From my perspective, a physical theory must be elaborated exclusively from experimentally obtained information, like for example, Newton's Theory, Maxwell's Theory, and Planck's concept of the quantum of action.

In the course of the past 100 years, all stable physically scatterable elementary particles, namely, the electron, the positron and quarks Up and Down , as well as all of their physical properties, have clearly been identified.

The observation that gravitation has not yet been explained, in spite of these verified findings, led me to suspect, like many others, each for a variety of reasons, that something very fundamental may have been misunderstood or neglected in fundamental physics.

This suspicion caused me to reconsider the accepted space geometry and to carefully reexamine what properties of particles had positively been verified, an exercise that led me to elaborate this theoretical solution, which is based exclusively on the objectively verified properties of stable fundamental particles.

Retrospectively, I find that the acceptance as physical theories instead of as simple handy mathematical tools, of Quantum Electrodynamics, which introduced the idea of virtual photons, and its direct offshoot Quantum Chromodynamics, which extended the concept of virtual photons to virtual particles, was a determining factor in the neglect during the past half century, of the importance of the Coulomb interaction at the fundamental level, because it generalized the perception that pseudo-quantized virtual entities could physically represent the Coulomb potential which is progressively induced between real particles during scattering and high energy collision events, as an inverse function of the square of the distance between the interacting particles.

I also believe that the general acceptance of the static Lagrangian method instead of the dynamic Hamiltonian method as suggested by Feynman in the framework of his definition of QED, has been instrumental in a loss of interest for the fact that scattering and collisions between particles are precise temporal sequences of events.

Feynman's conclusion that the use of the Hamiltonian was forcing the adoption of the field viewpoint rather than the interaction viewpoint is unfounded in my view, because it can easily be argued that a relative interaction between particles can be nothing other than simultaneous and mutual, just as in the field viewpoint.

If, as Feynman suggests, the Coulomb interaction is mediated solely by an exchange of virtual photons between the particles involved, the following questions jump to my mind:

• 1) How can mutual interaction be initiated if virtual photons are the sole mediators of the interaction, since a photon must first be emitted by one particle before it can be absorbed by the other?
• 2) What causes one of the particles involved to emit the first virtual photon of the exchange, and how is the direction of its emission determined?

I see an obvious causality problem here, because a mediation of the exchange by virtual photons as proposed by Feynman mixes two fundamentally very different aspects of the relation between particles:

• 1) the Coulombian interaction itself, or "Coulomb force", or "electrostatic force", whose nature and origin are still a mystery, which acts as a function of the inverse square of the distance between charged particles, and which is the cause of the acceleration of the particles towards, or away from each other (or should we rather more precisely say, which is the cause of the induction of an energy of motion in the particles that naturally manifests its presence by a change in velocity of the particles if no external constraint partially or completely prevents such a change in velocity);
  
  
• 2) and the unquantized quantity of energy of motion which is progressively induced between the particles as a function of the distance between them, whether or not a change in velocity occurs, and whose quantized form constitutes the very substance of all existing particles.

There is also the problem that virtual photons are by definition discrete quantities which seem to imply that the potential is induced in discrete increments between the particles, which is in direct contradiction with the fact that the quantity of energy of motion is progressively induced at any distance as a function of the infinitely progressive inverse square law of the distance.

Scattering and collision events not actually being physically instantaneous, I also think that there are good reasons to question Feynman's opinion when he declares, and I quote:

"In many problems, for example, the close collisions of particles, we are not interested in the precise temporal sequence of events. It is of no interest to be able to say how the situation would look at each instant of time during a collision and how it progresses from instant to instant." ([6], p.771)

Needless to say that I deeply disagree with Mr. Feynman, because this research philosophy has induced the respectful following generations of physicists to refrain from exploring the only remaining unexplored frontier in fundamental physics for the past 50 years:

A further argument supporting the view that virtual photons cannot be a physical reality, is Bohr's own observation that the quantized states of atoms being stable, these states can be accompanied by no radiation whatsoever, and that the existence of such non-radiating states is conform to the idea of quantic stability ([1], p.134). I also fully agree with de Broglie that the existence of quanta implies an inferior limit of a very special nature to the perturbations that can exist in the systems considered ([1], p.20).

Consequently, the perception that radiation could be emitted by electrons on rest orbits, for example, by means of virtual photons or otherwise, appears to be in direct contradiction with the very foundation of quantum mechanics, because Bohr's and de Broglie's observations seem to imply that some threshold of local excess intensity of energy relative to the local Coulomb potential equilibrium level must be reached or exceeded before a photon can be emitted; the reaching of such a threshold initiating the conversion to photon state and evacuation from the system considered of the measured portion of locally excessive unquantized potential that will allow the local equilibrium to be reestablished.

