In two previous papers, we showed that that the observed elementary particles masses spectrum agrees with a single resonance equation. Using those results we show that the resonance numbers address three distinct resonance schemes-one for each symmetry U(1) and SU(3), and one for massive bosons; we then deduce, from the equation parameters, a unique fundamental field "below" the standard model fields and forces, which we interpret as electric and magnetic poles and magnetic currents.

In the logic of the Universons assumption, we deduce the nature of De Broglie wave and periodic mass variation for particles. We verify consistency with quantum mechanics, in particular the Schrödinger equation.We analyze the hypothesis that elementary particle mass is momentum circulating at light speed. We discover resonance rules acting within elementary particles leading to a formula governing the quantization of masses.Applying this formula to the electrons, muons, tauons and quarks, we find resonances that match with current measurements. We deduce the energy of unknown massless sub-particles at the core of electrons, muons, and tauons.Geometrical constraints inherent to our formula lead to a possible explanation to only three generations of particles.Based on particles geometry, we verify the consistency of the deduced quarks structure with QCD and raise the hypothesis that color charge is magnetic. We verify consistency with QCD symmetry and find that P and CP symmetry are broken by the interaction, in agreement with weak force knowledge.Our logic leads to re-interpret the Dirac condition on magnetic monopole charge, explain why the detection of magnetic monopoles is so difficult and, when detected, why magnetic charge can depart from Dirac prediction.We deduce a possible root cause of gravitation, resulting in the Schwarzschild metric and probable non existence of dark matter.

We previously showed that the elementary particles mass spectrum is not random at all and probably originates in resonances of a single field below the known forces and fields. Here we first improve our demonstration leading to a single field; we show how resonances are compatible with the standard model symmetries and give coherent mass equation parameters. On this basis, we build a toy model of the field below which is consistent with those parameters and with the resonance numbers of quarks and massive bosons. It enables computing the W ± , Z 0 , and H 0 boson pole masses with high precision and the widths also come naturally. The resulting W ± mass is in close agreement with experimental data but it disagrees with the SM prediction. An important consequence is that nothing new should appear in the next LHC run because geometrical constraints show that there is probably nothing else to find. Finally, the fundamental resonance agrees with the Dirac condition; it explains the other coefficients of the theory (α and α S ) and shows the nature of the field.

A brief analysis of classical tachyons in Minkowski space shows that de Broglie wave phase velocity V = c²/v does not enable causality violations and gives an inversion of energy/momentum ratio between bradyons and tachyons. It leads to considering Vv = c² as a symmetry of Minkowski space where, for V > c, the signature of space-time is seen inverted. The inversion is shown coherent with Cramer’s transactional interpretation of quantum mechanics, but implies the physical existence of the past and the inexistence of the future.

In a recent paper we assume that the electron wave is a magnetic current at the origin of its mass; it leads to reversed coefficients with respect to the Dirac condition. Using space-time signature inversion we show that the monopole has, in linked electrons states, quantized velocities in agreement with the de Broglie wave phase velocity. The magnetic charge is relativistic and quantum in origin and comes from the Lorentz transformation of a quantum of current. We also show that gravitation is a natural consequence of the theory.

The predicted charges agree with experimental results from Ehrenhaft, Schedling, Ferber and Mikhaïlov. They also agree, in phenomenology, with recent results related to symmetry breaking in superconductors, and give plausible kinematics to the emission process in the Podkletlov and Poher experiments.

In previous paper, we showed that the elementary particles mass spectrum can be computed from theory using a resonance equation. The predicted H 0 mass agrees with the latest CERN publications. As a result, the H 0 acquires its mass exactly in the same geometry as the Z 0 and the W ± ; it is not a "purely scalar boson" and then quadratic divergences are inexistent. In this paper, we find an underlying structure of the field with 19 pure states, where 36 quark states (including color) and 3 or 6 neutrinos states are mixtures, and we show that the CKM and PMNS matrices elements come from the equation and the field structure. We conclude that the field is natural since over the 23 SM parameters, at least 19 are fully constrained by the field structure.