CURVATURAS VARIANTES

  • Four-Variable Jacobian Conjecture in a Topological Quantum Model of Intersecting Fields

    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 model’s Kummer-type geometry suggests a unified framework where abstract mathematical developments like Tomita-Takesaki, Gorenstein, and Dolbeault theories can…


  • Geometric Visual Approach to the Mass Gap Problem in N=1 Supersymmetric Yang-Mills Theory 
    Geometric Visual Approach to the Mass Gap Problem in N=1 Supersymmetric Yang-Mills Theory 

    *An updated version (En 9, 2024) of this post is provided in this pdf file: . Abstract: This paper introduces a non-conventional model within the framework of N=1 supersymmetric Yang-Mills theory [1], providing a visual explanation for the mass gap problem and the topological transformations of the supersymmetric atomic nucleus. The model is a supersymmetric…


  • Mass gap problem visual understanding
    Mass gap problem visual understanding

    The «mass gap» is considered one of the «millennium problems» by the Clay institute»: https://www.claymath.org/millennium/yang-mills-the-maths-gap/ In quantum field theory, the mass gap is the difference in energy between the lowest energy state, the vacuum, and the next lowest energy state. Mass gap – Wikipedia So, we have a subatomic particle at its low level of mass and energy, and that…


  • Hints for Two-time dimensional physics: 2-T, F-theory, and IIB superstring theories
    Hints for Two-time dimensional physics: 2-T,  F-theory, and IIB superstring theories

    Dear friends, I hope you’re well. I’m sharing this unfinished post as a work in progress that I’ll try to review and improve when I have more time. Looking for current atomic models that have already considered more than 1 time dimension, I found the Two times (2T) physics, a 4 spatial and 2 time…


  • A Conversation with Bard: Exploring New Mathematical Models for Physics and Their Mathematical Foundations

    The title of this post was suggested by the last version of Bard , the Google’s conversational Artificial Intelligence, who patiently and enthusiastically had a conversation with me about some of the topics I’ve developed on this blog. Thank you Google! Q. Hi Bard. Are bosons and fermions described by the complex Schrödinger equation and…


  • Conversations with AI about Lorentz Transformations and Special relativity

    Q. I want to know everything about Lorentz Transformations. A. Lorentz transformations are a set of equations that relate the space and time coordinates of two systems moving at a constant velocity relative to each other. They are important for the theory of special relativity, because they show how measurements of length, time, mass and energy…


  • Speaking about maths with Chat GPT 4

    Hi friends, how are you. I asked some questions to the new AI chatbot that Bing incorporates in Windows Edge, which is said to use the same AI as the already famous chat GPT. It was not my purpose to test it, but genuinely look to see if it could clarify some concepts. And I…


  • Matrices, functions and partial differential equations in the context of rotational atomic models.

    Let A1 be a 2×2 complex matrix. That is the way that mathematicians like to start their writings, letting a thing be something else. However, you must be warned that not only am I not one of them but also I have no idea about mathematics. If you still want to keep reading, I will…


  • On the inadequacy of linear partial differential equations to describe the evolution of composite topological systems that rotate.  
    On the inadequacy of linear partial differential equations to describe the evolution of composite topological systems that rotate.  

    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…


  • The role of partial differential equations on the insufficient description of the atomic nucleus  
    The role of partial differential equations on the insufficient description of the atomic nucleus  

    By means of the derivatives of a 2×2 complex matrix, this post 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 of all variables could not operate independently…


  • Differential equations and complex matrices on the description of the supersymmetric atomic nucleus.
    Differential equations and complex matrices on the description of the supersymmetric atomic nucleus.

