The significance of three right-handed sterile Majorana neutrinos

In the algebraic description of the standard model using complex split bi-octonions, the right-handed fermions are eigenstates of square-root mass in the Clifford algebra Cl(6). Square-root mass: This is given by a U(1) number operator which defines square-root mass, and has the eigenvalues (0, 1/3, 2/3, 1). These represent the right-handed sterile neutrino, the positron, the up quark, and the down quark, respectively. The right-handed fermions can be considered as excitations of the sterile neutrino.

Correspondingly, the left-handed fermions are excitations of the left-handed active neutrino, and the associated Clifford algebra Cl(6) has a U(1) number operator interpreted as electric charge, and having the eigenvalues (0, 1/3, 2/3, 1) which stand for the left-handed active neutrino, anti-down quark, up quark, and the positron. [Anti-particles are defined by complex conjugation of particle states].

In a very natural way, the Higgs boson arises in this algebraic description, as shown in the attached preprint, and the Higgs couples the right-handed fermions to the left-handed fermions, thereby giving mass to the charged fermions. In this setting it becomes physically clear as to why there is a universally prevailing Higgs field which gives masses to the particles.

The above is also a description of the standard model in a spinor space-time. The inclusion of the sterile neutrinos actually makes this the Left-Right symmetric extension of the standard model. And clearly, this L-R model is needed at all energy scales, or how else would the Higgs impart mass to the left-handed fermions?!

Quantum systems obey L-R symmetry at all energy scales but to see this we have to be able to experimentally measure and show that the Lorentz interaction (the right-handed counterpart of the weak force) violates parity. Such an experiment is extremely difficult to perform, because cosmological expansion prior to the L-R symmetry breaking [same as EW symmetry breaking] has set the particle masses to extremely low values, making gravity very weak, while no such corresponding reduction takes place in the value of the electric charge. As a result the fine structure constant remains order unity, the weak coupling is also measurable, and parity violating weak interaction is observed.

What then apparently breaks the L-R symmetry? It is the critical entanglement of sufficiently many fermions to form macroscopic objects and the concurrent emergence of 4D classical spacetime and gravity. Once gravity becomes classical, the parity violating spin-one Lorentz interaction is lost. What remains in view is the left-handed standard model. But this parity violation is apparent only when we study quantum systems on the classical Minkowski spacetime background.

How the electron sees the world is something very different from how we currently believe it sees the world. The truth is that even at today's low energies the electron sees a left-right symmetric universe, with the [difficult to measure] right-handed Lorentz interaction being would be gravity. This is how it is in the spinor spacetime, with the weak-Lorentz interaction spanning an equivalent 6D Minkowski spacetime. Color-electro spans 10D Minkowski spacetime. Together we have the unified color-elecro-weak-Lorentz force, a unification that is manifest even at low energies, provided we describe quantum systems on a spinor spacetime.

As the early universe cools, critical entanglement of fermions becomes possible, classical objects form, 4D spacetime and classical gravity emerge, and the L-R symmetry is broken. It is not broken for those fermions which are not critically entangled.

Reference: arXiv:2110.01858 [hep-ph]