Alfonso De Miguel - Academia.edu (original) (raw)

Papers by Alfonso De Miguel

This preprint article proposes an unconventional topological fields model based on two interactin... more This preprint article proposes an unconventional topological fields model based on two interacting fields that form a non-formal octonionic, bilateral structure.

Within this framework, nuclear interactions unfold through a complex time dimension that combines real past and imaginary future components, facilitating mass and energy exchanges between protons and antineutrinos or antiprotons and neutrinos during beta decay reactions. The neutron is reinterpreted as a transitional state in transformations between proton and neutrino and antineutrino and antiproton, or vice versa.
This octonionic configuration, with six spatial imaginary hyperdimensions, one imaginary time hyperdimension, and one real time dimension, brings highly abstract and advanced algebraic concepts to life through a concrete physical mechanism, offering a natural unification of the weak, strong, and electromagnetic atomic interactions.
Moreover, the octonionic approach provides a geometric interpretation of Quantum Chromodynamics (QCD), clarifying the internal structure and relationships between quarks and gluons.

Alfonso De Miguel Bueno, 2024

This paper proposes a possible relationship between bigravity and interacting Higgs fields, offer... more This paper proposes a possible relationship between bigravity and interacting Higgs fields, offering a broader framework that establishes a physical connection between the massive and massless ripples generated by gravitational fields. This framework also provides a unified scenario in which the four known fundamental forces — gravitational, electromagnetic, strong, and weak — are interconnected.

In addition, the model provides new insights into neutron mass, charge asymmetry, and the presence of an electric dipole moment (EDM), challenging the Standard Model’s assumption of perfect neutrality. By reinterpreting beta decay and introducing the antineutron as a transitional state in an antiproton-proton cycle, this framework offers fresh perspectives on long-standing issues such as proton decay and CP violation.

Alfonso De Miguel Bueno, 2024

This paper proposes a deterministic model that aims to unify the gravitational, strong, weak, and... more This paper proposes a deterministic model that aims to unify the gravitational, strong, weak, and electromagnetic interactions by examining the intersections of gravitational fields. The model draws upon bi-gravity theories, where interactions between two metric tensors associated with coupled curvatures drive changes in spacetime curvature. By coupling expanding and contracting gravitational fields, the model reinterprets singularities — typically viewed as infinite points in spacetime curvature — as abrupt, yet finite changes in curvature direction and, in some cases, its sign. This perspective bridges the behavior of singularities across both quantum and cosmological scales. The shared nucleus formed by these intersecting fields provides new insights into energy transfer, density distribution, and information preservation. Furthermore, the model addresses key theoretical challenges, including the nature of dark matter, reflection positivity, the mass gap problem, and the physical significance of Hodge cycles, offering a fresh approach to understanding the limitations of General Relativity in describing atomic and black hole structures. An additional Appendix on a purely relativistic interpretation of gravitational acceleration in a single field is provided at the end of the article.

This preprint introduces in a visual and conceptual way a model of two intersecting curved fields... more This preprint introduces in a visual and conceptual way a model of two intersecting curved fields with a shared nucleus, whose quantized dynamics offer potential cases of the four-variable Jacobian conjecture and a nonlinear Hodge cycle.

The Kummer type geometry of the model suggests a unified framework where abstract mathematical developments like Tomita-Takesaki, Gorenstein, and Dolbeault theories, can be conceptually linked to the Jacobian, Hodge, and Riemann conjectures.

Other mathematical physics topics, like the mass gap problem, reflection positivity, the emergence of imaginary time, or t-duality, are also considered within this context.

The fields model also lays the foundation of a novel deterministic quantum atomic system with a supersymmetric dual nucleus structure of matter and mirror antimatter.