In view of the possible existence of such a relative quantization threshold , the physical existence of virtual photons as mediators of an interaction which results in the induction between the particles involved, of an energy potential which is unquantized by definition, simply due to the fact that its local relative intensity has not yet reached that threshold, appears highly questionable to me, except as a convenient mathematical artefact.

Regarding Maxwell's geometry, the most elaborate description that I ever came across of the space geometry that must underlie Maxwell's Theory simply states that a magnetic field and an electric field orthogonally intersect each other and that both of them intersect the direction of motion of the energy in space at right angle.

Given that such wave energy, if it existed as such, would expand spherically in space, and although I never saw this point being emphasized, it eventually became obvious to me that contrary to the generally accepted view, the orthogonally intersecting magnetic and electric fields envisioned by Maxwell may not reside within our 3-dimensional space as we know it, since their intersection would appear to be better defined as being orthogonal to space itself, as we will soon see. The logical conclusion I drew was that they hinted at the existence of some as of yet unexplored extra-spatial dimensions.

To more easily visualize Maxwell's geometry, given that is seems impossible for us to visualize more than 3 dimensions at a time, I then took to the habit of mentally folding the 3-dimensions of normal space as if they were the ribs of an open three-rib metaphorical umbrella. This allowed me to view the whole geometry as if I was considering a normal 3-axes Euclidean geometrical system, the x-axis representing the magnetic field, the y-axis, the electric field, and the plane determined by the x and y axes moving at the speed of light along the z-axis, which represents normal 3-D space.

Having applied the "umbrella" idea to the normal space axis, the further step of eventually extending the idea to the other two axes was easily taken, thus defining an intriguing geometry of three orthogonally coexisting spaces, each of which internally possessing 3 dimensions, a metaphorical mental "Rubik's cube" that I became very found of playing with, opening and closing one at a time as needed, the little umbrellas to continue being able to easily visualize the whole geometry. Of course, this mental opening and folding of "umbrellas", has no impact on the real spaces that are represented. They are permanently open and fully extended at all times.

It is to this reference frame that I subsequently attempted to relate all verified properties of fundamental particles, each of which being the focus of a local occurrence of a 3-space interaction, and each of which being separated from all other particles by total vacuum.

The actual element of information that triggered the chain of reasoning that led to the solution proposed here, is a conclusion drawn by Louis de Broglie that photons must be constituted, not of one corpuscle as is generally assumed, but of two corpuscles, or half-photons, that would be complementary like the electron is complementary to the positron.

I eventually developed a clear vision of a mechanics of conversion that plausibly explained how such a photon, possessing sufficient energy, could convert to an electron/positron pair in such a geometry. Eventually, a plausible mechanics of interaction of electrons and positrons took shape that provided a key to understanding how protons and neutrons could come into being.

The result is a seamless series of clearly defined interaction sequences that provides an uninterrupted path of causality from the unquantized quantities of energy of motion which are induced between particles through Coulomb interaction, to the quantization of that energy in the form of photons when the relative quantization threshold is locally reached, to the creation of electrons and positrons from the destabilization of photons of sufficient energy, and finally to the creation of protons and neutrons from the interaction of electrons and positrons when they are forced into sufficiently small volumes of space.

Such a 9-dimensional 3-space local geometry is in my view, the most restricted reference frame that will still allow the elaboration of such a clearly defined causality thread.

The most surprising outcome however, appears to be a confirmation of Newton's Gravitational Theory in a more precise form which, by replacing the Newtonian concept of "point-like particles" with that of "charged point-like particles", provides an alternate explanation - to that of General Relativity - of the Newtonian error in the calculation of the perihelion advance of Mercury, of the correct calculation of the deflection of photons trajectories by the Sun, of the increase in frequency of cesium atoms in cesium clocks with altitude, and provide a gravitational solution to the observed unexplained anomalous constant residual acceleration directed towards the Sun observed for the Pioneer 10/11, Galileo and Ulysses spacecrafts ([7], p.1).

Surprisingly, this solution draws a natural bridge between Maxwell's electromagnetic theory - which it confirms in a manner that allows it to directly describe photons, Coulomb interaction and Newton's gravitational theory, and that it refocuses in a new perspective the bulk of accepted orthodox theories, namely Special Relativity, Quantum Mechanics, Quantum Electrodynamics and Quantum Chromodynamics, as well as many of the postulates that are now taken for granted.

Thank You

André Michaud
Service de Recherche Pédagogique