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Dirac's wave equation is a relativistic generalization of the Schr?dinger wave equation. In 1934 this brilliantly successful equation was shorn of half of its solutions by a questionable bit of mathematical slight-of-hand. Because it was ?politically correct,? this bit of juggling became the accepted interpretation. However, recent developments have shown the very basis of this mathematical trick to be invalid, in that it would involve massive violations of conservation. A reevaluation is therefore warranted. The Schr?dinger wave equation has been said to ?contain most of physics and all of chemistry.? Since Dirac's equation is a relativistic generalization of this already generally applicable wave equation, in formulating it Dirac expected that its solutions would describe ?everything that waves.? Since all matter and energy evolve as waves, Dirac thought his equation would be a unitary ?theory of everything.? However, the discovery of several new particles and peer criticism resulting in the truncation of the equation frustrated this expectation, and it is generally known at present as ?Dirac's equation of the electron.?

We have seen the power of Dirac's equation, when all of it is taken seriously. In a sense, though, Dirac took it even more seriously. It is not an equation of the electron, as it is popularly called. It is a relativistic generalization of the Schr?dinger wave equation, which is said to ?contain most of physics and all of chemistry.? Dirac thought of it as a Theory of Everything?he thought that its solutions should include ?everything that waves,? i.e. every possible particle. As he was deriving it, he hoped it would have only one solution - the one, unitary particle out of which everything could be made (Dirac, 1933). Then, when he found that it had multiple solutions, he thought that one of its solutions must be the proton?as at that time, the proton and the electron were the only known particles, and it was fervently believed that they were the only particles. This is why Dirac, in several of his early attempts to use the equation, entered in as the mass the average mass of electron and proton (Pais, 1994). This didn't work, convincing him that the other ?real? particle (the other positive energy one) had to have the same mass as the electron, but the opposite charge. Thus he predicted the positron, but gave up his dream that his equation was a ?Theory of Everything.? (Of course the discoveries of the neutron and the positron, and the conviction that the photon also was a particle, didn't help any.)

Dirac's wave equation is a relativistic generalization of the Schrodinger wave equation. In 1934 this brilliantly successful equation was shorn of half of its solutions by a questionable bit of mathematical slight-of-hand Because it was "politically correct" this bit of juggling became the accepted interpretation. However recent developments have shown the very basis of this mathematical trick to be invalid, in that it would involve massive violations of conservation. A reevaluation is therefore warranted.

Since Dirac's equation is a relativistic generalization of an already generally applicable wave equation, in formulating it Dirac expected that its solutions would describe 'everything that waves' - that it would be a 'unitary theory of everything'. However the discovery of several new particles and peer criticism resulting in the truncation of the equation frustrated this expectation, and it is generally known at present as 'Dirac's equation of the electron'.
Dirac's complete equation describes a quantum spinor field, which has as solutions four different kinds of electron: electrons and positrons of positive energy, and electrons and positrons of negative energy. This equation generalizes an already general wave equation: therefore, as shown herein, the equation directly predicts that 'everything that waves', i. e. the entire physical universe, can be made from these four kinds of electron. This study indicates this to be the case: all matter and all fields and forces seem to be necessary combinations and applications of just these four kinds of electron, fulfilling Dirac's unitary expectation.

As this is obviously a Work in progress, any comments, criticisms, or corrections that you might care to offer are both welcome and solicited.