Alfonso De Miguel Bueno, 2023

This paper introduces a supersymmetric dual-matter atomic model based on two intersecting fields ... more This paper introduces a supersymmetric dual-matter atomic model based on two intersecting fields that periodically vary in either the same or opposite phases, forming a shared nucleus of two transversal and two vertical subfields that represent the particles and antiparticles of the dual atomic nucleus.
The bosonic or fermionic characteristics of the nuclear subfields are determined by their topological transformations, which are caused by the pushing forces generated by the negative or positive curvatures of the intersecting fields during their contraction or expansion, and by the periodical synchronization and desynchronization of the phases of the intersecting fields while rotating.
With a mainly visual and conceptual approach, the model employs a set of 2x2 complex rotational matrices of eigenvectors related in a modular way to Sobolev interpolations and to Tomita-Takesaki theory, graphically illustrating Reflection positivity, the Mass gap problem, the Jacobian conjecture, or the arising of a purely imaginary time dimension, between other topics.
The article first explains the fields model in a general way, then it introduces some mathematical formalisms, translates the general system to the standard atomic terminology, and finally compares the model with already known developments and theories.

viXra, 2018

Thinking of the atom as a dual topological system of two intersected manifolds vibrating with the... more Thinking of the atom as a dual topological system of two intersected manifolds vibrating with the same or opposite phases, the submanifolds created by their intersection will be the subatomic particles of the nucleus shared by the dual atom, acting as fermions when the phases of variation of the intersecting manifolds are opposite and acting as bosons when those phases synchronize becoming equal. The quarks of the system - considered as the pushing forces caused by the displacement of the two intersecting manifolds while vibrating - will remain identical in the bosonic and fermionic times. The point of the intersection of the system, that also will remain the same during the whole phases of variation but moving left to right in the fermionic phase and upward and downward in the bosonic one, will be the point of convergence of all the fermionic and bosonic weak and strong interactions, constituting the structural unification of the gauge couplings.

Alfonso De Miguel Bueno, 2022

A loss of information about the fermionic antisymmetric moment of the atomic system would occur i... more A loss of information about the fermionic antisymmetric moment of the atomic system would occur in the Schrodinger complex partial differential equation, causing the misleading notion of two separate kind of nuclear spaces that only can be probabilistically described. The interpolation of partial complex conjugate derivatives would be necessary for a complete description of the evolution of the topological nucleus.

Alfonso De Miguel Bueno

This article proposes that fermions and bosons would be the same topological spaces super symmetr... more This article proposes that fermions and bosons would be the same topological spaces super symmetrically transformed through time, being fermions the +1/2 or -1/2 partial complex conjugate derivative of bosons and vice versa. Ordinary and complex conjugate equations could not operate independently of each other, but should be combined to avoid the deletion of half of the system on the description of the rotatory atomic nucleus.

Alfonso De Miguel Bueno, 2022

Schrodinger equation is a complex partial differential equation of second degree that does not us... more Schrodinger equation is a complex partial differential equation of second degree that does not use its complex conjugates derivatives, although they allow an alternative complex conjugate solution. That implied a separate description of the symmetric bosons (described by the complex equation) and the antisymmetric fermions (described by its complex conjugate).
This article suggests that the complex wave function is not integrated by its second derivative (the inverse function) but by the complex conjugate + and - derivatives that also will integrate the inverse function.
To leave out of the function the complex conjugate derivatives would imply, when it comes to describing rotational variations, to leave out half of the system.
The article suggests that without removing from the function the complex conjugates derivatives, bosons and fermions would appear to be be the same topological spaces transformed through time when their phases of vibration synchronise or desynchronise while the supersymmetric nucleus rotates.
Acting as bosons they would correspond to the imaginary part of the system while acting as fermions they would form its real part.

Alfonso De Miguel Bueno, 2022

By means of the groups of symmetry between the angles equal, larger, or shorter than 90 degrees t... more By means of the groups of symmetry between the angles equal, larger, or shorter than 90 degrees that can be formed with a inclined line and with its mirror reflected counterpart while rotating them through different intervals, a proof about the Euclid's fifth postulate is suggested.

