Pleasure, and thanks in turn! These calculations mean that the basics of the Einsteinian era are completely wrong. By now this is widely known and accepted, so the scientific world has split in two, those who really understand what is going on, and those who just regurgitate dogma. I will now rework 313(6) and the final published result will contain yet more terms not present in the 1902 second Bianchi identity upon which the Einstein field equation is based directly. The second Bianchi identity is made proportional through the Einstein constant k to the covariant derivative of the canonical energy momentum tensor. Once torsion is included, that procedure becomes totally wrong, so the ECE equations take over.

To: emyrone@aol.com
Sent: 27/04/2015 13:52:10 GMT Daylight Time
Subj: Fwd: Discussion of note 313(5)

Lots of thanks for explaining this so thoroughly. It is astonishing that the few mathematicians who saw through this (although without torsion) got so much confidence that a whole profession believed them (although science is not “believing”).

It is remarkable that adding the vector V to which the identies are to be applied, introduces a summation that is not present in the original identities. Simply writing down some tensor equations and understanding them seem to be two different things…

Horst

Agreed about Eq. (14), I will implement the sign changes in the final paper. Eq. (5) has the right commutator sign and this should be the same in Eq. (14). These are the key equations of the proof, introducing the Ricci identity (8). So this proof could have been used by Ricci in 1880 and rediscovered by Bianchi in 1902. On cyclical summation the last two terms of Eq. (9) vanish because of the first Bianchi identity, leaving Eq. (10). However they do not vanish in Eq. (16), because of the Cartan identity, so I will rework this note from Eq. (14) onwards. The final result is that there will be more terms in the JCE identity, making the Einsteinian theory completely unworkable.

To: emyrone@aol.com
Sent: 27/04/2015 15:25:23 GMT Daylight Time
Subj: note 313(6)

In eq.(14) the sign of the second term in second row seem to have to be changed because of the outer commutator D sub rho. Consequently the signs in the last row have to be changed. In Eq.(16) the signs are correct again.

It is not clear to me how you arrived at eq.(17). From the preceding equations, there must be additional terms like

(R sup kappa sub lambda mu nu * D sub rho + cycl.) V sup k

and

(R sup lambda sub rho mu nu + cycl.) Dsub lambda Vsup kappa.

These seem not to be identical with any other identity developed so far, but I may have overlooked something.

Horst

Agreed, Eqns. (22) and (23) are the Jacobi Cartan Evans identity and the First Evans identity. These are what should have been used in the twentieth century Einsteinian type general relativity. My name is there just to distinguish them from the other well known identities.

To: emyrone@aol.com
Sent: 27/04/2015 13:34:41 GMT Daylight Time
Subj: Re: Notes for UFT313, note 7

I just got it, eq. (22) is eq.(10) of note (5).

Horst Eckardt <mail@horst-eckardt.de> hat am 27. April 2015 um 13:58 geschrieben:

I just studied note 7. most of it is clear to me. in eq.(2), 3rd line, some typos are in the last term, no problem.

What I do not understand is the end of the note. What does eq.(20) mean? Obviously this comes form comparing (18) with (14), but torsion has one index less than curvature so you added the alpha. I guess that for each alpha the term

T sup kappa sub rho, lambda

is different although it has the same indices.

I do not understand eq.(22). From where did you infer it? The last line has an additional index alpha which does not appear in other terms. Is this formally correct?

(in addition, lambda is a summation index there but not in the other terms but that is only a matter of naming).

Horst

EMyrone@aol.com hat am 27. April 2015 um 12:39 geschrieben:

Many thanks for going through this stuff. Sean Carroll lectured to Harvard graduates, then at UCSB, Chicago and Caltech. I will concentrate around Note 313(6) to extend the second Bianchi identity to include torsion. The expressions for the covariant derivative of any tensor and for the commutator of covariant derivatives acting on any tensor are given by Carroll in his chapter three, and in many UFT papers, giving much more detail than Carroll. The first Evans identity (the cyclical torsion identity) was discovered a few months after UFT88 in UFT109 and is an exact identity like the Jacobi identity and Cartan identity. The main theme of the paper is to show that the second Bianchi identity becomes completely different when torsion is included. It develops UFT88, UFT109, UFT255 and UFT281. As you know the Einstein field equation rests directly on the original 1902 second Bianchi identity without torsion, so the Einstein field equation is totally wrong. No longer does this statement generate waves of shock horror.

In a message dated 27/04/2015 10:35:58 GMT Daylight Time, writes:

Understanding these notes requires really some concentration. With your comments it becomes clearer now. Could you please resend notes 5 and 6, I do not have them at hand here today.

