Alpha Institute for Advanced Studies

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1) Negative energy is not meaningful and the ECE fermion equation produces positive energy.
2) The fermion equation produces the Lande factor of the electron (g = 2) more simply than the Dirac equation and without negative energy.
3) Half integral spin is intrinsic to the fermion equation.
4) The anti fermion equation is produced by parity inversion.
5) The wave equation with ECE spinor is an example of an ECE wave equation in the general spacetime, and part of a generally covariant unified field theory.
6) The complete details in the notes show that all calculations are correct

a172ndpapernotes6.pdf

M. W. Evans and L. B. Crowell, “Classical and Quantum Electrodynamics and the B(3) Field” (World Scientific, 2001) (see Omnia Opera of www.aias.us).

The value of 2 is in fact an approximation of relativistic quantum mechanics and is not exact. It is also changed by the well known radiative corrections. The next note will deal with the probability current of Dirac.

a172ndpapernotes7.pdf

c (p squared) power half = c modulus p bold = (E squared – m squared c fourth) power half

which is the Einstein energy equation with POSITIVE root (no negative energy). The Einstein energy equation of special relativity is a restatement of the relativistic momentum (p = gamma mv) and is

E squared = p squared c squared + m squared c fourth

or

p sup mu p sub mu = (mc) squared

Dirac was once interviewed and asked whether the general public would understand relativistic quantum mechanics, and he said: “No”. When asked why he did not predict the positron he answered “pure cowardice” (this is another standard model myth, the positron was predicted by Oppenheimer after some remarks by Weyl. Dirac had done all the dogwork however and played it safe when he predicted the proton as the antiparticle of the electron. Understandable in view of the way some people dislike new thought and knee jerk to ad hominem attacks). Even a Lucasian Professor does not like that, and come to think of it, neither does a Civil List Scientist. My colleague Grigolini met Dirac when he was an old man in Tallahassee, Florida. More accurately he saw him studying in the library but was too shy to talk to him.

(d’alembertian + R) psi = 0

This can also be interpreted as a Proca equation for the boson, or the Klein Gordon equation for the spinless particle, and also as a Majorana equation. The usual Dirac equation is obtained by rearranging the 2 x 2 psi in to a 1 x 4 psi and factorizing the d’alembertian with Dirac matrices. Finally take the limit of R = (mc / h bar) squared to obtain the original Dirac equation. The ECE fermion equation of UFT 129 and 130 shows that the fermion equation can be written as a first order equation with a 2 x 2 psi (see also notes for UFT 171 and the forthcoming UFT 172). The 2 x 2 psi is obtained from the definition of the tetrad as a matrix linking 2 spinors (column 2 vectors) in two different representations: 1) R and L; 2) 1 and 2. Similarly the tetrad for electromagnetism is defined as the 4 x 4 matrix linking two four vectors, one in (0), (1), (2), (3) rep, the other on 0, 1, 2, 3 rep. Similarly we can define the tetrad in any SU(n) rep space, or any rep space. This gives a generally covariant unified field theory based on geometry and the philosophy of relativity. The tetrad in ECE is more broadly defined than in the original work of Cartan, which used a tangent Minkowski spacetime labelled a at point P to a base manifold labelled mu.

A = (omega sub 2 + omega sub 1) (omega – omega sub 2) /
(( omega squared – omega sub 0 squared) power half cos theta)

This note was not used for paper 171, in which all hand calculations have been checked for correctness by computer by co author Horst Eckardt.