A composite topological atomic model of intersecting curved spaces and subspaces that vibrate wit... more A composite topological atomic model of intersecting curved spaces and subspaces that vibrate with same or opposite phases would provide visual insight about the physical mechanism underlying the "handshake" transactions of the subatomic quantum states that occur in the strong and weak interactions between a retarded wave that evolves forward in time and its advanced complex conjugate that evolves backward in time, clarifying the notion of time reverse or anti-time considered by the "Two state quantum formalism", the Wheeler-Feynman "Absorber theory", or the "Transactional" or the "Two Time" interpretations of Quantum Mechanics, making sense of the concepts and paradoxes of quantum mechanics in a logical way.

Alfonso De Miguel, 2020

By means of interferences of separate prime functions, the article suggests the relation between ... more By means of interferences of separate prime functions, the article suggests the relation between the Riemann Z function and the distribution of prime numbers in the sense that the -1/2 real part of a nontrivial zero will be placed from the valley (or real zero point) of a cycle of an harmonic prime function different than 3 (only when it's not convergent at that point with the valley of a cycle of the function 3) to the critical strip determined by an extension of that real point in the complex plane to the imaginary point that represents the imaginary part of the non-trivial zero. When two harmonic functions interfere with a a same cycle of the function 3 (that does not have its valley at those points), no prime number will be placed there. A possible hidden asymmetry is examined there. And when there is no interference with the amplitude of a cycle of the function 3 (there won't be any nontrivial zero) two consecutive prime numbers will be always located there. A visual geometric interpretation of the Riemann critical strip and critical line, and his trivial and non-trivial zeros is attempted to conceptually understand the Riemann Zeta function, its later generalizations, and the Riemann hypothesis

Considering the electromagnetic atom a topological structure of two intersecting (partially merge... more Considering the electromagnetic atom a topological structure of two intersecting (partially merged) manifolds (longitudinal waves or branes) vibrating with the same or opposite phases, their cobordian submanifolds created in and by such intersection will be the subatomic particles of the nucleus shared by this dual system, acting as fermions when the phases of variation of the intersecting manifolds are opposite and acting as bosons when those phases synchronize becoming equal. The quarks of the system - considered as the pushing forces caused by the displacement of the intersecting fields while vibrating - will be identical in the bosonic and fermionic times, that is to say, supersymmetric. The point of the intersection of the system, that remains the same during the whole phases but moving left to right in the fermionic phase and upward and downward in the bosonic one, will be the point of convergence of all the fermionic and bosonic strong and weak interactions naturally explaining the unification of the gauge couplings.

It's possible to arrange geometrically a sequence of prime numbers that represent Galois prime ex... more It's possible to arrange geometrically a sequence of prime numbers that represent Galois prime extensions following a same Galois group, showing a correspondence between each antisymmetric pair.

Projecting the square 1 through the diagonal of its hypotenuse we can build a new prime square 1 ... more Projecting the square 1 through the diagonal of its hypotenuse we can build a new prime square 1 with an irrational symmetry. Combining the rational and irrational symmetries we can get new prime squares which roots will be irrational. The zero points displaced in this way through the infinite diagonal should be coincident with the Riemann function zeros. But it seems it also could be necessary to consider other different lines related to the mirror symmetry of the Riemann's critical line.

An approximation to the demonstration and refutation of the Fermat's Last Theorem, from a relativ... more An approximation to the demonstration and refutation of the Fermat's Last Theorem, from a relativistic point of view which reconsiders the consistency of Fermat's Last Theorem with the Pythagorean One. On this perspective, it could be said that Fermat's Last Theorem can be true and false at the same time, depending on the perspective which the cube formed with the hypotenuse of the Pythagorean theorem has been built from.

I think irrationality is the consequence of the disproportion that appears when combining differe... more I think irrationality is the consequence of the disproportion that appears when combining different planes with different referential lengths on the same space.

This article presents A theoretical model of two intersecting fields that vary periodically with ... more This article presents A theoretical model of two intersecting fields that vary periodically with the same or opposite phases which explain rationally the existence of six different quarks and why they switch from one to another.