Horst

EMyrone@aol.com hat am 26. April 2015 um 08:52 geschrieben:

Eq. (15) of Note 313(2) is constructed from Eq. (14) of that note, which is an exact identity. So Eq. (15) is also an exact identity. Eq. (16) of that note is Eq. (105) of UFT255. It is assumed that Eq. (16) is a solution of Eq. (15). Adding Eqs. (15) and (16) gives Eq. (1) of Note 303(4), which shows that Eq. (16) is true, and so is a solution of Eq. (15). The identities (5) and (6) of Note 313(4) are obtained from the identity (3) by cyclic permutation of the indices lambda, nu and rho. In the same way, these indices can be cyclically permuted in the Cartan identity (2).

Sent: 25/04/2015 16:17:03 GMT Daylight Time
Subj: note 313(4)

Eq.(1) is constructed in a way that the terms in each line come from
known identities, thus making their sum valid.
I do not understand why the new identities (4-6) should be valid in
general. These seem to be constructed from columns of eq.(1). In this
way their validity is sufficient to validate (1), but the conditions
(4-6) are not necessary to fulfill (1), it is not an equivalence relation.
Eq.(3) is the second Bianchi identity and

valid independently.

Horst

Many thanks for going through this, agreed about Eq. (2), I accidentally duplicated the last term in the first line. This does not affect the rest of the note or UFT109. The correct expression is Carroll’s (3.13) of his online notes. Eq. (20) is just a symbolic representation of a possible relation between curvature and torsion. This will not be used in the final paper.

To: emyrone@aol.com
Sent: 27/04/2015 12:58:17 GMT Daylight Time
Subj: Re: Notes for UFT313, note 7

I just studied note 7. most of it is clear to me. in eq.(2), 3rd line, some typos are in the last term, no problem.

What I do not understand is the end of the note. What does eq.(20) mean? Obviously this comes form comparing (18) with (14), but torsion has one index less than curvature so you added the alpha. I guess that for each alpha the term

T sup kappa sub rho, lambda

is different although it has the same indices.

I do not understand eq.(22). From where did you infer it? The last line has an additional index alpha which does not appear in other terms. Is this formally correct?

(in addition, lambda is a summation index there but not in the other terms but that is only a matter of naming).

Horst

EMyrone@aol.com hat am 27. April 2015 um 12:39 geschrieben:

Many thanks for going through this stuff. Sean Carroll lectured to Harvard graduates, then at UCSB, Chicago and Caltech. I will concentrate around Note 313(6) to extend the second Bianchi identity to include torsion. The expressions for the covariant derivative of any tensor and for the commutator of covariant derivatives acting on any tensor are given by Carroll in his chapter three, and in many UFT papers, giving much more detail than Carroll. The first Evans identity (the cyclical torsion identity) was discovered a few months after UFT88 in UFT109 and is an exact identity like the Jacobi identity and Cartan identity. The main theme of the paper is to show that the second Bianchi identity becomes completely different when torsion is included. It develops UFT88, UFT109, UFT255 and UFT281. As you know the Einstein field equation rests directly on the original 1902 second Bianchi identity without torsion, so the Einstein field equation is totally wrong. No longer does this statement generate waves of shock horror.

In a message dated 27/04/2015 10:35:58 GMT Daylight Time, writes:

Understanding these notes requires really some concentration. With your comments it becomes clearer now. Could you please resend notes 5 and 6, I do not have them at hand here today.

Horst

EMyrone@aol.com hat am 26. April 2015 um 08:52 geschrieben:

Eq. (15) of Note 313(2) is constructed from Eq. (14) of that note, which is an exact identity. So Eq. (15) is also an exact identity. Eq. (16) of that note is Eq. (105) of UFT255. It is assumed that Eq. (16) is a solution of Eq. (15). Adding Eqs. (15) and (16) gives Eq. (1) of Note 303(4), which shows that Eq. (16) is true, and so is a solution of Eq. (15). The identities (5) and (6) of Note 313(4) are obtained from the identity (3) by cyclic permutation of the indices lambda, nu and rho. In the same way, these indices can be cyclically permuted in the Cartan identity (2).

Sent: 25/04/2015 16:17:03 GMT Daylight Time
Subj: note 313(4)

Eq.(1) is constructed in a way that the terms in each line come from
known identities, thus making their sum valid.
I do not understand why the new identities (4-6) should be valid in
general. These seem to be constructed from columns of eq.(1). In this
way their validity is sufficient to validate (1), but the conditions
(4-6) are not necessary to fulfill (1), it is not an equivalence relation.
Eq.(3) is the second Bianchi identity and valid independently.

