April 26, 2015
To Trustees, Newlands Family Trust,
I will discuss the maintenance of this historic 1839 chapel with the Treasurer on Thursday, in particular the donation of funds to maintain the building, grounds and graveyard. It is more or less a family chapel (Jones, Hopkin, Havard) and I also think that all the chapels in Mawr should be Grade A listed by CADW and rigorously protected. If volunteers could help clean up the grounds and graveyard it would be much appreciated, but I can discuss finding a gardener to do this. Precious heritage such as this should always be kept in pristine condition and never sold. I think that legislation should be introduced to prohibit people living in chapels and churches. Many people think that this is not right. The Italians would not allow anyone to live in the Pazzi Chapel in Florence for example. The French would not allow anyone to live in Chartres or Vezelay. I think that the Llan Giwg Community could work with Elim to make use of it for readings of cynghanedd and so on, and of course for the traditional Welsh Baptist service and singing. All these traditions should be revived. I think that an ecumenical line of thought is needed, otherwise the entire culture will disappear.
April 26, 2015
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 second Bianchi identity of 1902 it had already become cut in stone, and was already erroneously thought 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.
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.
April 26, 2015
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.
April 26, 2015
Agreed with this, the final version of this method is Note 313(6), which develops the Ricci identity.
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
April 26, 2015
Agreed with this, the main purpose of UFT313 is to check UFT255, Eq. (105) and to show that when torsion is considered the Einstein theory becomes unworkable, the entire twentieth century in general relativity becomes meaningless. This series of papers started of course with the famous UFT88. The second Bianchi identity with torsion can give a field equation which may be worth developing, but the ECE field equations based on the Cartan identity (UFT303) are far simpler and more powerful, and by now highly developed. What is more, the entire world of enlightened science seems to agree.
Sent: 25/04/2015 15:05:37 GMT Daylight Time
Subj: note 313(2)
This note is more clear than the previous one. The second Bianchi
identity (16) is combined with (14) which is derived from the first
Field equations can be derived, but the curvature terms in (20) remain.
It could be that they can be related to the charge and current densities
as defined in earlier work. In (19) you used the second Bianchi identity
without additional terms from (17), this is reasonable, otherwise it
would unnecessarily complicate the new field equations.
April 26, 2015
OK many thanks, in Eq. (26) second terms, left hand side, there is a typo, mu should be lambda. The final version of this note is 313(2).
Sent: 25/04/2015 14:37:01 GMT Daylight Time
Subj: note 313(1)
In eq.(27) you added the second Bianchi identity (with torsion) and the
three equations (26) directly obtained from the first Bianchi identity
by covariant differentiation. This is correct. However you did an index
permutation. I cannot verify this. For example the third term of (26)
D_mu D_nu T ^kappa_rho mu
should correspond to the fifth term in (26):
D_mu D_nu T ^kappa_rho lambda.
In the first case there is a common index mu, in the second case not.
How did you do the permutation?
April 26, 2015
There were 2,246 files downloaded from 432 reading sessions during the day, main spiders baidu, google, MSN, yandex and yahoo. Evans / Morris papers 404, Scientometrics 225, F3(Sp) 208, Auto1 207, Auto2 71, Eckardt / Lindstrom papers 184, Principles of ECE Theory 168, UFT88 123, UFT311 116, Engineering Model 92, Evans Equations 79, Proof One 54, Proof Two 17, Proof Five 17, Proof Four 16, Proof Three with Additional Notes 13, Llais 60, CEFE 52, Englynion 51 (second book of poetry) UFT99 48, Autobiography Sonnets 17 (first book of poetry) to date in April 2015. Russian Federal Nuclear Centre UFT282; Institute of Atomic and Molecular Sciences Academia Sinica Taiwan AIAS Fellows; University of Kent UFT18. Intense interest all sectors, updated usage file attached for April 2015.
April 25, 2015
All 312 UFT items on www.aias.us hit the coveted number one spot on Google and this is indeed a phenomenon, as mentioned by Simon Clifford. Often a UFT item holds the top four or five positions on Google. There are about two hundred Google criteria, the most important are: high quality, a popular page and website, relevance of the keywords. Google has a careful quality control filter which filters out bad websites. The wikipedia site on ECE has been ignored and / or refuted many many times over. So AIAS cannot be doing any better, and congratulations to all staff. Many people would give their eye teeth to be on Google’s page one.
April 25, 2015
This is the cyclical torsion identity, Eq. (1), first discovered in UFT109. It is conveniently named the first Evans identity to distinguish it from the first Cartan Evans identity in four dimensions, Eq. (15). In electrodynamics and gravitation it becomes a cyclical identity between field tensors. As shown in Note 313(6) it is part of the Jacobi Cartan Evans (JCE) identity. The second Evans identity is Eq. (18), which is true if and only if there is a special relation between curvature and torsion, Eq. (20). So the final JCE identity is Eq. (22). The first Evans identity (23) of all tensor analysis and any kind of geometry is true in any mathematical space of any dimension. There does not appear to be a way of proving Eq. (18) in general, but with further analysis this may turn out to be the case. It is clear that the 1902 second Bianchi identity used by Einstein in 1915 is not true in general because of its neglect of torsion. So the entire Einsteinian era becomes obsolete – van der Merwe’s post Einsteinian paradigm shift. There are many well known scientometrical indications that this great paradigm shift in physics has been accepted worldwide. Not often in mathematics are new identities discovered. So it is well worth naming them as an explorer would name a newly discovered land. After all, my ancient uncle Olaf was a Viking. a313thpapernotes7.pdf