**Subject:** The Fallacy of Negative Energy in the Dirac Equation

**Date:** Wed, 1 Apr 2009 10:04:51 EDT

The rest energy in the Dirac equation is taken directly from the classical rest mass equation, the famous:

E0 = m c squared

which quantizes to

E0 psi = gamma0 m c squared psi

where psi is the Dirac spinor and gamma0 is the zero’th Dirac matrix. Note carefully that teh unit 4 x 4 matrix is implied in this notation to multiply the left hand side term. Written in terms of the Pauli spinors phiR and phiL, and using:

E0 = i h bar partial / partial t

the E = m c squared equation becomes

i partial / partial t [ phiR ] = (mc squared / h bar) [phiL ] [ phiL ] [phiR ]

For a particle at rest there is no helicity, so

phiR(0) = phiL (0)

Note that it is nowhere indicated by these equations that m can be negative. Ryder asserts at the foot of his page 44 of the second edition of “Quantum Field Theory” (Cambridge 1996) that gamma0 has four eigenvalues, +1, +1, -1, -1, two indicating positive energy, two indicating negative energy. This obscure statement only makes sense if the negative energy comes fro the starting classical equation:

E = – m c squared = – h bar omega

So I think that the negative energy problem of the Dirac equation is pure mathematics with no physical meaning. The usual de Broglie equation is

E = m c squared = h bar omega

and angular frequency is radians per seconds, it does not make sense in physics to use a negative angular frequency. So there is no Dirac sea, and the vacuum is not filled with virtual particles. This has been the source of endless confusion throughout the twentieth century, leading to a great deal of nonsense physics. The Dirac equation in other respects is a triumph. ECE shows that it is the result of the tetrad postulate of Cartan geometry. The ECE vacuum is filled simply with the voltage density cA(0).

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