# On the Refutation of the Riemann Hypothesis

I have reviewed all this post on the next one: On the Prime Antinumbers at 7 September 2014. Thanks for reading.

Some mathematicians have tried an approach to the Riemann Hypothesis by means of the spectral theory. This is the case of the Hilbert-Pólya conjecture.

It is possible to question if there is a physical mechanism which emission’s frequencies correspond with the Riemann zeroes. In this sense some physicists have tried to apply quantum mechanics looking for a perfect “Riemannium”.

They hope that finding the physical correspondence with the Riemann function about prime numbers periodicity they could understand what prime numbers are and what is the law that governs.

What I am going to do in this post is an approximation to the Riemann hypothesis through the non conventional atomic model that I defend on this blog:

I consider that gravitational fields vary periodically, they expand and contract.

Two entangled (intersected) gravitational fields that vary periodically with the same or opposite phases, create in their mutual intersection 4 new fields that correspond with the “subatomic particles” of a shared nucleus.

When the two entangled gravitational fields vary with opposite phases, the four subatomic particles created in their intersection are fermions ruled by the Pauly exclusion principle, there is an antisymmetry at the horizontal plane because of the periodical displacements toward the left and right sides.

Wen te two entangled gravitational fields vary with te same frequency te four subatomic particles are bosons, ere te antisymmetry occurs at te vertical level because of the periodical up and down displacements.

I think that between each expansion and contraction of each entangled gravitational field there is a time when those entangled fields do not vary. It is the instant when the field finishes expanding and start contracting, or the time when the field stops contracting and starts expanding. This instant can be consider as a time of zero force, because form the perspective of the subatomic particles the gravitational variations and their spatial displacements are experienced as forces of pressure.

Because of this periodical delay I think that fermions transform gradually into bosons and bosons into fermions periodically. The phases of the periodical variation of the entangled gravitational fields led gravitational fields synchronize and desynchronize periodically.

We can look at this periodicities and oscillations looking for a relation with the zeros Riemann’s periodicity. The Riemann hypothesis supposes that all these zeros are placed at the same line.

In the figures above, when it comes to fermions, the field that moves toward the left side, when the left entangled gravitational field is contracted and the right is expanded, is an electron; the dotted field that moves toward the right side (it is the same electron field but at a later time) when the left dotted gravitational field is expanded and the right dotted is contracted, is a positron.

When it comes to bosons the periodicity occurs at the vertical plane.

¿Where are placed the zeros points of those periodical variations? ¿are there at the same line?

The zero point in these representations is the point where the field that moves stops for starting moving toward the opposite side. In the case of the electron, when it comes to bosons, it is the point where the electron reaches the maximum left distance from the central axis of symmetry between electron and positron. It occurs when the left entangled gravitational field stops contracting to start expanding and the right entangled gravitation al field stops expanding to start contracting. When the electron field become a positron moving toward the right side, the zero point is the point where the positron reaches the maximum distance from the central axis of symmetry, when the left entangled gravitational fields stops expanding to start contracting again, and the right entangled gravitational fields stops contracting to start expanding again. Those zero points occur at the same line.

But while in fermions the oscillations occurs in the horizontal axis, in bosons they occurs in the vertical axis. In bosons the zero point take places when the central ascending field reaches the highest elevation and when it reaches the lowest elevation in the decay of its energy. (This energy decay has its counterpart in the convex side of the gravitational entanglement and it would be antigravitational as I have commented on other posts). In bosons the zero point of the periodical variations take place at the same line, but it is different from fermions.

I consider that fermions transforms periodically into bosons and bosons into fermions because the periodical synchronization and desynchronization of the phases of variation of the entangled gravitational fields.

If the periodical variations of fermions or boos purpose on this atomic model had correspondence with the frequencies of the Riemann function the Riemann Hypothesis would be false

Another zero point of reference could be the point when the horizontal (in the case of fermions) or vertical (in the case of bosons) symmetry is broken.

on the other hand, if we consider the spatial fluctuations that affect masses and energies when it comes to other subatomic particles of the shared atomic nucleus, the zero points follow different lines too:

If the Riemann hypothesis is true, these fields with zeros at different lines will not equiparable with the prime numbers. In this model these subatomic particles (protons, neutrons, neutrino or antineutrino) are composite fields created by the multiplication of the pressure forces (like in the case of neutron and proton) or by the division of decompressing forces (like in the case of neutrino or antineutrino). You can read more about it in the post that I commented the Hodge conjecture and the mass gap problem on this blog.

If we think outside the six dimensions that all these fields are and think about the whole net of entanglements that are nest inside others in an infinite way, the lines of the zero points will result at different places anyway:

With respect to the prime numbers’ frequency I think that this atomic (and astrophysical) model should be applicable for looking a more accurate, non average periodicity too. I think it would be useful here use like analogy the espectral lines that emit the “atomic” elements of matter and antimatter. I miss here anti-prime numbers or dark-prime numbers. Because the ideas that I have in this regard are non conventional either, you can read them in other posts from this blog if you are interested.

On the other hand, I have mentioned in other posts too the role that, in my opinion, relativistic complex numbers and non commutative spaces have in the creation of the periodical masses of the subatomic particles.

I think that a number that only is divisible by itself or by the unit has analogy with a particle that is at the its own antiparticle, a Majorana antiparticle. You can read about Majorana and Dirac antiparticles in other posts on this blog.

I hope these ideas, although expressed by analogies and with non mathematical terms, could inspire you for thinking about this matter by yourself.

Kind regards.

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