    Let four positive vectors arrange on two rows and two columns being the elements of a 2×2 hamiltonian complex matrix. Rotate the vectors 90 degrees to obtain their complex conjugate; rotate 90 degrees the complex conjugate matrix to invert all the initial signs; and rotate the negative matrix to obtain their negative complex conjugate. The…


  • Special relativity and quantum mechanics in Euclid’s fifth postulate proof

    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. The complementarity between angles larger and shorter than 90…


  • Transactional Handshake of Nuclear Quantum States and the Meaning of Time Reverse in the Context of a Composite Atomic Model 
    Transactional Handshake of Nuclear Quantum States and the Meaning of Time Reverse in the Context of a Composite Atomic Model 

    Abstract: 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…


  • Two-state Vector Formalism and Transactional Interpretation of Quantum Mechanics from a Common Sense Point of View.
    Two-state Vector Formalism and Transactional Interpretation of Quantum Mechanics from a Common Sense Point of View.

    Wikipedia wonderfully tells us that «the two-state vector formalism (TSVF) is a description of quantum mechanics in terms of a causal relation in which the present is caused by quantum states of the past and of the future taken in combination.» This is very interesting, isn’t it? Because any sensible person will agree that any effect only can be…


  • Composite extradimensional quantum supersymmetric system

    Have a wonderful day


  • Re-flexiones sobre física simétrica, antisimétrica y asimétrica

    Estimados amigos, lectoras y lectores del blog. Hola de nuevo. Nada causa más terror en el ser humano que lo asimétrico. Bien debe saberlo el señor Vladimir Putin, quien hace no mucho amenazaba a occidente con una respuesta «asimétrica, rápida y dura» si – promoviendo o llevando a cabo actos de enemistad (entiéndase revoluciones primaverales,…


  • Kummer surfaces and geometric phases in a dual atomic model of intersecting waves

    Dear friends, how are you? I changed the blog url coming back to the default wordpress.com direction. That implies Google is punishing the blog in the search results (as now there are in the internet some – not too much anyway – broken links). Sorry for the inconveniences. Today I’m pleased to introduce you the…


  • Mass gap in a topological vector system of two intersecting spaces and subspaces vibrating with same or opposite phases

      Hi friends. I hope you’re doing well. I watched this interesting conference of professor of theoretical physics David Gross about the Yang Mills theory and the «mass gap» Millennium problem and decided to write about it here:   Reading or hearing anything about quantum mechanics from professional physicists can be a tough task because…


  • Coherencia y decoherencia cuántica

      «De Broglie mostró detalladamente cómo el movimiento de una partícula, pasando sólo a través de una de las dos rendijas de una pantalla, podría estar influenciado por las ondas que se propagan a través de ambas rendijas. Y tan influenciado que la partícula no se dirige hacia donde las ondas se cancelan, sino que…


  • Anyons, Majorana fermions, and supersymmetric quarks in a topological quantum dual system

      «De Broglie showed in detail how the motion of a particle, passing through just one of two holes in screen, could be influenced by waves propagating through both holes. And so influenced that the particle does not go where the waves cancel out, but is attracted to where they cooperate. This idea seems to…


  • ‘Cuántica’, anyones multidimensionales y fermiones de Majorana

    Hola amigas y amigos, cómo están? Espero que sigan bien. Hace unas semanas estuve viendo algunos vídeos divulgativos en los que habla coloquialmente el profesor José Ignacio Latorre, que es un prestigioso catedrático de física teórica de la Universidad de Barcelona. También dirige algunos proyectos importantes sobre computación cuántica en varios países, y es director…


  • Galois Extensions, Lie Groups and the Algebraic and Geometrical Solvability of Fifth and Higher Polynomials

    A friend of the blog also interested on visual geometry asked me the other day about some books for visual representations of Riemann spaces, and Galois, and Lie groups. I do not know those books. They only things I found are remote analogical representations that are not geometrical figures although are something visual and I…


  • Extensiones de Galois y grupos de Lie en la resolución de ecuaciones de quinto y superior grado

