Since 1927 quantum theory has incorporated Heisenberg’s Uncertainty Principle with its  probability densities.  Associated with these is the Copenhagen interpretation that teaches that quantum theory does not give a description of reality but deals only with the probabilities of observing, or measuring,  energy quanta that do not fit the classical wave-particle model.  According to quantum theory the act of observing or measuring causes the set of probabilities to instantly and randomly ‘collapse’. This is termed wavefunction collapse and was devised by Niels BohrWerner Heisenberg and others in the years 1924–27. While there have been other physical interpretations this is the most accepted concept amongst quantum physicists.

One of the amazing facts about Self-Field Theory (SFT) is that it does away with uncertainty, to be precise Heisenberg’s Uncertainty Principle (HUP).  The spinorial solutions are deterministic, no need for probabilities. There’s a whole lot of history in this.  But first let’s put the facts out there.

The history of quantum field theory (QFT) began with the evolution of Schrödinger’s non-relativistic equation to Dirac’s relativistic equation. Schrödinger expressed the phase of a plane wave as a complex factor (2a). The Klein-Gordon equation (2b) is a relativistic version of Schrödinger’s equation. Using Feynman notation (2c) we see how the Klein-Gordon equation can be analytically factorized to yield the positive and negative energy versions of the Dirac equation (2d) where the are  bispinors. Dirac thus predicted the electron’s anti-particle the positron via these equations.  Although Dirac’s equation is first-order it is derived from a second order wave equation and it is this that demands gauge symmetry and invariance under conformal transformations.

Schrödinger’s equation

Klein-Gordon Equation:


Dirac Equation(s):



Looking at the problem of a system of over constrained equations take the case of a linear system of equations  Amn where m>n e.g. m=4 and n=3


The system is over constrained and there are no solutions. However we can instead solve the over constrained case by choosing a metric for instance least squares, the Pythagorean distance, to minimize the error. This example is a direct analogue to the case of quantum theory where uncertainty is present and the photon is modeled without taking its internal structure into account.


Occam’s Razor says choose the hypothesis that offers the simplest explanation of the effect. There are a number of similar physical situations like this one when we come to choosing the simplest hypothesis, either quantum probabilities or some alternative physical reason. For instance quantum theory teaches that the double slit experiment,  the EPR thought experiment, Shrodinger’s cat,  are all demonstrations of the way quantum theory makes  choices out of a selection of possibilities.

So (a) is the Copenhagen Interpretation correct or (b) are the equations of electromagnetics over constrained?  According to Occam’s razor there is no choice, the equations of electromagnetics must be over constrained, otherwise we must choose a physically marginal reason about the way probabilities occur.


What does it mean then that the equations of electromagnetics are over constrained? It means we are missing an ordinate similar to the case shown in (2). In the case of the Maxwell's equations we need another ordinate, and here the obvious way to go is to choose another radius.  This was the reason for the bispinorial solution form chosen in Self-Field Theory.


for further information see

A.H.J. Fleming, Self-Field Theory – New Photonic Insights, PIERS Proceedings, Xi'an, China, March 22-26, pp. 644 - 647  

A.H.J. Fleming, V. N. Matveev, O. V. MatvejevSelf-Field Theory and General Physical Uncertainty Relations, PIERS Proceedings, Marrakesh, MOROCCO, March 20-23 2011, pp. 1689 - 1692