Three Dimensional Orbits

August 28, 2014

The abstract expressionists could have done no better. I am delighted and amazed at these results by Horst, all coming out of the every day spherical polar coordinates. The Eckardt ellipses indeed have a special meaning. So I will proceed to writing up UFT269 now. The code can be made available on www.aias.us so that the readers can study the results with their own input parameters.

Graphics of 3-D Orbits

August 28, 2014

Many thanks again! These are full of interest and can be used in the final UFT269. This is what a three dimensional orbit would look like. They are works of art as well as of science so I am letting the general group here have a look at them. The Eckardt orbits must have a definite significance. So these orbits may exist and the astronomers can have a look for them. It would be interesting to study the transition to a planar orbit as theta get closer and closer to pi / 2 and L sub theta closer and closer to zero. Then the familiar planar orbit will emerge, an ellipse as first realized by Kepler.

To: EMyrone@aol.com
Sent: 28/08/2014 15:24:53 GMT Daylight Time
Subj: Re: Discussion of 269(9) – graphics

These are 3D graphs of the r surfaces of the theta and phi ellipses. The theta elliptic surfuce is rotational symmetric in phi because it does not depend on phi, looks like a hat or UFO.
The phi elliptic surface looks like a snail shell and is shown from two oposite directions.
The graphics are for L=3 L_theta = 3 L_phi, ie. it is an Eckardt orbit.

Horst

The main result is the non planar orbit (28), which can be graphed in a 3-D spherical polar plot and animated. Under well defined conditions (25) and (26) it reduces to an Eckardt orbit. The usual theory of orbits is the Kepler Hooke Newton theory which gives the planar ellipse (27). In three dimensions it becomes the precessing ellipse (28).The new subsidiary equations of the lagrangian analysis are Eqs. (16) (17) and (18). So now I will proceed to writing up UFT269. Since this is a fundamental discovery in orbital theory there is a lot of mileage in it. No one can argue with spherical polar coordinates. This is a part of x theory, a subsidiary theory of ECE unified field theory. It is also applicable in all detail to the classical orbit of an electron around a proton. The usual hamiltonian is being used, expressed in spherical polar coordinates. This alone is sufficient to produce a vast amount of new information for astronomers to test out. An orbit need not be planar, and as GJE points out, the reason for planar orbits must be found. It must be due to a force additional to the inverse square. The planar constraint is theta = pi / 2, L sub theta = 0, L = L sub phi. This is highly artificial. So planar orbits are a small class of orbits which happen to occur in our solar system due to evolution.

Computer analysis of Note 269(9)

August 28, 2014

OK thanks, this could be a useful subsidiary condition but the analysis leading to the precessing ellipse is the important one.

To: EMyrone@aol.com
Sent: 28/08/2014 14:58:52 GMT Daylight Time
Subj: Re: Note 269(9) Corrigendum

Eq.(17) can be resolved for theta dot, and this can be inserted into (9), removing the variable theta dot. But this does not give any simpler expression.

Horst

EMyrone@aol.com hat am 28. August 2014 um 14:22 geschrieben:

Combine Eqs. (9) and (17), not (9) and (16). this leads back to Eq. (10), which is a subsidiary constraint. However, Eq. (10) is overcomplicated and the simplest constraint should be used, Eq. (16). This all comes out of the lagrangian analysis with lagrangian variables in a basically straighforward way, giving though a very useful result (28).

269(9).pdf

The Minimalist Poetry of R. S. Thomas

August 28, 2014

He was a fellow Nobel Prize nominee, Fellow of the Cymrodorion Society and Queen’s Gold Medal for poetry, taught himself the Welsh language, wrote his autobiography in Welsh and poetry in English, friend of the artist Sir Kyffin Williams and many others. I have one or two letters from him in Welsh in the www.aias.us historical source documents section. Ordained Priest of the Church in Wales, Rector of Manafon, Vicar of Aberdaron, among the most admired poets from Wales. He developed a minimalist style of poetry, which is seemingly simple but very profound, with many layers of meaning different for each reader. For example two stanzas of “Here”:

I am like a tree,
From my top boughs I can see
The footprints that led up to me

I have nowhere to go,
The swift satellites show
The clock of my being is slow.