    Ya saben ustedes que este blog es especulativo (por cierto el post de los anterior en español sobre números primos no lo he corregido, pero lo desarollé y aclaré más en la versión en inglés), está dedicado a pensar y explorar. (Lo digo para que tengan precaución quienes vengan buscando información para aprender sobre alguna…


  • Hidden Asymmetries in the Riemann Zeta Function to Refute the Riemann Hypothesis

    By means of interferences between prime functions this post 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…


  • Riemann Zeta Function, Functions Interferences, and Prime Numbers Distribution

    Updated April 21 Interference and non-interference between prime functions explain the distribution of prime numbers. We also show some cyclic paths, and some similitudes to interpret in a different way the Riemann Zeta function and his known hypothesis about prime numbers. You can read or download an almost literal pdf version of this post here:…


  • Función Zeta de Riemann, Interferencia de funciones, y distribución de números primos

    (Actualizado el 20 de abril) He representado aquí el orden de los números primos entre los números 1 y 100. Distribuyendo los números naturales en dos columnas, una par y otra impar, podemos formar diferentes funciones con los distintos números primos, sumando cada uno de ellos dos veces (una en la columna par y otra…


  • Hidden Variables in the Bell Inequality Theorem? When non locality does not imply non causality

      SARS Coronavirus 2 update (March 27, 2020): —————————————————- You will know that Newton, during the Great Plague that hit London and forced to close the Trinity Colle of Cambridge, took advantage of his confinement to develop his theory of gravity and  infinitesimal calculus that would determine the whole development of physics until the XX…


  • El final del viejo paradigma monista del campo único, independiente, e invariante

    Queridas amigas y amigos, cómo están? Quería comenzar este primer post del nuevo año con una noticia que leí hace poco: la Compañía automovilística Porche ha diseñado en colaboración con Lucasfilm – ya saben, los de la saga de Star Wars – esta maravilla de vehículo volador. No es bonito? Lo llaman «Starship Star Wars…


  • ‘Fundamentos de matemáticas y física un siglo después de Hilbert’ siguiendo la reseña de Juan Carlos Baez

    El post de hoy va a ser largo. Recuerden, si llegaron aquí buscando información para estudiar, que este es un blog especulativo y que las ideas que pongo son heterodoxas. Si llegaron hast aquí buscando inspirarse y pensar por sí mismos o simplemente para entretenerse, sean ustedes bienvenid@s. Están ustedes en su casa. (Los banners…


  • La torre bosónica de Benidorm, supremacía cuántica, y carta abierta al profesor Raúl Rabadán

    Queridas amigas y amigos, cómo están? He visto las noticias del nuevo rascacielos que se ha construido en Benidorm, el llamado «Intempo», de 192 metros de altura, la mayor en un edificio residencial en España y una de las mayores de Europa (creo que en Asia nos llevan cierta ventaja a este y otros respectos).…


  • Gravitational Entanglements. Open email to Caltech Prof. Hiroshi Ooguri

    Hi friends. Almost a year later I´m here again. At the end of July 2019 I sent an email to a Caltech professor, Hiroshi Oguri, as I found some familiar to me images related to his works about gravitational entanglements and I thought he could understand what I talk about on this blog. Unfortunately he…


  • Relativistic Supersymmetric 6 Quarks Model

    *Note: The ads you will see on this blog are automatically set and own by WordPress; I complained about it because I don’t like to show ads, but this is a free blog and they put those advertisements to get some profit. To quite the ads I would purchase a WordPress premium acount. I’m currently…


  • Ideas for an Unconventional Atomic Model to CERN

    Today I started to read the book «Lost in Math. How Beauty Leads Physics Astray», by Sabine Hossenfelder. At some point of the beginning, she speaks about a conversation with the head of theoretical physics at CERN, the Conseil Européen pour la Reserche Nucléaire. (CERN operates the largest particle collider, the LHC, which is providing a…


  • «Why might the Pythagorean theorem exist?»

