hywel Dda, does not allow theft of any kind. Obviously I should have stayed in Ithaca in the United States. I was unaware that society here had degenerated to such an extent.

Finally I will start on the long essays suggested by Alex Hill.

I hold no doubt that our research is better than that of Santilli.

The reasons for forwarding the email below do not relate to the possibility of corresponding with him, but to take note of two details:

1) Santilli has also been attacked by Wikipedia, which seems to have adopted as a rule to make a target out of anybody who might threaten EinsteinÂ´s supremacy in physics, as is described below. Therefore, now it seems clear our team will remain a target for Wikipedia as long as we continue proving his maths were not wrong, but simply obsolete after Cartan, i.e. forever.

2) Now there is jurisprudence in the US regarding slander towards scientists, so if you ever wish to take action against your attackers, the courts to go to will not be in the US, but in Europe, as the email states Santilli is also planning to do after this adverse verdict by a US Federal Court.

Sorry for not clarifying these points in my original email.

Regards,

]]>This note shows that the Dirac H atom is also a Thomas precession, and gives the relativistically corrected Thomas half in Eq. (22). It is well known that the Dirac atom gives the correct spin orbit structure for atomic H but the Sommerfeld atom does not. Llewellyn Thomas developed the Thomas half theory in the same golden age of physics. So all atoms and molecules can be described in terms in terms of the Thomas half in a completely new way, on the non relativistic and relativistic levels. This is a major advance in understanding, accompanied by the fact that the Thomas half is now understood in terms of a generally covariant unified field theory, ECE and ECE2. These major advances are being made all the time, and the millions of colleagues of the ECE school know all about them. These colleagues have effectively discarded the old guard of physics, and did so fifteen years ago.. It is clear that funding for the old Einstein theory should be discontinued, and used for something useful. It is well known that Nobel prizes awarded for large parts of the old physics are obsolete. The only thing that matters is geometrical correctness and Baconian physics. All else is anthropomorphic and transient.

]]>After completing an extensive literature search on the Sommerfeld atom the next note will explain how the Thomas / ECE2 precession appears in the atom. For a useful site google "Sommerfeld H atom energy levels" and third site that comes up. The Thomas / ECE2 precession is the angular precession of the semi major axes of the elliptical orbitals per orbital angle. This gives the famous rosette structure that Sommerfeld sketched in a letter to Einstein. The Lorentz / ECE2 factor is (1 – (alpha / n) squared) power minus half, and the Thomas half enters as described in a previous note , and is the same as for the Schroedinger H atom: v / c = alpha / n. The energy levels of the Sommerfeld atom are the same as those of the Dirac atom, and Sommerfeld introduced the azimuthal quantum number. He was nominated eighty four times for a Nobel Prize, many of his students and post docs (e.g. Debye, Pauli and Heisenberg) were Nobel Laureates, but Sommerfeld was never awarded a Nobel Prize. Obviously one should not read too much into a Nobel Prize, it has become a completely arbitrary, politicised, procedure. My case shows that very clearly. I was nominated several time for B(3), but people like the fraudster Bruhn were able to attack the Royal Swedish Academy. Bruhn also attacked the Welsh Assembly and mocked the British Head of State, Queen Elizabeth II. The fraudsters were overwhelmed by a huge tide of support for the work of my colleagues and myself in developing B(3) into ECE and ECE2, and the old system of physics was overturned. It can no longer cynically censor ideas which interest millions of the colleagues worldwide. After Elsevier tipped me for a Nobel Prize in its Sci Topics feature it was also attacked by the same fraudsters who set up the Wikipedia site. Now that it is known that the Schroedinger atom is a Thomas / ECE2 precession, it will be shown in the next note that the Bohr and Sommerfeld atoms are also Thomas / ECE2 precessions. Alfred Nobel did not intend his name to be dragged in the mud in this way. Otto Stern was nominated eight two times and was finally awarded a Nobel Prize. Bertrand Russell from Wales was nominated once and got the Literature Prize. He was capable of course, but he was a philosopher, not a poet or novelist. Dylan Thomas, the enfant terrible, was never nominated. Reverend R. S. Thomas was nominated against his will about six times or so, but the Prize went to Seamus Heaney. Yassir Arafat, a terrorist, as awarded a Peace Prize. Jean-Paul Sartre refused the prize. Bub Dylan didn’t turn up for the ceremony. Wikipedia in the wrong hands is a dangerous rag because it is used to destroy careers and lives, so it is best to shut it down.