Horst

There were 1,691 files downloaded from 421 reading sessions, main spiders baidu, google, MSN, yandex and yahoo. Evans / Morris papers 473, Scientometrics 238, F3(Sp) 225, Auto1 224, Auto 79, Eckardt / Lindstrom papers 187, Principles of ECE 170, UFT88 128, UFT311 119, Engineering Model 100, Evans Equations 79 (numerous Spanish), Llais 63, Proof One 58, Proof Five 19, Proof Two 18; Proof Four 17, Englynion (second book of poetry) 55, CEFE 52, UFT99 51, Autobiography Sonnets 21 to date in April 2015. Technical University of Kaiserslautern UFT81; Syddansk University Denmark Essay 24 on the derivation of the Pauli Exclusion Principle from the fermion equation; University of Colorado UFT177; Reed College Portland Oregon UFT166; University of South Dakota UFT110; Department of Chemical Physics Autonomous University of Madrid general; Ecole Polytechnique UFT8 (one of the selective and prestigious French Grandes Ecoles); University of Poitiers general; Universite de la Reunion (University of Reunion Island) 2D article; European Patent Office UFT81; Poznan University of Medical Sciences Main Library UFT309; Bilkent University Turkey AIAS Fellows. Intense interest all sectors, updated usage file attached for April 2015.

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Many thanks for going through this stuff. Sean Carroll lectured to Harvard graduates, then at UCSB, Chicago and Caltech. I will concentrate around Note 313(6) to extend the second Bianchi identity to include torsion. The expressions for the covariant derivative of any tensor and for the commutator of covariant derivatives acting on any tensor are given by Carroll in his chapter three, and in many UFT papers, giving much more detail than Carroll. The first Evans identity (the cyclical torsion identity) was discovered a few months after UFT88 in UFT109 and is an exact identity like the Jacobi identity and Cartan identity. The main theme of the paper is to show that the second Bianchi identity becomes completely different when torsion is included. It develops UFT88, UFT109, UFT255 and UFT281. As you know the Einstein field equation rests directly on the original 1902 second Bianchi identity without torsion, so the Einstein field equation is totally wrong. No longer does this statement generate waves of shock horror.

In a message dated 27/04/2015 10:35:58 GMT Daylight Time, writes:

Understanding these notes requires really some concentration. With your comments it becomes clearer now. Could you please resend notes 5 and 6, I do not have them at hand here today.

Horst

EMyrone@aol.com hat am 26. April 2015 um 08:52 geschrieben:

Eq. (15) of Note 313(2) is constructed from Eq. (14) of that note, which is an exact identity. So Eq. (15) is also an exact identity. Eq. (16) of that note is Eq. (105) of UFT255. It is assumed that Eq. (16) is a solution of Eq. (15). Adding Eqs. (15) and (16) gives Eq. (1) of Note 303(4), which shows that Eq. (16) is true, and so is a solution of Eq. (15). The identities (5) and (6) of Note 313(4) are obtained from the identity (3) by cyclic permutation of the indices lambda, nu and rho. In the same way, these indices can be cyclically permuted in the Cartan identity (2).

Sent: 25/04/2015 16:17:03 GMT Daylight Time
Subj: note 313(4)

Eq.(1) is constructed in a way that the terms in each line come from
known identities, thus making their sum valid.
I do not understand why the new identities (4-6) should be valid in
general. These seem to be constructed from columns of eq.(1). In this
way their validity is sufficient to validate (1), but the conditions
(4-6) are not necessary to fulfill (1), it is not an equivalence relation.
Eq.(3) is the second Bianchi identity and valid independently.

Horst

a313thpapernotes5.pdf

a313thpapernotes6.pdf

a313thpapernotes7.pdf

There were 3,127 files downloaded from 416 reading sessions during the day, main spiders baidu, google, MSN, yandex and yahoo. Evans / Morris papers 417, Scientometrics 236, Auto1 214, Auto2 73, F3(Sp) 212, Eckardt / Lindstrom papers 186, Principles of ECE 169, UFT88 124, UFT311 117, Engineering Model 95, Evans Equations 79 (numerous Spanish), Llais 62, Proof One 58, Proof Two 17, Proof Four 16, Englynion 55 (second book of poetry); CEFE 52, Autobiography Sonnets 17 (first book of poetry) to date in April 2015. University of Arizona UFT202; Harvard University general; Cambridge University Essay 15, General Relativity and Particle Scattering. Intense interest all sectors, updated usage file attached for April 2015.

Unauthorized

This server could not verify that you are authorized to access the document requested. Either you supplied the wrong credentials (e.g., bad password), or your browser doesn’t understand how to supply the credentials required.

Additionally, a 404 Not Found error was encountered while trying to use an ErrorDocument to handle the request.