    Yesterday I answered a question in Quora about the Pythagorean theorem and I wanted to publish it as well on the blog. The question was: «Why might the Pythagorean theorem exist? Is it a purely an arbitrary relationship observed in nature?» My answer was: Hi Ari, I think this is a very interesting question. The…


  • Cranks of All Countries, Unite!


  • Galois Theory, Hodge Conjecture, and Riemann Hypothesis. Visual Geometric Investigations.

    (Before starting I will say that this post, as the whole blog, is speculative and heterodox. I wanted to say it for the case that someone arrives here looking for info to study these subjects. The purpose of this blog is to think and to inspire others, not to teach them. I propose you to…


  • Teoría de Galois, Conjetura de Hodge e Hipótesis de Riemann. Investigaciones geométricas.

    (Antes de empezar quiero aclarar que este post, como todo el blog, es especulativo y heterodoxo. Quería mencionarlo por si alguien llega hasta aquí en busca de información para estudiar. Este blog no es para aprender ni estudiar, es para investigar, pensar, y tal vez inspirar). Como sabrán, uno de los llamados problemas matemáticos del…


  • Grupos de Galois y orden de los números primos

    Es posible encontrar un orden lógico para determinados números primos que representando extensiones de Galois siguen un mismo grupo de simetría de Galois, teniendo además cada elemento correspondencia con su par antisimétrico. Así: (7+83), (11 + 79), (19 + 71), (23 + 67), (31 + 59), (43 + 47) = 90 Estos números primos serían…


  • Prime Numbers Distribution

    There’s a beautiful symmetry related to this distribution of prime numbers when ordering those between the first 100 numbers that converge at Y+ or Y+. Combining the prime numbers of Y + and Y – there is a continuitity forming which seems a ring related to the number 90: The addition of the initial 7…


  • Representación no algebraica de grupos complejos e hipercomplejos de Galois.

    r’iéa Hoy voy a explicar cómo entiendo yo los grupos de Galois de una manera que se pueda entender, es decir, sin álgebra. Este post es más bien especulativo y puede que diga alguna inexactitud, es para mí saber si lo que digo aquí es correcto porque los matemáticos no me han dado feedback sobre…


  • How to Build a Regular Heptagon with a Compass and a Straightedge

    The heptagon can be drawn but it is considered that it cannot be constructed with just a compas and a straightedge. I tried this construction by using as the lenght of the sides a combination of the rational and irrational symmetry, the segment from the point R1 to i2 (in green color). I linked to…


  • To Galois or not to Galois? That (between others) is the Question

    This is an heterodox approach to groups symmetries from a geometric – non algebraic – point of view. It states that it’s possible to create a quintic or higher degree mirror reflected counter-function that converges with its 5th or higher degree function building them as extensions of a same 4th degree function and starting them…


  • Solving Quintic and Higher Functions in Terms of Radicals by Means of their Mirror Symmetric Counter-Functions.

    I’ve edited this article to make it clearer, updating it with a part of the post titled «To Galois or not to Galois». Below, I kept the previous versions of the post. Have a good day. I’ve drawn a right handed 4th degree «function» starting from the zero point (at the center of the circumference)…


  • Ecuaciones quínticas y grupos de Galois

    A principios del Siglo 19, Evariste Galois, un joven Escorpio de 20 años, dejó escrito la noche antes de batirse en un duelo mortal que las ecuaciones representan algebraicamente grupos de simetría y que esta simetría se rompe viniendo a ser mucho más compleja con las de quinto y superior grado; es por ello que…


  • Why do we need to learn the Pythagorean theorem?

    En tiempos de locura, no hay nada más creativo que el sentido común ni nada más disruptivo que la razón. Someone asked in Quora why do we need to learn the Pythagorean theorem. This is what I anwsered there today: The Pythagorean theorem is a wonderful gateway, a surprisingly beautiful starting point, to our mathematical…


  • Es el fotón compuesto de de Broglie un modelo de átomo compuesto?

