**Subject:** Fwd: Helicity and Chirality in the Dirac Equation

**Date:** Fri, 17 Apr 2009 12:26:47 EDT

Excellent Myron, and I wonder in time if it will emerge that there are in reality only two elementary particles (electrons and positrons) that build up the quarks that make up the nuclei of atoms. This could explain the preponderance of electrons over positrons in nature (if more positrons have been used in making up the nuclei of atoms leaving relatively more freely detectable electrons). Whatever, our understanding is already improved and simpler and more easily accepted.

Best, Gareth

**Date:** Fri, 17 Apr 2009 07:54:58 -0400 **Subject:** Helicity and Chirality in the Dirac Equation

The helicity is sigma dot p and is part of gamma sup mu p sub mu in the Dirac equation, which in ECE is derived from geometry. For example sigma sup 3 p sub 3 is the helicity of an electron moving in Z. If the sign of sigma 3 is reversed then the helicity is reversed and gamma5 is reversed. This is because gamma3 is reversed while gamma0, gamma1, and gamma2 remain the same. Therefore helicity is directly related to chirality. It is well known to chemists that reversing the chirality of an optically active molecule produces a different molecule. So reversing the chirality or helicity of an electron produces a different elementary particle, called the positron. The electric charge must be reversed to conserve CPT. It is thought that CPT is always conserved in elementary particle theory. Note carefully that for the same helicity in the Dirac equation, there are right and left Pauli spinors. Therefore the spin up and spin down electron are described by the right and left Pauli spinors for constant sigma1, sigma2 and sigma3. The spin up and spin down electron states are observed in the Stern Gerlach experiment, ESR, NMR, MRI, Zeeman effect, spin orbit coupling, Fermi Dirac statistics, Pauli principle and so on, and are the two spin half states of the same particle (the electron). ESR, NMR and MRI, the Zeeman effect and so on are described by resonance between the two states of the third Pauli spinor sigma3. Obviously this process occurs for the electron. This process does not involve the positron. The Lande factor of 2 from the Dirac equation also does not involve the positron, the essential origin of this factor 2 is the algebra of the Pauli matrices as explained in the book by Crowell and myself on the Omnia Opera of http://www.aias.us. So in order to generate the positron, the sigma3 matrix is reversed. This reverses the helicity for the same direction of momentum. So P is changed but T is not changed, meaning that C must be changed. All this in ECE comes from geometry.

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Interesting suggestion, experimentally, as in Ryder page 21 ff of the second edition, an electron and positron annihilate to form quarks, which combine with other quarks and antiquarks to give hadrons of all types. This uses virtual photons and the Feynman method. However I want to avoid all that because of its indeterminacy and complexity, and loose parameters. Also, paper 85 does not give any confidence in the claims of QED to accuracy. In the standard model the electron is a “point particle” with no substructure. IN ECE there is no point particle, there is a finite volume for ever elementary particle. The point particle idea leads to infinities which are removed with the amazing gymnastics of renormalization. It is claimed that the electron and positron annihilate on collision to form quarks through virtual photons, but we now know that this has all kids of problems. Neither the electron nor the positron is made up of quarks, yet they are said to annihilate to give quarks. In the old standard model, electrons are cerated by big bang and Hawking radiation at the event horizon of a black hole. In the development of ECE we have shown all these ideas to be basically incorrect. So I decided to go right back to the start and thoroughly reinvestigate the Dirac equation itself to start with. ECE is now widely accepted, so we are at the start of a new physics. Your ideas are as good as anyone’s. If the basics are wrong, as we no know them to be, there is no point in further elaboration fo teh dogma. That reduces physics to party political manifesto. The Dirac equation is not taught very well, so I decided to write it out in full detail. The results are surprising, the concepts as taught do not clearly emerge, and one exameple is the Dirac sea, which does not exist in Baconian science. There seem to be all kinds of contradictions if oen goes into things thoroughly.