Tuesday, June 04, 2024

About the generation of matter-antimatter asymmetry in the TGD Universe?

I have developed a rather detailed view of interaction vertices (see this). Everything boils down to the question of what the creation of a fermion-antifermion pair is in TGD. Since bosonic fields are not primary fields (bosons are bound states of fermions and antifermions), the usual view about generation of fermion antifermion pairs does not work as such and the naive conclusion seems to be that fermions and antifermions are separately conserved.

Holography=holomorphy identification leading to an explicit general solution of field equations defining space-time surfaces as minimal surfaces with 2-D singularities at which the minimal surface property fails, is the starting point. A generalized holomorphism, which maps H to itself, is characterized by a generalized analyticity, in particular by a hyper-complex analyticity. The analytic function from H to H in the generalized sense depends on the light-like coordinate or its dual ( say -t+z and t+z in the simplest case) and the 3 remaining complex coordinates of H=M4/ti,esCP2.

Let's take two such functions, f1 and f2, and set them to zero. We get a 4-D space-time surface that is a holomorphic minimal surface with 2-D singularities at which the minimal surface property and holomorphy fails. Singularities are analogs of poles. Also the analogs of cuts can be considered and would look like string world sheets: they would be analogous to a positive real axis along which complex function z^(i/n) has discontinuity unless one replaces the complex plane with its n-fold covering. The singularities correspond to vertices. and the fundamental vertex corresponds to a creation of fermion-antifermion pair.

There are at least two types of holomorphy in the hypercomplete sense, corresponding to analyticity with respect to -t+z or t+z as a light-like coordinate defining the analogs of complex coordinates z and its conjugate. Also CP2 complex coordinates could be conjugated.

These two kinds of analyticities would naturally correspond to fermions and to antifermions identified as time-reflected (CP reflected) fermions. This time reflection transforms fermion to antifermion. This is not the reversal of the arrow of time occurring in a "big" state function reduction (BSFR) as TGD counterpart of what occurs in quantum measurement, which corresponds to interchange of the roles of the fermionic creation and annihilation operators.

When a fermion pair, which can also form a boson as a bound state, is created, the partonic 2-surface to which the fermion line is assigned, turns back in time. At the vertex, where this occurs, neither of these two analyticities applies: holomorphy and the minimal surface property are violated because at the vertex the type of analyticity changes.

Now comes the crucial observation: the number theoretic vision of TGD predicts that quantum coherence is possible in macroscopic and even astrophysical and cosmological scales and corresponds to the existence of arbitrarily large connected space-time regions acting as quantum coherence regions: field bodies as counterparts of Maxwellian fields can indeed be arbitrarily large.

For a given region of this kind one must choose the same kind of generalized analyticity, say -t+z or t+z even at very long scales. Only fermions or antifermions but not both are possible for this kind of space-time sheets! Does this solve the mystery of matter-antimatter asymmetry and does its presence demonstrate that quantum coherence is possible even in cosmological scales?

See the article What gravitons are and could one detect them in TGD Universe? or the chapter with the same title.

For a summary of earlier postings see Latest progress in TGD.

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.

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