    Encontré el otro día un artículo de un profesor de California llamado Richard Gauthier en el que habla del modelo de «fotón compuesto». Mi primera reacción fue de completa sorpesa por no decir estupefación. Porque lo primero que dice en la introducción es que «ha habido un continuo interés en la posibilidad de un modelo…


  • Is the Gödel ‘s Incompleteness theorem applicable to multidimensional systems ruled by a dualistic logic?

    (Versión en español más abajo). Is the Gödel’s incompletness theorem applicable when it comes to multidimensional systems ruled by a dualistic logic? Think about two intersecting fields varying periodically with equal or opposite phases. We can agree that the expanded field F is false and the contracted field T is true. F is not false…


  • Aritmética para niñas y niños que piensan los por qués.

    En España, en tercero de primaria, cuando tienen unos 9 años, las niñas y niños que piensan a cerca de los por qués de las cosas y tienden a lo visual, lo artístico y lo concreto, comienzan a confirmar con horror en sus notas del colegio que ellas y ellos no entienden las matemáticas (las…


  • El Grial dualista de los cátaros.

    Es conocida la leyenda que relaciona a los cátaros con el Santo Grial. Antes de ser exterminados como herejes por los cruzados en las laderas de Montsegur, varios de ellos se habrían descolgado por el vertical acantilado de una de las alas del castillo llevándose consigo la santa reliquia que custodiaban y su secreto. El…


  • Einstein, Lovachevski, Joaquín de Fiore y el Santo Grial cátaro.

    En los últimos 10 años he enviado varios miles de correos a prácticamente todas la universidades de Física – y de algunas otras materias relacionadas – del mundo, desde las más prestigiosas (sin excepción) a las más desconocidas. La verdad es que he sido enormemente persistente porque los destinatarios, profesores todos ellos, casi nunca han…


  • Atomic and Solar System model. Intersecting longitudinal fields varying periodically.

    Atomic and Solar System model. Intersecting longitudinal fields varying periodically. (Pictures) Fermions. Opposite phase of variation. Not ruled by the Pauly exclusion principle: Moment 1 Moment 2 Bosons. Equal phase of variation. Ruled by the Pauli Exclusion Principle. Fermions: Bosons: Carbon «atom»:


  • Differential Geometry in the Pythagorean Theorem.

    Exploring heuristically the Pythagorean theorem by means of differential geometry it appears that when ‘a’ and ‘b’ are not equal there is no equivalence between the internal and external elements of the quadratic system. It seems the broken equivalence could be saved by combining the parabolic and hyperbolic geometries, or by using periodically variable or…


  • Geometría diferencial, parabólica, e hiperbólica en el Teorema de Pitágoras

    Cuando en el Teorema de Pitágoras a y b son iguales, el área a^+b^2 coincide (es equivalente pero no igual) con el área de c^2 porque los 8 lados racionales de a^2 y b^2 equivalen a las cuatro hipotenusas racionales (hay que contar las dos caras de cada hipotenusa) de c^2, y los cuatro lados…


  • El orden de los números primos

    ¿Cuál es la regla que rige el orden de los números primos? Hoy voy a explicar por qué, desde mi punto de vista, los números primos aparecen en el orden en que lo hacen. Por ejemplo, tenemos las parejas de primos (los llamados «gemelos») 5-7, 11-13, 17-19, y entonces viene un número primo sin pareja,…


  • When a Number N is Prime.

    In Spain we would say this is the «old woman’s account», but I think it explains visually what prime numbers are and why they follow the order they have. Numbers are not purely abstract entities, any quantity implies distribution and distribution implies a space and a center. Numbers represent symmetries related to a real and…


  • Los campos de gravedad se expanden y se contraen.