The first one looks back at his life and the soil from which he grew. The second he seems to use special relativity to show that he does not like contemporary society at all. Neither does any intelligent being. I don’t think he understood special relativity but used it as a metaphor, or so it seems to me. I first came across his minimalist style at Oxford in 1975, in Blackwell’s bookshop on Broad Street, in the volume “H’m” in which he is mercilessly honest about the then Somalia famine. Totally and starkly honest. Completely different style from the equally great poet Dylan Thomas. Both are very profound. “Over Sir John’s Hill” is I think the best poem by Dylan Thomas, influenced by John Donne, and my ancestral cousins George Herbert and Henry Vaughan, the metaphysical poets. RST was a shy man, as I am , but ferociously principled and an inspiration to many, including myself. He was most at home among his parishioners in Aberdaron, all fluent Welsh speakers in Gwynedd dialect, a fine dialect. He did not want to be nominated for a Nobel Prize by a remote establishment. He thought that they could not possibly understand him or his work. In the end he was nominated a few times. Shakespeare uses metaphor in a memorable way and brings abstraction into human form. R. S. Thomas hardly uses metaphor at all sometimes, and relies on the idea. Neither has the very brilliant technique of Dafydd ap Gwilym and of cynghanedd. RST would freely admit that, but he was a great poet. I think that he would have written very fine cynghanedd.

The Connection Antisymmetry

August 28, 2014

This is very easy to understand as follows (proofs one to five):

C(mu, nu) A = – gamma (mu nu) B + ……

where C is the commutator and gamma the connection. Both objects are antisymmetric in mu and nu:

C(mu, nu) = – C(nu. mu)
gamma(mu, nu) = – gamma (nu, mu)

A symmetric commutator (mu the same as nu) is zero. A symmetric connection is therefore zero and a symmetric commutator means that torsion and curvature are BOTH zero. No way out of it, one cannot throw away torsion. The old physics was a howling wolf, it used a symmetric connection in an era when torsion was not known. It made matters infinitely worse by just saying that torsion can be neglected (put to zero). If this happens the commutator is zero, and the curvature vanishes – no gravitation at all. The commutator is worked out in all detail in UFT99 and always gives the two Cartan structure equations in their tensor formulation. So it gives the whole of geometry. The torsion works itself through all of geometry, right down to the ordinary spherical polar coordinates with which we are working now. They are ordinary but give a tremendous amount of new information because they are fundamental.

The Loudest Howlers in the Old Relativity

August 28, 2014

There have been many wolves howling away for a century, the loudest are the following.

1) The old theory does not work, it completely fails in whirlpool galaxies.
2) It was developed without torsion. The commutator method of the definitive proofs of www.aias.us show that neglect of torsion results in the curvature becoming zero, and no gravitation.
3) The Binet equation shows that planetary precession cannot be described by the old theory without it developing an infinity (UFT264).
4) It has been replaced completely by ECE and x theory.

In other areas of the old theory UFT225 shows that electroweak theory is crass rubbish, it is completely meaningless. So the old theory is obsolete. There are many other refutations on www.aias.us. So I think that funding for obsolete physics should be transferred to something useful. The behaviour of the old dogmatists means that they should not be publicly funded. In no other area of culture would people behave so badly.

Rebuttal of ‘t Hooft by Stephen Crothers

August 28, 2014

This is an important paper and will make Principles of ECE a valuable book. So even after torsion had been left out of consideration, the old relativity was still full of errors. Arrogance is usually a sign of lack of confidence. I don’t bother with ‘t Hooft, ECE is too interesting.

In a message dated 28/08/2014 13:00:44 GMT Daylight Time, writes:

Dear Scientists,

My long paper motivated as a response to ‘t Hooft is almost complete. ‘t Hooft is a rather ignorant fellow, and as arrogant as they can come. I will release my paper soon. ‘t Hooft shall receive a copy from me. It is this paper that I shall offer as my contribution to the latest AIAS book.

Last month I had long and acrimonious exchange with that old biggot ‘t Hooft on ResrearchGate. All he did was regurgitate the standard demonstrable codswallop on General Relativity and black holes etc. However, after 4 years, and continued stonewalling on this latest at ResearchGate, ‘t Hooft finally admitted before all and sundry that he does not even know what a first-order intrinsic differential invariant is, and so he doesn’t know either that they don’t exist. Yet ‘t Hooft, and Einstein and his followers, employ Einstein’s pseudotensor, which implies a first-order intrinsic differential invariant, and they do calculations with it! . Assume Einstein’s pseudotensor has mathematical validity. Contract it therefore. A first-order intrinsic differential invariant results. But the pure mathematicians proved in 1900 that first-order intrinsic differential invariants do not exist! Thus, the axiom is false, and so, by reductio ad absurdum, Einstein’s pseudotensor is a meaningless concoction of mathematical symbols. ‘t Hooft does calculations with it nonetheless. Marvellous!

One can construct first-order differential invariants, but to do so requires an additional extraneous quantity to augment the metric tensor. Consequently, they are not intrinsic.

Steve Crothers

On Thursday, 28 August 2014 5:15 PM, “EMyrone@aol.com” <EMyrone@aol.com> wrote:

Fully agreed, as a Civil List Pensioner I am gravely concerned about its overt dishonesty, the way in which it tries to ignore refutations. So if I were Permanent Under Secretary Sir Goronwy Daniel I would advise whether this is entirely wise, Minister.

