Dr Tony Fleming


There's now a new mathematics, Self-Field Theory (SFT) to test against the physical world in addition to the various quantum theories.  So this is 'the new kid on the block'.  One of the new features of this form of mathematical physics is that it does not use Lagrangians but rather uses what are called Maxwellians. In other words, this is a maths that is one degree of differentiation below the Lagrangian; essentially it is about fields and forces rather than potentials. I've italicized 'field' because it has been traditional to use the term field when we are actually talking about potentials; further, field has a special, reserved meaning in electromagnetics. Moreover, potentials should only be used in connection to wave equations and not where actually fields such as electric, magnetic, and acoustic fields are involved. So don’t get confused about what a field is in SFT, nor a potential.

So let’s look at the hydrogen atom. If we take the four Maxwell equations and add the Lorentz equation, we find we can solve this system of equations totally deterministically, no probabilities. The solution is closed form in the tradition of classical solutions. If we look at our equations, we have two curl and two divergence equations. We find the solution is a bispinor. The solution is the addition of two spinors. Note these are NOT the same as Dirac spinors that are unitary and used within the algebra of quantum theory. Here, a spinor is a physical entity, like a vector that rotates, for instance a particle motion. So we have a solution consisting of two rotating vectors. These two rotations are why relativity works when we come to studying the photon, but this is moving ahead of ourselves in this first blog.

To those of you who can remember your early mathematics, this is a solution to a system of partial differential equation of the first order. Even further back you studied the theory of general and particular solutions of such equations. Our solution is a form of particular equation that relates to a general solution. What is most intriguing about our 'general' solution in this case is that it turns out to be very general indeed it is fractal, so this is an imbedded series solution within a family of Maxwell-Lorentz (ML) equations. This fractal solution applies across physics. We find for instance that the gravitational field is a form of differential in relation to the solution to the EM solution to the atom we found above. But further, we find that the EM solution can be reformulated to apply to the other known forces. For instance we can form new Maxwellians. To which we must add new modified Lorentz equations. So similar to the way the Lagrangian can be modified to suit various arenas of physics, so too can the Maxwellian

There’s an intimate meaning to those four equations of Maxwell. We have two curl, two divergence, and now two rotations. Does this imply that one curl equation, and one div equation can be related to one rotation? What if we add a curl and a divergence, does this now refer to a third rotation? Is this what is happening inside the strong nuclear region of atoms? Yes. Our new Maxwellian and our new system of ML equations can be solved and depending on the parameters relating to the third set of curl and div equations, the equations are stable. So does this relate to the insights of particle physics? In brief, yes. But again we move too quickly for this first blog.

So if you’ve picked yourself up from the floor, and caught your breath about what you’ve just read, we’ll summarize. We’ve found a solution to the atom that is deterministic and another by modifying the ML equations that may apply to the nucleus, and another by taking a differential form of the ML equations to form a gravitational solution, involving dielectrics and diamagnetics.  All these solutions are deterministic rather than the probabilistic forms of quantum theory. Further, there’s a general solution in the form of a fractal that applies across physics from photon to multiverse and beyond.

So there you are. We are seeing a closed form family of solutions across physics.That’s where we’ll stop for today. Much more to relate as you can see.

Just to give you some insight into where we are at this point in time now with this theory, there’s reason to believe that the Earth’s magnetic flip is behind the ozone depletion, glacial melting, and climate change we are observing. We may be going through a flip right now, or maybe just the beginning of a large excursion.  This is related to the composite photon and the fact that at high energies, such as inside the Sun and the Earth, the internal state of the photon can change, in fact it can flip its inherent 'spin', its magnetic field. After we've spoken about some more theoretical matters such as uncertainty and determinism, Planck's 'constant', the speed of light and relativity, we'll talk about the composite photon, and some time down the track we'll get to Earth's magnetic flips.

For further information see

A.H.J. Fleming, EM Self-Field Theory: Electron and an 'Infinite Mass' Proton in Hydrogen Atom, Physics Essays, Volume 18, Number 3, September 2005, pp. 265-285 

A.H.J. Fleming, Self-Field Theory - a Mathematical Description of Physics, PIERS Proceedings, Marrakesh, MOROCCO, March 20-23 2011, pp. 1680 - 1683