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The very first mathematical model unifying the four known fundamental interactions into a single geometrical frame with a natural supersymmetric extension to include fundamental matter fields was proposed in [V1], in the context of Einstein’s general relativity. Physical processes were still assumed to be elementary, meaning that complexity was not taken into account yet. Two years later, the first bioquantum theory was built and it was historically the first to be consistent with physics, mathematics and observation at all scales.

A large-public book was written, showing the applications of the theory to parapsychology, its most extreme case [V2]. That was the first attempt to insert complexity into the physical world, within the frame of Nottale’s scale relativity, a natural extension of Einstein’s space-time relativity. However, this model was still deeply anchored in the physics of the 20 th century. Consequently, it was rather big and heavy to handle: But the mathematical proof that time could be eliminated from the physical frame to the benefit of the Universal Vacuum, in Octoberchanged everything [V3] and a second bioquantum theory, better called the bioquantum synthesisquickly came to replace the old version.

That second “theory of everything” everything known, of course also showed to be the final one, as it appeared to be minimal, natural and easy to handlewhile being much more powerful and simple than the first one, that already managed to explain no less than fourty-two parapsychological phenomena including of course Extra-Sensorial Perception or ESP — telepathy, remote viewing, precognition and retrocognition – telekinetics and psychokinetics.

All this work clearly showed that one did not need a “new physics with still unknown properties”, as was believed by many experts, but rather a complete and thorough reorganization of fundamental physics, covering the three last centuries, from Galileo Galilei up to our days. This is explained in details in the large-public book [V4]. So, let us now turn to the bioquantum synthesis.

We start out with the mathematical definition of the Elementary Quantum World. V is the vacuum state of the vielbein e. Then, we have a propagator [LL1]: Inserting 4 into 5 gives: When V is non zero, the second term on the right is the kinetic energy of V 2. Therefore, V 2 is a Green function with propagator: V is the Universal Vacuumthat is, the gravitational vacuum on QW 0. These terms are negligible. The presence of the negative sign before V 2 clearly shows that quantiue 0 2 is not invariant under the action of SU 9but under that of the larger non-compact group SU 9,1.

The tensor decomposition 14 is formally equivalent to the Euclidian product: The canonical decomposition 15 is called the objective representation of QW 0 and the canonical decomposition 16the subjective representation of QW 0.

QW 0 is supersymmetric. We will limit ourselves to OW 0 as the proof is similar for IW 0. The first part of 17 therefore represents the symmetric “bosonic” part of the metric, while the second part of 17 represents the skew-symmetric “fermionic” part of it.

One gets a similar result for IW 0. The difference between the two spin structures stands in their physical representation: The duality between OW 0 and IW 0 is the de Broglie wave-corpuscle duality or Feynman’s quantization formalism, in the general situation of continuous fields: See section 4 below.

This is an additional argument in favour of a maximum of three families of leptons in the universe. The mirror symmetry M then makes sure that there is an equal number of particles with positive energy and of “antiparticles”, i.

Quantiquue all 24 particles interact, they transform into each other, which is precisely what is expected from a unified theory of both matter quantiquee radiation fields. Proposition 4 self-polarization of the Universal Vacuum: Let us sum up the situation. From two independent 3-dimensional double universes OW 0 and IW 0 each one having mirror symmetry, we can build the Electrodynamiqur Quantum World QW 0 in three different yet equivalent ways: So, basically, what we need is only a 3-dimensional mirror universe appearing in three internal or external configuration states and we can build the single unified quantum frame containing all known fundamental interactions and matter fields.

The primal interaction is quantum supergravity. In the bioquantum frame, this is nothing else than the physical display of the geometry of QW 0as the mirror symmetry automatically induces supersymmetry between radiative and electrrodynamique fields see the proof of Proposition 3 hereabove. So, everything can emerge from a supersymmetric quantum gravitational vacuum or Universal Vacuum, at the birth of the universe, that is, from quantum statistical space.

Let us now turn to the fundamental interactions. Developing the base metric ds 2 on QW 0 in the objective representation 15 gives: Indeed, all three principal parts in 18 have SU 3 -invariance. To conciliate both views, the simplest solution is to consider two GSW electroweak fields or, equivalently, a complex GSW model.