I think it could be demonstrated that neutrinos have positive mass working with a non conventiona... more I think it could be demonstrated that neutrinos have positive mass working with a non conventional atomic model where two entangled fields that vary periodically create the subatomic particles. I guess that there is some kind of link between the solution of the Mass gap problem and the Hodge Conjecture. I attached a picture at the end for easier understanding the neutrino's mass.

I consider there are conceptual similarities in the genesis of prime and irrational numbers that ... more I consider there are conceptual similarities in the genesis of prime and irrational numbers that should be recalled for clarifying the meaning and functions of prime numbers, looking for the laws of their regularities and their appearance in the physical nature. I suggest there is also a similarity between prime numbers and subatomic particles.

This preprint article proposes an unconventional topological fields model based on two interactin... more This preprint article proposes an unconventional topological fields model based on two interacting fields that form a non-formal octonionic, bilateral structure.

Within this framework, nuclear interactions unfold through a complex time dimension that combines real past and imaginary future components, facilitating mass and energy exchanges between protons and antineutrinos or antiprotons and neutrinos during beta decay reactions. The neutron is reinterpreted as a transitional state in transformations between proton and neutrino and antineutrino and antiproton, or vice versa.
This octonionic configuration, with six spatial imaginary hyperdimensions, one imaginary time hyperdimension, and one real time dimension, brings highly abstract and advanced algebraic concepts to life through a concrete physical mechanism, offering a natural unification of the weak, strong, and electromagnetic atomic interactions.
Moreover, the octonionic approach provides a geometric interpretation of Quantum Chromodynamics (QCD), clarifying the internal structure and relationships between quarks and gluons.

Alfonso De Miguel Bueno, 2024

This paper proposes a possible relationship between bigravity and interacting Higgs fields, offer... more This paper proposes a possible relationship between bigravity and interacting Higgs fields, offering a broader framework that establishes a physical connection between the massive and massless ripples generated by gravitational fields. This framework also provides a unified scenario in which the four known fundamental forces — gravitational, electromagnetic, strong, and weak — are interconnected.

In addition, the model provides new insights into neutron mass, charge asymmetry, and the presence of an electric dipole moment (EDM), challenging the Standard Model’s assumption of perfect neutrality. By reinterpreting beta decay and introducing the antineutron as a transitional state in an antiproton-proton cycle, this framework offers fresh perspectives on long-standing issues such as proton decay and CP violation.

Alfonso De Miguel Bueno, 2024

This paper proposes a deterministic model that aims to unify the gravitational, strong, weak, and... more This paper proposes a deterministic model that aims to unify the gravitational, strong, weak, and electromagnetic interactions by examining the intersections of gravitational fields. The model draws upon bi-gravity theories, where interactions between two metric tensors associated with coupled curvatures drive changes in spacetime curvature. By coupling expanding and contracting gravitational fields, the model reinterprets singularities — typically viewed as infinite points in spacetime curvature — as abrupt, yet finite changes in curvature direction and, in some cases, its sign. This perspective bridges the behavior of singularities across both quantum and cosmological scales. The shared nucleus formed by these intersecting fields provides new insights into energy transfer, density distribution, and information preservation. Furthermore, the model addresses key theoretical challenges, including the nature of dark matter, reflection positivity, the mass gap problem, and the physical significance of Hodge cycles, offering a fresh approach to understanding the limitations of General Relativity in describing atomic and black hole structures. An additional Appendix on a purely relativistic interpretation of gravitational acceleration in a single field is provided at the end of the article.

This preprint introduces in a visual and conceptual way a model of two intersecting curved fields... more This preprint introduces in a visual and conceptual way a model of two intersecting curved fields with a shared nucleus, whose quantized dynamics offer potential cases of the four-variable Jacobian conjecture and a nonlinear Hodge cycle.