]]>All is OK here I think because only the expectation value < v squared> is actually used. This is worked out from < p squared / (2m)> . after working it out it is used inside the gamma factor. So the use of the wording "expectation value of gamma" should be avoided. agreed with the second point. The calculation needs the expectation value <1 / r > which you have worked out in previous papers. For n = 1 it is the Bohr radius. Agreed about the virial theorem. This is the first inroad to the relativistic theory. As usual some checking and development work will follow.

407(4): Development of the New Theory of Atoms

To: Myron Evans <myronevans123>

Can the expectation value (statistical average value) of gamma in eq.(16) be transferred to <v^2> ? This is not a linear transformation, and for any function f(v) we have

< f(v) > not equal f( <v> )

because f weights the values of v differently.

In (28) the factor <1/r^2> seems to be missing. Isn’t this the Bohr radius for the H atom, at least for n=1?

Perhaps another point to consider: The so-called Virial theorem:

<T> = – 1/2 <U>.

Normally this only holds for certain forms of the potential energy (type 1/r^n) but only in the non-relativistic case. This theorem is fulfilled here.

Horst

Am 13.05.2018 um 13:49 schrieb Myron Evans:

]]>407(4): Development of the New Theory of Atoms

The major new insight is given by Eq. (1), which is developed into a relativistic theory. This gives several new insights on the non relativistic and relativistic levels. For example the energy levels of the Schroedinger H atom are the negative of the expectation values of the electronic kinetic energy in each orbital. The energy levels of the Sommerfeld atom are the Thomas precession per radian multiplied by the rest energy, m c squared. The force equation and spin connection are derived, and the expectation value of the Lorentz factor defined. The ordinary non relativistic kinetic energy is the Thomas half multiplied by the rest energy. So elements of relativistic theory combine to give a familiar non relativistic result. The Thomas half is obtained by spinning the ECE2 line element.

Second Method of Refutation of de Sitter Precession

In the third term of Eq. (1) it is the radius of the earth, better denoted r sub E for clarity. In the second term it is the electron proton distance. The expectation value of the third term is the term itself, because it is a macroscopic quantity. So this is worked out in the note.

What is the variable r in this note? In eq.(1) ist is the radius of the earth, but in (3) it seems to be the radius of the H atom. De Sitter precession is smaller than <U_C> in my earlier calculation.

Horst

Am 13.05.2018 um 15:20 schrieb Myron Evans:

]]>Second Method of Refutation of de Sitter Precession

This is an improvement on Note 407(3) and shows that the de Sitter theory imparts an unquantized positive energy to the energy levels of the H atom. This is a thousand times larger than the observed negative valued energy levels of the H atom, elegantly described by the Thomas / ECE2 precession. This comes from the gravitational interaction of the electron with the earth’s mass. The electron is never free of the earth’s gravitational field, and its energy levels are known with great precision. The de Sitter theory’s predictions are never observed, Q. E. D. I encourage the colleages within AIAS / UPITEC and elsewhere to find other trivial refutations like this of the marbles in EGR. Many thanks to Horst for pointing out the need to simplify Note 407(3). The famous "Evans Eckardt dialogue" always lands up with improvements. I should think that EGR is a load of old cobblers, with none of its marbles left upon which to carve ineluctable wisdom. If I were a standard modeller I would be a white haired raving maniac trying to deal with numerous refutations and having lost all my marbles entirely. "Trivial" in this context means very simple, and very profound – Ockham’s Razor – keep it as simple as possible without losing precision and mathematics. The gravitational interaction of the electron and proton is completely negligible, but not the gravitational interaction of the electron and the earth, moon, other planets and sun. It is OK now to criticise Albert Einstein. In fact he would have encouraged criticism.

The major new insight is given by Eq. (1), which is developed into a relativistic theory. This gives several new insights on the non relativistic and relativistic levels. For example the energy levels of the Schroedinger H atom are the negative of the expectation values of the electronic kinetic energy in each orbital. The energy levels of the Sommerfeld atom are the Thomas precession per radian multiplied by the rest energy, m c squared. The force equation and spin connection are derived, and the expectation value of the Lorentz factor defined. The ordinary non relativistic kinetic energy is the Thomas half multiplied by the rest energy. So elements of relativistic theory combine to give a familiar non relativistic result. The Thomas half is obtained by spinning the ECE2 line element.

