The Gospel according to Mathew is thought to be based largely on the gentile Mark (written about 60 A. D onwards). So my ancestor St. Eurgain would have been acquainted with teachings of St. Paul in Rome around about 40 to 50 A. D. This kind of teaching would have been taken back to modern Llan Illtud Fawr near Cardiff in an era when the Druidical teaching had predominated already for several thousand years. If a Llan has a circle of yew trees around it, it is Druidical. Yew trees around the Llan (later the Norman church) at Defynnog have been dated to more than five thousand years old. So the very earliest Christian teaching arrived in Wales with St Eurgain ferch Caradog ap Bran (daughter King Caratacus son of Bran (The Raven King).
This new interpretation is that v sub 0 of the Lorentz factor gamma is bounded above by Eq. (12), i.e. v sub 0 of the Lorentz factor is bounded above by c / root2. This allows the Poincare / de Broglie / Vigier photon mass to be alwys non – zero, and immediately gives the correct light deflection due to gravitation, Eq. (13), without use of general relativity. These are major advantages over the usual interpretation, which allows v sub 0 of the Lorentz factor to go to c, so that gamma becomes infinite and unphysical and forces the mass of a particle movng at c to vanish, again an unphysical result. In the usual interpretation the relativistic momentum of the massless particle becomes indeterminate, the well known hyper-relativistic limit, generated by v sub 0 goes to c. So we arrive at a new fundametal axiom of special relativity:
The maximum velocity that can be attained by v0 squared of the Lorentz gamma factor is c squared / 2.
With this axiom a particle of finite mass can travel at c, and the photon may have mass as postulated by Henri Poincare in 1905, a hundred and ten years ago. The axiom immediately gives the correct experimental light deflection by gravitation using special relativity, and allows the massive photon to travel at c for all practical purposes.
This book has been very influential, Merzbacher became chair of physics at UNC Chapel Hill, and my have attended my lecture, circa 1992 / 1993. on B(3). It was very useful for quantum tunnelling theory applied to LENR in UFT226 ff.
This is highly recommended reading at advanced level. Note 326(6) is typical of the kind of notes I used to prepare on classical mechanics at UNCC at honours and masters level. The students liked my teaching because my first wfe and I worked hard to typeset all slides. Eugen Merzbacher (1921 – 2013) was born in Berlin and emigrated to Turkey in 1935 to escape persecution. He earned a Ph. D. at Harvard and worked at the Princeton Institute. He died in 2013 in Chapel Hill, North Carolina, where I lectured on B(3) to UNC Chapel Hill. There were no objections to the then radically new concept from some of the best faculty in the States. Horst and I checked Merzbacher’s calculations on quantum tunnelling with computer algebra and they are correct in all detail. Atkins’ calculations on the same subject are incorrect, and severely so. In the book by Kerry Pendergast, “The Life of Myron Evans”, Merzbacher appears in a group photograph with Dirac at the invitation of Prof John B. Hart at Xavier University Ohio. John B. Hart was one of the international referees for my Civil List Pension, all the documents on which are posted for historical resons.
I worked out everything in Note 326(6) after thinking about your comments. The end result is completely clear and self consistent, the clearest format for quantization appears to be Eq. (39) of Note 326(6). I decided to skip the early 1913 Sommerfeld quantization and to go to Schroedinger / Dirac quantization. The overall idea is to remove the crude approximations used by Dirac. He got the right result but by using approximations like gamma m c squared = m c squared as in our previous UFT papers. The complete quantization and solution of the Dirac H atom is very complicated as you know, and gives the right energy levels except for radiative corrections (Merzbacher, “Quantum Mechanics” (second edition Wiley, kindly sent to me by Alwyn van der Merwe some years ago). The Sommerfeld atom does not give the right energy levels of the H atom, but is of course of great importance historically. It is now known that the Sommerfeld orbitals must be related to your precessing ellipses of UFT324 / 325. That route could be pursued using various quantization schemes. We could also develop relativistic LENR with note 326(6) using relativistic quantum tunnelling theory. The number of ideas in ECE2 are endless.
Sent: 01/09/2015 10:41:38 GMT Daylight Time
Subj: AW: Discussion of 326(5), Part Two
Ps: would it make more sense to compute the inverse functio p0(E) for quantization?
Von meinem Samsung Gerät gesendet.
Thanks again and fully agreed, I clarified everything in Note 326(6).
Sent: 01/09/2015 10:08:29 GMT Daylight Time
Subj: Re: Discussion of 326(5), Part Two
My critique was related to a relation of E in dependence of kappa which is not possible.
The dependence E(p0) can be calculated, see attachment.