The Kummer type geometry of the model suggests a unified framework where abstract mathematical developments like Tomita-Takesaki, Gorenstein, and Dolbeault theories, can be conceptually linked to the Jacobian, Hodge, and Riemann conjectures.

Other mathematical physics topics, like the mass gap problem, reflection positivity, the emergence of imaginary time, or t-duality, are also considered within this context.

The fields model also lays the foundation of a novel deterministic quantum atomic system with a supersymmetric dual nucleus structure of matter and mirror antimatter.

Alfonso De Miguel Bueno, 2023

This paper introduces a supersymmetric dual-matter atomic model based on two intersecting fields ... more This paper introduces a supersymmetric dual-matter atomic model based on two intersecting fields that periodically vary in either the same or opposite phases, forming a shared nucleus of two transversal and two vertical subfields that represent the particles and antiparticles of the dual atomic nucleus.
The bosonic or fermionic characteristics of the nuclear subfields are determined by their topological transformations, which are caused by the pushing forces generated by the negative or positive curvatures of the intersecting fields during their contraction or expansion, and by the periodical synchronization and desynchronization of the phases of the intersecting fields while rotating.
With a mainly visual and conceptual approach, the model employs a set of 2x2 complex rotational matrices of eigenvectors related in a modular way to Sobolev interpolations and to Tomita-Takesaki theory, graphically illustrating Reflection positivity, the Mass gap problem, the Jacobian conjecture, or the arising of a purely imaginary time dimension, between other topics.
The article first explains the fields model in a general way, then it introduces some mathematical formalisms, translates the general system to the standard atomic terminology, and finally compares the model with already known developments and theories.

viXra, 2018

Thinking of the atom as a dual topological system of two intersected manifolds vibrating with the... more Thinking of the atom as a dual topological system of two intersected manifolds vibrating with the same or opposite phases, the submanifolds created by their intersection will be the subatomic particles of the nucleus shared by the dual atom, acting as fermions when the phases of variation of the intersecting manifolds are opposite and acting as bosons when those phases synchronize becoming equal. The quarks of the system - considered as the pushing forces caused by the displacement of the two intersecting manifolds while vibrating - will remain identical in the bosonic and fermionic times. The point of the intersection of the system, that also will remain the same during the whole phases of variation but moving left to right in the fermionic phase and upward and downward in the bosonic one, will be the point of convergence of all the fermionic and bosonic weak and strong interactions, constituting the structural unification of the gauge couplings.

Alfonso De Miguel Bueno, 2022

A loss of information about the fermionic antisymmetric moment of the atomic system would occur i... more A loss of information about the fermionic antisymmetric moment of the atomic system would occur in the Schrodinger complex partial differential equation, causing the misleading notion of two separate kind of nuclear spaces that only can be probabilistically described. The interpolation of partial complex conjugate derivatives would be necessary for a complete description of the evolution of the topological nucleus.

Alfonso De Miguel Bueno

This article proposes that fermions and bosons would be the same topological spaces super symmetr... more This article proposes that fermions and bosons would be the same topological spaces super symmetrically transformed through time, being fermions the +1/2 or -1/2 partial complex conjugate derivative of bosons and vice versa. Ordinary and complex conjugate equations could not operate independently of each other, but should be combined to avoid the deletion of half of the system on the description of the rotatory atomic nucleus.

Alfonso De Miguel Bueno, 2022

Schrodinger equation is a complex partial differential equation of second degree that does not us... more Schrodinger equation is a complex partial differential equation of second degree that does not use its complex conjugates derivatives, although they allow an alternative complex conjugate solution. That implied a separate description of the symmetric bosons (described by the complex equation) and the antisymmetric fermions (described by its complex conjugate).
This article suggests that the complex wave function is not integrated by its second derivative (the inverse function) but by the complex conjugate + and - derivatives that also will integrate the inverse function.
To leave out of the function the complex conjugate derivatives would imply, when it comes to describing rotational variations, to leave out half of the system.
The article suggests that without removing from the function the complex conjugates derivatives, bosons and fermions would appear to be be the same topological spaces transformed through time when their phases of vibration synchronise or desynchronise while the supersymmetric nucleus rotates.
Acting as bosons they would correspond to the imaginary part of the system while acting as fermions they would form its real part.