]]>1) I first expressed the Coulomb potential (11) as U sub C = – alpha h bar c / r. Its expectation values are given by Eq. (15), <U sub C> = -(alpha / n) squared m c squared.

2) It follows that the gravitational potential is U sub g = 2mMG / r = 2 x alpha h bar c / r. its expectation value is <U sub g> = – 2 x <U sub C> = 2 x (alpha n) squared m c squared. The missing factor 2 has been reinstated here.

3) So the energy levels of the H atom are Eq. (21) with x replaced by 2 x. These are the energy levels in a gravitational field because the Thomas precession is replaced by a de Sitter precession in a gravitational field. This is of course the dogma of the standard model.

4) I worked out x with the data of Eq. (23). It is x = 1.5752 ten power ten, and this is very large and not observed. So the de Sitter theory is refuted, Q. E. D.

The electron of the H atom experiences the gravitational field of the proton and also the gravitational field of the earth, the moon, the sun and other planets. The gravitational pull of the proton is negligible because the proton mass is very small. I simply used eq. (18) to work out the expectation value of 2mMG / r. in Eq. (18) mMG is multiplied and divided by alpha h bar c. For the electron in the gravitatonal field of the earth:

x = mMG / (alpha h bar c) = 1.575 ten power ten.

So the Coulombic expectation value, Eq. (15), is multiplied by – 2x. The factor – 2x is much smaller for the proton / electron gravitational interaction, which is negligible compared with the proton / electron electrostatic interaction. For r I used the radius of the earth, i.e. l assumed that the H atom is in a laboratory on the earth’s surface. The main point is that the standard model’s rotating Schwarzschild metric (de Sitter precession) gives complete nonsense. However the rotating ECE2 metric (Thomas precession) gives a perfect and original description of the H atom as in Note 407(1).

There are some points unclear to me: How did you equate the gravitational term

< m M G / r > = x < alpha hbar c / r >

to

x (alpha/n)^2 m c^2 ?

The latter is from the Coulomb potential and does not appera in <U_grav>.

Another question: Why did you use the electron mass orbiting around the earth and not the proton mass of the H atom?

Inserting the constants (with the factor 2 which seems to be missing) gives

<U_grav> = 2 < m M G / r > = Joule.

With 1 Rydberg = Joule

This is a small correction of four orders of magneitude below the H ground state energy, comparable to spin-orbit splitting.

Horst

Am 11.05.2018 um 14:40 schrieb Myron Evans:

]]>Trivial Refutation of the de Sitter Precession

Once it is realized that the H atom is a Thomas precession, the de Sitter precession is trivially refuted as attached, by considering an H atom in the Earth’s gravitational field. The spinning Schwarzschild line element used by de Sitter gives a very large correction to the H atom energy levels, and this is never observed experimentally.

Many thanks again and much appreciated!

I had noticed the error with alpha but had forgotten to mention it in my earlier email. Eq. 37 is a rally important result, and (43) gives a vivid explanation of alpha.

Horst

Am 11.05.2018 um 13:22 schrieb Myron Evans:

]]>Subject: Final Version of Note 407(1)

This version corrects minor typographical errors in the original Note 407(1), the factor alpha should have been alpha squared in various equations. The corrected version gives the neat result (37). for the H atom v / c = alpha / n, a completely new result of quantum mechanics. Here n is the principal quantum number, v is the orbital velocity of the electron, alpha is the fine structure constant, and c the universal constant known as the speed of light in vacuo. It is immediately clear that the familiar H atom can be described relativistically, even though it is a solution of the supposedly non relativistic Schroedinger equation. Its Thomas half is given by Eq. (37). So the H atom is a Thomas precession. The AIAS is named after the fine structure constant, alpha. This final version will now be used to give a trivial refutation of the de Sitter precession in Note 407(3). By "trivial" I mean "very simple" but also of key importance to the whole of physics.