    La noción de espacio que se subyace en los modelos aceptados por la física es la de un universo único y estático en el que los objetos celestes se mueven por inercia y las múltiples asimetrías que se observan se entienden producidas por azar. Cuesta mucho tiempo y esfuerzo cambiar los paradigmas asumidos. Es como…


  • «Geometría e imaginación» de David Hilbert. Una lectura crítica.

    Un amable profesor de matemáticas ruso a quien envié por email unas figuras geométricas preguntándole su opinión me recomendó un libro de David Hilbert titulado en inglés «Geometry and the Imagination» («Geometría e imaginación»); el título original en alemán es «Anschauliche Geometrie» (Geometría descriptiva»). Por su puesto, no estás traducido al español, ¿para qué iba…


  • Curvaturas hiperbólicas y parabólicas en el círculo.

    La geometría hiperbólica es aquella que tiene (o está relacionada con) una curvatura cóncava, de signo negativo; La geometría parabólica es la que tiene (o está relacionada con) una curvatura convexa, de signo positivo. Pero ¿si cóncavo y convexo son dos perspectivas distintas – la de dentro y la de afuera – de una misma…


  • Euclidean and non-Euclidean Parallel lines on Lobachevsky’s Imaginary Geometry.

    Non-Euclidean or hyperbolic geometry started at the beginning of the XIX century when Russian mathematician Nicolai Lobachevsky demonstrated that the fifth Euclid’s postulate – the parallel postulate – was not applicable when it comes to curved lines and so that more than one parallel can be traced through a point external to another line. As…


  • Demostrando el quinto postulado de Euclides.

    Desde que Euclides escribió los «Elementos» varios siglos antes de Cristo, en el que recogió todos el conocimiento matemático de entonces, se ha venido discutiendo mucho a cerca del postulado quinto conocido hoy como el postulado de las paralelas. El postulado 5º afirma que: “Si una recta al incidir sobre dos rectas hace los ángulos…


  • Virtual and Mirror Convergences on the Demonstration of the Euclid’s Fifth Postulate.

    Summary: 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 are not Euclidean because they do not follow the Euclid’s definition of parallels. The fifth postulate of the Euclid’s Elements states that “If a straight line…


  • On the Demonstration of Euclid’s Fifth Postulate.

    Several centuries before Christ, Euclid’s «Elements» stablished the fundaments of the known Geometry. Those fundaments remained unquestioned until the XIX century. It stablished 5 simple and self evident postulates, from which Euclid deduced and remonstrated logically all the Geometry. But fifth postulate created many difficulties to mathematicians through the History. Many of them thought, from…


  • On the meaning of Mathematical Incommensurability in Euclidean and Non-Euclidean Geometries.

      «It is possible, of course, to operate with figures mechanically, just as it is possible to speak like a parrot; but that hardly deserves the name of thought». (Gottlob Frege. «The Foundations of Arithmetic»). Think about how human beings could have started to measure linear lengths and areas. I guess to measure a linear length for…


  • Reinterpreting the Riemann’s Lecture «On the Hypotheses which lie at the Bases of Geometry».

    I am going to write some comments around the famous Bernard Riemann’s lecture «On the Hypotheses which lie at the Bases of Geometry».  As you may already know, it is considered one of the most important texts in the History of modern mathematics having had also a decisive influence in other different realms of knowledge, particularly in modern Physics. I…


  • Solving Quintic Equations with radicals from a geometrical point of view.

    (Note: I’ve removed my non-ads subscription in WordPress, which is a premium feature I had purchased for the blog until now; also I won’t renew the blog’s domain name. I wanted to clarify I won’t get any profit with the advertisements that can appear on this blog). I think quintic functions could by understood as a rotational fractal formed by…


  • Squaring the Circle in a Projective Way

    I think it could be possible to explain the area of the circumference in a simple and rational way by projecting the square on the radius through the Z diagonal until the point that touches the circle and adding an additional extension. In the picture above, the coloured spaces represent the area of the circumference.…


  • The Pythagorean Theorem in the Complex Plane.