Alfonso De Miguel Bueno, 2022

By means of the groups of symmetry between the angles equal, larger, or shorter than 90 degrees t... more By means of the groups of symmetry between the angles equal, larger, or shorter than 90 degrees that can be formed with a inclined line and with its mirror reflected counterpart while rotating them through different intervals, a proof about the Euclid's fifth postulate is suggested.

A composite topological atomic model of intersecting curved spaces and subspaces that vibrate wit... more A composite topological atomic model of intersecting curved spaces and subspaces that vibrate with same or opposite phases would provide visual insight about the physical mechanism underlying the "handshake" transactions of the subatomic quantum states that occur in the strong and weak interactions between a retarded wave that evolves forward in time and its advanced complex conjugate that evolves backward in time, clarifying the notion of time reverse or anti-time considered by the "Two state quantum formalism", the Wheeler-Feynman "Absorber theory", or the "Transactional" or the "Two Time" interpretations of Quantum Mechanics, making sense of the concepts and paradoxes of quantum mechanics in a logical way.

Alfonso De Miguel, 2020

By means of interferences of separate prime functions, the article suggests the relation between ... more By means of interferences of separate prime functions, the article suggests the relation between the Riemann Z function and the distribution of prime numbers in the sense that the -1/2 real part of a nontrivial zero will be placed from the valley (or real zero point) of a cycle of an harmonic prime function different than 3 (only when it's not convergent at that point with the valley of a cycle of the function 3) to the critical strip determined by an extension of that real point in the complex plane to the imaginary point that represents the imaginary part of the non-trivial zero. When two harmonic functions interfere with a a same cycle of the function 3 (that does not have its valley at those points), no prime number will be placed there. A possible hidden asymmetry is examined there. And when there is no interference with the amplitude of a cycle of the function 3 (there won't be any nontrivial zero) two consecutive prime numbers will be always located there. A visual geometric interpretation of the Riemann critical strip and critical line, and his trivial and non-trivial zeros is attempted to conceptually understand the Riemann Zeta function, its later generalizations, and the Riemann hypothesis

Considering the electromagnetic atom a topological structure of two intersecting (partially merge... more Considering the electromagnetic atom a topological structure of two intersecting (partially merged) manifolds (longitudinal waves or branes) vibrating with the same or opposite phases, their cobordian submanifolds created in and by such intersection will be the subatomic particles of the nucleus shared by this dual system, acting as fermions when the phases of variation of the intersecting manifolds are opposite and acting as bosons when those phases synchronize becoming equal. The quarks of the system - considered as the pushing forces caused by the displacement of the intersecting fields while vibrating - will be identical in the bosonic and fermionic times, that is to say, supersymmetric. The point of the intersection of the system, that remains the same during the whole phases but moving left to right in the fermionic phase and upward and downward in the bosonic one, will be the point of convergence of all the fermionic and bosonic strong and weak interactions naturally explaining the unification of the gauge couplings.

It's possible to arrange geometrically a sequence of prime numbers that represent Galois prime ex... more It's possible to arrange geometrically a sequence of prime numbers that represent Galois prime extensions following a same Galois group, showing a correspondence between each antisymmetric pair.

Projecting the square 1 through the diagonal of its hypotenuse we can build a new prime square 1 ... more Projecting the square 1 through the diagonal of its hypotenuse we can build a new prime square 1 with an irrational symmetry. Combining the rational and irrational symmetries we can get new prime squares which roots will be irrational. The zero points displaced in this way through the infinite diagonal should be coincident with the Riemann function zeros. But it seems it also could be necessary to consider other different lines related to the mirror symmetry of the Riemann's critical line.