This version corrects minor typographical errors in the original Note 407(1), the factor alpha should have been alpha squared in various equations. The corrected version gives the neat result (37). for the H atom v / c = alpha / n, a completely new result of quantum mechanics. Here n is the principal quantum number, v is the orbital velocity of the electron, alpha is the fine structure constant, and c the universal constant known as the speed of light in vacuo. It is immediately clear that the familiar H atom can be described relativistically, even though it is a solution of the supposedly non relativistic Schroedinger equation. Its Thomas half is given by Eq. (37). So the H atom is a Thomas precession. The AIAS is named after the fine structure constant, alpha. This final version will now be used to give a trivial refutation of the de Sitter precession in Note 407(3). By "trivial" I mean "very simple" but also of key importance to the whole of physics.

]]>Many thanks to Dr Horst Eckardt for pointing out that Note 407(1) is a remarkable result that shows that the "non relativistic" solutions of the Schroedinger equation are inherently relativistic and that the gamma factor is obtained a priori from rotation of the ECE2 covariant line element. He also points out that the standard model uses the idea of the Lorentz boost as being purely linear. As shown in Note 407(2), the "Thomas half" comes out of the commutator of boost matrices. This is also a new development because usually, the commutator of boost generators of the Lorentz group is used to give rotation generators. That procedure does not make clear that the Thomas half is given by a commutator of boost matrices. The Schroedinger equation is the non relativistic limit of the ECE2 fermion equation (the ECE2 covariant development of the Dirac equation), so it is natural (in retrospect) that the Schroedinger equation should also be relativistic. When I first derived this result a few days ago, it was a complete surprise. The ECE2 fermion equation gives spin orbit interaction, and also gives the Thomas factor of a half. Eq. (38) of Note 407(1) shows that the Thomas half enters into the description of the energy levels of the H atom. This is completely new to quantum mechanics.

Note 407(1): Thomas Precession in Planetary Orbits and the H Atom Orbitals

This is a highly interesting result that the energy levels of the H atom are directly related to Thomas precession. This shows that even the "non-relativistic" SchrĂ¶dinger solutions are inherently "relativistic". The appearance of the gamma factor is derived from rotation a priori, this is remarkable because special relativity is based on constant linear motion and is not valid for rotational systems (although it is often used as "relativistic mechanics" – one of the obvious contradictions in standard physics).

I eqs. (13,14) of the note and related equations I would prefer writing "a" instead of "r" because Delta_phi_T should be a constant value, but this is marginally.

Horst

Am 06.05.2018 um 13:08 schrieb Myron Evans:

]]>Note 407(1): Thomas Precession in Planetary Orbits and the H Atom Orbitals

This note shows that the well known energy levels of the H atom are due to Thomas precession as given by Eq. (38). This is a very remarkable result not known hitherto. So the well known Schroedinger H atom can be developed in terms of the fine structure constant, the Einstein rest energy m c squared, and the electron rest frequency m c squared / h bar. These are all relativistic concepts. Here n is the principal quantum number. Choosing n = 1 shows that there is a Thomas precession of 4.14 degrees as given by Eq. (41). Also, for n = 1 in atomic H, (v / c) squared = alpha , where alpha is the fine structure constant, so v / c = 0.0854. Alpha is 1 / 137. This is one way of showing that Thomas precession is not a small effect in atoms and molecules. It is well known that it emerges from the ECE2 fermion equation, a development of the Dirac equation. The Thomas precession (1) from rotating the ECE2 covariant line element (1) looks completely different but the two effects are based on the same theory. The EGR has fallen apart completely, so the only thing that can be claimed theoretically now is that the Thomas precession of a nearly circular orbit, Eq. (46) is part of the observed precession. Thomas precession is numerically a third of the de Siitter or geodetic precession, but the latter is incorrectly calculated from a geometry without torsion. It is of key importance to note that the standard model always gives the result (40) from its own equations. The standard result (49) refutes the standard claim (51), and the entire structure of EGR collapses completely. It was bound to to so because its geometry is completely wrong. There are many schools of ECE thought building up in essentially all universities of any note that are interested in physics, and a vast amount of interest from various sources in up to 192 countries. This is clear from the scientometrics. The next note will deal with commutators of Lorentz boosts in order to find exactly how the Thomas precession emerges. A complete new theory is in place, based on vacuum fluctuations.