    The square 1 that we build with the referential segment of length 1, is an abstraction: we do not measure the lines and points there inside of it; We convey that the space inside of the square 1 has the value 1, 1 square, and we are going to use it as reference for measuring…


  • The Role of Irrationality in the Planck Constant.

    I think light does not travel at any speed, the photon is periodically formed by the periodical convergence of waves that are related to different kind of symmetries. I consider the point of the periodical convergence is the particle aspect of light. If the Planck constant describes the particle aspect of light, it will be…


  • On the Representation of the Riemann Z Function Zeros in an R2 Space and their relation to Irrationality.

    Abstract: 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 irrational Number 1

    I think it could be told that there is a rational number and an irrational number . For drawing the picture above I followed the next steps: 1. Draw a circumference with a radius 1 (or ) 2. Draw its exterior square. Each of its sides represent the 3. Draw another circumference outside of the…


  • The Hidden Rationality of the Pythagorean Theorem, the Square Root of 2, and the Pi number.

    We construct the square areas of the legs and in the Pythagorean theorem placed on and related to the specific spatial coordinates and . When the value of the leg  is 1 , the square area constructed is our primary square area 1. To say that the space that exists inside of a square area with…


  • «Solar Winds» and «Shock Waves». Is not Gravity a Force of Pressure?

    This artistic picture was published by NASA. It represents the interaction between the «solar winds» and the Pluto’s atmosphere. (Credits: NASA/APL/SwRI) Looking at that picture, I think it seems reasonable to deduce that the solar winds create a force of pressure on the Pluto’s atmosphere which resists to be pass through. This interaction between a…


  • Aleph and Irrationality

    I want to share some ideas that I’ve had related to the lost geometrical meaning of old alphabets. Aleph is the first letter of the Hebrew alphabet. It exists too in other alphabets as the Arabic, Phoenician and Syriac. I’m getting those data from Wikipedia. Aleph, or Alpha, represents the number one, and as it…


  • On the demonstration and refutation of Fermat’s last theorem and the Pythagorean’s one

    I consider Fermat’s last theorem is true to the same extent that the Pythagoras’s theorem is false. But it could be said too they both are wrong, or even that Fermat’s Last theorem is at the same time right and wrong depending on the perspective of the observer. When we create a square area we…


  • On the Refutation of the Pythagorean Theorem

    When we draw a square we make it on the base of 2 specific spatial coordinates (XY). We can delete our draw and create another independent square of the same dimensions based upon any other 2 spatial coordinates. In both cases, our referential coordinates will be the same, X and Y. We can change the…


  • Ciencia e irracionalidad

    Desde antiguo el ser humano ha tratado de situarse en el mundo, ordenarlo, comprenderlo y manipularlo, contándolo, pesándolo y midiéndolo. Todavía hoy muchos piensan que pesar, medir y contar es conocer. Cuanto más pequeños sean sus fragmentos, con más exactitud podrá ser examinada y conocida la cosa que conforman. La idea misma de justicia y…


  • Irrational Numbers Are Not So «Irrational»

    Drawing a diagonal in our referential coordinates X and Y we should ask ourselves if we are expanding the referential space or we are contracting it. Was it contracted or expanded previously? We modify the referential space, transforming it, folding or unfolding it, each time we displace our spatial coordinates without displacing in the same…


  • Noncommutative Geometry on 147

    Likely the first mesures were made with a simple step. The primary reference for next mesures should be the length of a unique step. As we created a first and unique reference for measuring straight lines – we can name it «1 step» – we invented the idea of length for organizing our world and…


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  • Our Tilted Universe

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  • Six Quarks Atomic Model

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  • Prime and Irrational Numbers

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  • Complex Prime Numbers and the Riemann Hypothesis

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  • On the Refutation of the Riemann Hypothesis

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  • Mass Gap Problem and Hodge Conjecture