An approximation to the demonstration and refutation of the Fermat's Last Theorem, from a relativ... more An approximation to the demonstration and refutation of the Fermat's Last Theorem, from a relativistic point of view which reconsiders the consistency of Fermat's Last Theorem with the Pythagorean One. On this perspective, it could be said that Fermat's Last Theorem can be true and false at the same time, depending on the perspective which the cube formed with the hypotenuse of the Pythagorean theorem has been built from.

I think irrationality is the consequence of the disproportion that appears when combining differe... more I think irrationality is the consequence of the disproportion that appears when combining different planes with different referential lengths on the same space.

This article presents A theoretical model of two intersecting fields that vary periodically with ... more This article presents A theoretical model of two intersecting fields that vary periodically with the same or opposite phases which explain rationally the existence of six different quarks and why they switch from one to another.

I think it could be demonstrated that neutrinos have positive mass working with a non conventiona... more I think it could be demonstrated that neutrinos have positive mass working with a non conventional atomic model where two entangled fields that vary periodically create the subatomic particles. I guess that there is some kind of link between the solution of the Mass gap problem and the Hodge Conjecture. I attached a picture at the end for easier understanding the neutrino's mass.

I consider there are conceptual similarities in the genesis of prime and irrational numbers that ... more I consider there are conceptual similarities in the genesis of prime and irrational numbers that should be recalled for clarifying the meaning and functions of prime numbers, looking for the laws of their regularities and their appearance in the physical nature. I suggest there is also a similarity between prime numbers and subatomic particles.

The TIQM lets making sense of some illogical paradoxes of quantum mechanics that have not been so... more The TIQM lets making sense of some illogical paradoxes of quantum mechanics that have not been solved by the Standard model or its different interpretations; but the mechanism of the "handshaking" that closes the transaction between the wave and its complex conjugate remains something abstract, and it also presents the apparently unreasonable assumption that the advanced complex conjugate wave can travel backwards in time, from future to past. On this article it's suggested that a dual composite atomic model of intersecting longitudinal waves would clarify the handshaking transactional mechanism not only between particles of two different atoms but also between the particles of a same atomic nucleus, describing the evolution of the quantum states of those subatomic particles and the supersymmetric link between bosons and fermions. In this context, retrocausation and time reverse waves can be rationally understood.

By means of interferences between prime functions the article shows how an asymmetry between comp... more By means of interferences between prime functions the article shows how an asymmetry between complex conjugates non-trivial zeros inside of the critical strip appears in the Riemann Zeta Function when the prime harmonic functions have a different phase, which could challenge the Riemann Hypothesis while clarifying the relation between prime numbers and the Riemann non-trivial zeros.

Alfonso De Miguel, 2020

By means of interferences of separate prime functions, the article suggests the relation between ... more By means of interferences of separate prime functions, the article suggests the relation between the Riemann Z function and the distribution of prime numbers in the sense that the -1/2 real part of a nontrivial zero will be placed from the valley (or real zero point) of a cycle of an harmonic prime function different than 3 (only when it's not convergent at that point with the valley of a cycle of the function 3) to the critical strip determined by an extension of that real point in the complex plane to the imaginary point that represents the imaginary part of the non-trivial zero. When two harmonic functions interfere with a same cycle of the function 3 (that does not have its valley at those points), no prime number will be placed there. A possible hidden asymmetry that would not be follow the Riemann statement is examined there. And when there is no interference with the amplitude of a cycle of the function 3 (there won't be any nontrivial zero) two consecutive prime numbers will be always located there. A visual geometric interpretation of the Riemann critical strip and critical line, and his trivial and non-trivial zeros is attempted to conceptually understand the Riemann Zeta function, its later generalizations, the Riemann hypothesis and its relation with prime numbers distribution.

Working with two parallel lines, one of them virtually existent, it can be demonstrated the conve... more Working with two parallel lines, one of them virtually existent, it can be demonstrated the convergence of two non-parallel lines mentioned on the Euclid’s fifth postulate. Non-Euclidean geometries would not be Euclidean because they would not follow the Euclid’s definition of parallels.