Many thanks again for going through these difficult and very complicated calculations. The final version of the Jacobi method to be used in UFT313 is Note 313(6). In general the commutator [D sub mu,
D sub nu] is not zero, as you know, so covariant derivatives cannot be exchanged, in the sense that D sub mu D sub nu – D sub nu D sub mu acting on a vector or tensor is not zero. In other words they do not commute. Note 313(6) was the method used by Ricci and Bianchi. It took me more than twenty years of research to find this method, which is by no means obvious in any way. Ryder casually mentions that the method is obvious and Carroll gives no details. They both leave it to the student. I guess that no student ever went through it. In Eq. (1) the Jacobi identity acts on a vector. That is the first important point. Both Ryder and Carroll omit the vector. Considering the first term as in Eq. (2) the Leibnitz theorem is used. This introduces the commutator acting on a rank two tensor, D sub rho V sup kappa. The general formula for the covariant derivative acting on any tensor is Eq. (6), which is exceedingly intricate. Bianchi in 1902 omitted torsion and used Eq. (4). We know now that he should have used Eq. (3). Eq. (4) is simply wrong, because if torsion is omitted, mu = nu in Eq. (3) and the commutator and curvature both vanish, and gravitation vanishes. By now the enlightened colleagues worldwide have accepted this point. So Bianchi arrived at Eq. (5) in which the first term of the second Bianchi identity of 1902 can be seen on the right hand side, but a commutator term is subtracted from it. By reducing the general formula (6) this commutator term becomes the Ricci identity (8). This is not even mentioned in the the vast majority of textbooks, including Ryder and Carroll. No student could possibly have ever derived it. So by using the complete Jacobi identity the result (9) is obtained. Using the first Bianchi identity one finally arrives at Eq. (10), establishing the relation between the exact Jacobi identity and inexact torsionless second Bianchi identity. Note that there is summation of repeated lambda indices so the usual second Bianchi identity is a special solution. The actual result is equivalent to A dot B = 0. and obviously A = 0 is only one out of many possible solutions.Now restore torsion and the correct second Bianchi identity with torsion becomes eq. (20). This is named the Jacobi Cartan Evans identity to make it clear that torsion changes things entirely. We can use my cyclical torsion identity of UFT109, Eq. (21), to simplify this a little. I name this the first Evans Identity because it was missed completely during the entire Einsteinian era. Eq. (22) may be true in special circumstances, so I name that the second Evans identity. Then the JCE identity reduces to Eq. (23). There is no way that any student could ever have derived this result. Finally Note 313(7) gives the proof of the first Evans identity, first given in UFT109. I went through all the calculations again and checked everything. It relies on the exceedingly intricate formula (2) for the covariant derivative of any tensor. I think that the readership threw up when they saw this snowstrom of indices, but I like this identity very much, it is elegant and can be used to derive a cyclical identity of field tensors in electromagnetism and gravitation. It is most satisfactory to find that it is part of the JCE identity. When Grossmann told Einstein about the secoind Bianchi identity of 1902 it has already become cut in stone, and was already erroneously though to be exact (circa 1905). In fact it is totally wrong. So if people go on using it they would have left things to the student. Any lecturer can do that by not turning up at lectures.

To: Emyrone@aol.com
Sent: 25/04/2015 16:47:02 GMT Daylight Time
Subj: note 313(5)

Can two covariant derivatives be interchanged? The derivatives could
impact the contained Christoffel symbols/spin connections differently.

Eq. (15) of Note 313(2) is constructed from Eq. (14) of that note, which is an exact identity. So Eq. (15) is also an exact identity. Eq. (16) of that note is Eq. (105) of UFT255. It is assumed that Eq. (16) is a solution of Eq. (15). Adding Eqs. (15) and (16) gives Eq. (1) of Note 303(4), which shows that Eq. (16) is true, and so is a solution of Eq. (15). The identities (5) and (6) of Note 313(4) are obtained from the identity (3) by cyclic permutation of the indices lambda, nu and rho. In the same way, these indices can be cyclically permuted in the Cartan identity (2).

Sent: 25/04/2015 16:17:03 GMT Daylight Time
Subj: note 313(4)

Eq.(1) is constructed in a way that the terms in each line come from
known identities, thus making their sum valid.
I do not understand why the new identities (4-6) should be valid in
general. These seem to be constructed from columns of eq.(1). In this
way their validity is sufficient to validate (1), but the conditions
(4-6) are not necessary to fulfill (1), it is not an equivalence relation.
Eq.(3) is the second Bianchi identity and valid independently.

Horst

Agreed with this, the final version of this method is Note 313(6), which develops the Ricci identity.

To: Emyrone@aol.com
Sent: 25/04/2015 16:08:50 GMT Daylight Time
Subj: note 313(3)

In eq. (4) one could write the vector V outside of the commutators, then
the left-side operator could be avoided, but this is only a formal aspect.
The new identities are true “operator equations” because the derivatives
of the vector V they operate on have to be taken, reminds to quantum
mechanics.

Horst