The scenario is as follows. QW 0 can be viewed as a “Yang-Yin cousr, where Yang stands for the copy filled with positive energies and Yin, the copy filled with negative energies. The mirror symmetry exchanges both copies, so that “particles” filling Yang are sent onto their “antiparticles” filling Yin and conversely.

So, there can be baryon asymmetry as well as chiral-invariance violation in each copy, since Yang quite exclusively contains matter of positive energy and left-hand leptons, while Yin quite exclusively contains matter of negative energy or “antimatter” and right-hand “antileptons”.

However, baryon symmetry as well as chiral invariance are always preserved in QW 0thanks to the mirror symmetry. So, in QW 0there is as many matter as there is antimatter and as electrodynamiqie left-hand and right-hand leptons.

Indeed, as the Universal Vacuum is absolutely neutral and Yang and Yin are just the mirror images of each other, attributing a definite sign to the energy of particles and to their charges is again a matter of pure convention, the physical laws being exactly the cokrs in both Qjantique and Yin.

So, assuming that we live in Yang, what we call “antimatter” is nothing else than matter in Yin and what we call “right-hand antileptons” are nothing else than left-hand leptons in Yin.

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The reason is that, in Yang, the helicity of leptons is negative, while it is positive in Yin. And this opposition simply vanishes in QW 0 where leptons have both negative and positive helicity. So, what we have is two topological transitions: This last transition is physically interpreted as the spontaneous gauge symmetry breaking between the weak and electromagnetic interactions in the GSW model. What enables the first transition is a Higgs mechanism on V 2. What enables the second transition is a Higgs mechanism on the vacuum state of the electroweak field.

### jean-michel gerard

In all cases, transitions are made through a restructuring of a specific vacuum. But these specific vacua are actually nothing else than specified manifestations of the primal Universal Vacuum. We now introduce complexity in our bioquantum frame through a positive real-valued parameter l.

It is measured in meters m. Our central tool will be The Prigogine trick [P]: Consider a collective process involving a large number of individuals or a chaotic situation involving dense sheaves of trajectories. Instead of trying to describe the dynamics of such complicated structures with statistical distributions having their support in a deterministic frameit appears equivalent but much easier to describe these dynamics using deterministic functions taking their values in a random frame.

The Prigogine trick thus suggests making randomness an inherent property of the physical frame and not of dynamical systems. It is statistically equivalent to making gravitation an inherent property of the geometry of space rather than a force external to the physical frame and acting upon it. The regular function U l is called the evolution operator.

At this scale, all processes will be considered as elementary, that is, one will assume their structure to be point-like. If we are dealing with dynamical processes, their size will be the width of the largest sheaf of trajectories. In practice, l will belong to a compact interval [l minl max ] with l min non-zero and l max finite.

Duality is done through the conformal metrical tensor: Consequently, all the mathematical results obtained in section 1 remain valid in the structured case. Even the physics of elementary particles naturally extends without any qualitative change to objects and fields of any complexity! A simple example that well illustrates this is the wave equation in R 3: According to the Prigogine trick, 23 is equivalent to the heat equation: Both kernels then have to be equivalent.

H l ], then the Hamiltonian energy operator will be: OW and IW are dual to each other through the so-called wave-matter dualitywhich writes in the field representation: It can be complex-valued, so as to include chaotic situations.

Yet, one is still quantum in a random frame, despites everything happens as if one were deterministic. Finally, the reciprocal of the field representation? They can model Bohm’s implicate order and be used to solve the problem of the E. We give here the main geometrical properties of the physical frame of the bioquantum synthesis, beginning with the elementary i. Follows a physical discussion of the obtained results, then the survey of the structured case, reduced to the very minimum thanks to the use of the Prigogine trick.

Finally, we introduce the wave-matter dualitya structured extension in complex dimension of Louis de Broglie’s wave-corpuscle duality.

This document can also be downloaded in Adobe Acrobat format here: IV, “Electrodynamique quantique”, Mir, La parapsychologie, enfin une science?