To: EMyrone@aol.com
Sent: 28/08/2014 07:52:33 GMT Daylight Time
Subj: Re: Unites States Airforce Reads Gareth Evans

His work has become irrelevant and he has become insignificant as you and Horst have pressed on with the new physics. Says a lot about the Nobel Prize!!

Sent from Samsung Mobile

Note 269(9) Corrigendum

August 28, 2014

Combine Eqs. (9) and (17), not (9) and (16). this leads back to Eq. (10), which is a subsidiary constraint. However, Eq. (10) is overcomplicated and the simplest constraint should be used, Eq. (16). This all comes out of the lagrangian analysis with lagrangian variables in a basically straighforward way, giving though a very useful result (28).

Er Cof am Blant y Grithig

August 28, 2014

Thanks for your interest in the poetry. As you know Grithig is situated under a rocky mountain opposite Craig y Nos Castle and across the river. “Y Grithig” means “The Scarred Place” because of the rocks (“craethog” in modern Welsh). There is not much good land. So the Grithig Children were delicately carved from rock which remains eternal in memory. Similarly Bernini brought delicate carvings to life from marble, and Rodin brought Balzac to life. As in music the interpretation is endless and left to the reader’s imagination. The original englyn is designed to condense and be memorable.

In a message dated 28/08/2014 12:55:20 GMT Daylight Time, writes:

I can only read the English version. What does “cut of rock” mean in this context? That the scars of Grithig are hard like rock? Or does it relate to the hour, a “hard hour”?
I know, it is difficult to understand lyrics in a non-native language.

Horst

EMyrone@aol.com hat am 28. August 2014 um 12:49 geschrieben:

Dyma farwnad i Blant y Grithig. Here is an elegy for the Grithig Children.

Er Cof am Blant y Grithig

Y graith hon o fron Grithig; – aethant y
Plant or byd; y Plant elwig,
Ymaeth rhed awr fel mwyth rhig,
Cred gwir y Plant caredig.

In Memory of the Grithig Children

Cut from scars of Grithig; – the Children
Have gone from the world; noble Children,
Away runs the hour, delicate cut of rock,
With the generous Children’s creed.

This is the englyn described in the online Oxford University course on cynghanedd, developed by my ancestral cousin Dafydd ap Gwilym in the fourteenth century. The transliteration is a poetic scan that retains only the meaning. In the first line for example there is a double cynghanedd, consonantal alliteration and internal rhyme. There is a crossed internal rhyme between the end of the first line after the hyphen, and the beginning of the second line, and the third and fourth lines contain consonantal alliteration. The four lines must rhyme, the last couplet must be a cywydd couplet. Above all there must be poetic art, not too much strain after cynghanedd. When narrated this poetry begins to sing and is often set to the harp. This is a traditional elegy in the form of an englyn. The last two Grithg children Raumond and Nan, died recently, but being formed form the scars of Grithig, they are there eternally in all weathers of memory.

Discussion of 269(9)

August 28, 2014

You are right, the phi I used should have been phi dot. We should just run it through the computer to make sure all is right and I will post a corrigendum shortly. The main result Eq. (28) is not affected, and that is the result of interest for astronomy. The subsidiary constraints will provide additional infomration that will also be useful for astronomers.

In a message dated 28/08/2014 12:37:11 GMT Daylight Time, writes:

How exactly did you derive eq.(18)? When I combine eqs. (9) and (16) I obtain additional terms.
Will plot the surfaces r(theta,phi) with constraints and then try an animation of an orbit.

Horst

EMyrone@aol.com hat am 28. August 2014 um 11:43 geschrieben:

The main result is the non planar orbit (28), which can be graphed in a 3-D spherical polar plot and animated. Under well defined conditions (25) and (26) it reduces to an Eckardt orbit. The usual theory of orbits is the Kepler Hooke Newton theory which gives the planar ellipse (27). In three dimensions it becomes the precessing ellipse (28).The new subsidiary equations of the lagrangian analysis are Eqs. (16) (17) and (18). So now I will proceed to writing up UFT269. Since this is a fundamental discovery in orbital theory there is a lot of mileage in it. No one can argue with spherical polar coordinates. This is a part of x theory, a subsidiary theory of ECE unified field theory. It is also applicable in all detail to the classical orbit of an electron around a proton. The usual hamiltonian is being used, expressed in spherical polar coordinates. This alone is sufficient to produce a vast amount of new information for astronomers to test out. An orbit need not be planar, and as GJE points out, the reason for planar orbits must be found. It must be due to a force additional to the inverse square. The planar constraint is theta = pi / 2, L sub theta = 0, L = L sub phi. This is highly artificial. So planar orbits are a small class of orbits which happen to occur in our solar system due to evolution.


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