Am 31.08.2015 um 11:29 schrieb EMyrone:
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
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
Fully agreed, I have just sent over a set of notes on the subject meant to give all details. I also solved for p0 in terms of kappa and found a new relativistic Compton wavelength in the sense that this is not usually written out in textbooks.
Sent: 01/09/2015 10:01:01 GMT Daylight Time
Subj: Re: The Velocity of the Lorentz Factor
yes, there is only one velocity, and in a relativistic framework it is a bit confusing to speak of a Newtonian velocity which by definition here is the same as the relativistic one in the observer frame.
Am 31.08.2015 um 11:48 schrieb EMyrone:
This is defined directly from the Minkowski metric as is well known, so it is the velocity in the observer frame, v. Perhaps I should describe it in this way instead of as “the Newtonian velocity”. However the two velocities are the same. The velocity of the particle in the ticked frame which moves with the particle is zero. The time in the ticked frame is the proper time tau, so we get
c squared dtau squared = (c squared – v squared) dt squared.
and gamma = dt / dtau = (1 – v squared / c squared) power minus half = gamma. The time in the observer frame is t, and the ticked frame moves with respect to the observer frame at v. The observer frame is the frame in which v is non zero. In a Newtonian context the Galilean transform applies and
dr’ squared = dr squared
In special relativity the Lorentz transform applies and
c squared dt’ squared – dr’ squared = c squared dt squared – dr squared
dt’ squared = dtau squared
the infinitesimal of proper time.
This note is a baseline calculation for the next note on the relativistic H atom, carried out for the free particle, and calculated without the crude approximations used by Dirac and contemporaries. Note carefully that this development is part of ECE2 generally covariant unified field theory, which is Lorentz covariant so all the equations of special relativity can be applied. The note gives detailed derivations of all aspects of special relativity and demonstrates complete and very well known self consistency in many ways. This is not surprising because these equations are those of special relativity. The notes show how the Lorentz gamma factor is derived and derives all the main equations of special relativity in detail. The velocity of the gamma factor is derived in complete detail. A relativistic velocity is nowhere used. The velocity of the Lorentz factor gamma is the non relativistic velocity of the observer frame, as is very well known. The main result is that the Compton wavelength is changed to Eq. (44) for a relativistic particle, and this equation can be graphed. The classical momentum / wave number relation of de Broglie for a relativistic particle is Eq. (54) and this can also be graphed. The calculations can be extended to the rotational relativistic particle on a ring straightforwardly. The next step in the next note is to extend them to the relativistic H atom but without using the rough approximations used by Dirac. The latter did very important work of course, but no one really knows why his rough approximations work. For example he approximated E = gamma m c squared by the rest energy m c squared. In the age of computers that need not be done any longer. This note removes that approximation for the free particle. I have been very careful to distinguish between the classical momentum p0 and the relativistic momentum p. Chemists and engineers should study this note carefully. In the main part, they will not be familiar with the concept of the relativistic momentum, nor of the Lorentz transform. My Ph. D. supervisor knew nothing about special relativity at all, so could teach to a certain point but no further. Nevertheless he was considered to be a distinguished chemist.
There were 2,313 hits from 338 distinct visits, main spiders baidu, google, MSN and yahoo. The following records how many times the following selected items of particular interest to me were read in August 2015. Collected Scientometrics 681, F3(Sp) 655 (chapter three in Spanish translation by Alex Hill of “The Evans Equations” on Quantum Theory), The 26 Evans / Morris papers 620 (estimated at 20 a day), Collected ECE2 papers 518 (UFT313-320, UFT322 – 325), Autobiography volumes one and two 336, Barddoniaeth / Collected Poetry 311, Eckardt / Lindstrom papers (UFT292 to UFT299) 220, Proofs that no torsion means no curvature and no gravitation and complete refutation of Einsteinian general relativity 197, The Principles of ECE (UFT281 – UFT288) 194, UFT88 136, “The Evans Equations of Unified Field Theory” by Laurence Felker 131 (UFT302); Translation of Welsh language newspaper article by Dewi Lewis in “Llais” 102, “The ECE Engineering Model” collected equations collated by Horst Eckardt) 101, UFT311 (first circuit paper) 85, “Criticisms of the Einstein Field Equation” (UFT301) 74, UFT321 (second circuit paper) 63, UFT322 57, UFT320 54, UFT318 52, UFT319 50, UFT314 45, UFT317 44, UFT324 43, UFT323 40, UFT313 39, UFT316 38, UFT315 34, UFT325 22 for August 2015. University of Rostock Edyn3, Istella Media Italy general, extensive private spidering, Izhevsk region general. Intense interest all sectors, usage file attached for August 2015.
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.