I agree with these points, for the free particle, E = T, thi sis just a matter of notation. It is clear from page 5 that the velocity appearing in gamma is the Newtonian velocity, see the steps in Eq. (38), page five. I also agree that it does not come from a classical analysis. It comes form the relativistic Minkowski metric as described for example in Marion and Thornton. So the theory is rigorously self consistent and also consistent with the lagrangian theory.
To: EMyrone@aol.com
Sent: 30/08/2015 20:56:45 GMT Daylight Time
Subj: Re: 326(5): Final Version of Note 326(4)In eq.(15), E is obviously the total energy without rest mass, in contrast to (5).
eq.(24): hbar squared kappa squared
eq.(25): wouldn’t it be better to write mT intead of mE? E is without restmass again here.
eq. (29) allows computing the relativistic kinetic energy if the classical kinetic energy T_0 is known:T_0 = 1/2 (1+gamma)/gamma^2 T
or
T = 2 gamma^2/(1+gamma) T_0.However this is not a self-consistent procedure, see below:
Eq.(32) can be written with the classical momentum p_0 but this does not mean that this comes out from a non-relativistic theory. This is rather a “back-transfomation” to a non-relativistic case from a self-consistent relativistic solution of quantum or Lagrange equations. We solved them in paper 325 for example.
Considering the limit gamma –> 1 gives the correct non-relativistic limit, that is o.k.
Horst
Am 30.08.2015 um 15:07 schrieb EMyrone:
I went through my calculations again and found that the correct free particle quantization equation is Eq. (29) with gamma defined by Eq. (32) and the de Broglie wave particle dualism by Eq. (33). So these equations can be solved by computer algebra to give E in terms of p sub 0, the classical momentum, and kappa. The cross check on page (5) confirms that everything is self consistent. Having gone through this baseline calculation the particle on a ring and H atom can be defined in a relativistic context. The answer to the computer algebra must be:
E squared = (h bar kappa c) squared + m squared c fourth
so this gives a check on the results of the computer algebra. The fermion equation for the free particle is therefore Eq. (29) where gamma is given by Eq. (32). and where the de Broglie wave particle dualism is given by Eq. (33). Although these equations look like familiar special relativity they are the quantization of the ECE2 Lorentz force equation.