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  • Mass Gap Problem Solution

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  • Recap. The Next Copernican Revolution

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    Física para gente de Letras. Parte I. Me gustaría hacer un resumen de lo que llevo escrito en este blog, pensando sobre todo en las personas que se consideran así mismas “de letras” y que nunca han entendido nada sobre “ciencias”. He de advertir a los demás lectores que la ciencia no va a salir…


  • Antimatter in the Periodic Table of Elements

    I consider that gravitational fields vary periodically, they expand and contract. They are fields of pressure. I think that the Hydrogen atom represents the curvature of a gravitational field when it is expanded. The curvature has its lowest tension and it creates the lowest pressure on matter. The Helium atom represents the gravitational curvature  from…


  • Hydrogen and Helium Gravitons and Higgs Bosons

    Aristotle’s cosmovision prevailed during fifteen centuries as the unique and very true explanation of reality between most western people. But all the prestigious of his world vision disappeared with the European scientific revolution, in the European Renaissance. As you very well know, Copernicus and Galileo proved that it was the Sun and not the Earth…


  • Quantum Physics and Cancer Research

    Current atomic physicists, chemists, biochemists, biologists, physiologists, electrical engineers, etc, work with a model that asume electrons are subatomic particles that do not have a known relation with the gravitational fields we exist inside. Today, our science do not know the relation between gravity and electromagnetism, and at atomic level it is currently believed that…


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    El pasado verano envié más de mil correos a profesores, doctores y catedráticos de física de distintas universidades del mundo. Trataba de explicarles las ideas que había desarrollado sobre física atómica y astrofísica durante casi 6 años de mucho pensar apasionadamente, con mucho esfuerzo. Dado que yo no soy físico, hice la carrera de Derecho…


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  • Subatomic Particles Are Imaginary Numbers

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Ideas for an Unconventional Atomic Model to CERN

Today I started to read the book «Lost in Math. How Beauty Leads Physics Astray», by Sabine Hossenfelder.

At some point of the beginning, she speaks about a conversation with the head of theoretical physics at CERN, the Conseil Européen pour la Reserche Nucléaire. (CERN operates the largest particle collider, the LHC, which is providing a lot of information that need to be analyzed by physicists). And when she asked that person about what they «make of the recent LHC data», he answered: «We are so confused».

She did not clarify if the confusion comes from the enormous amount of data to be interpreted or from the difficulty to interpret and understand it with the existing or other alternative models, but as the book mentioned that the professor Giudice’s research  «has focused on developing new theories of particle physics that hold the prospect of solving problems in existing theories», I immediately got excited – my enthusiasm seems to be inexhausted yet – about the idea of sharing with him the atomic model based on intersecting fields varying periodically I try to explain on this blog for a long time.

I never lose the hope that some ideas of non-professionals – I prefer when they contemptuously call us «cranks» than when they indulgently say  «amateurs» – can be inspirational to professional physicists who actually seem to be really stuck in a deep rat.

But as I’m very afraid that in CERN nobody is going to have time to read and make the effort of trying to understand the crazy ideas that without any mathematical equation come from unsolicited emails of crank people, I decided to publish on my blog the whole email I just sent him.

This is something I think I’m going to do since now because although the ideas and pictures I always send are almost always the same, I formulate them in different ways that maybe could be clearer for someone interested here:

«Dear professor Giudice,

I’m not a scientist but I wanted to tell you some ideas about an unconventional atomic model that I hope could be inspirational to your theoretical researches at CERN.

If you had time I’d like very much to know your opinion about them.

I suspect the idea of quantum superposition or overlapping resulted from a misinterpretation of what Riemann spaces were for Riemann himself (I mean, without the later interpretations like the one made by Hermann Weyl). To me, Riemann surfaces or fields are not about superpositions but about actual intersections, considering those intersections as partial fusions. When it comes to two parallel longitudinal fields that intersect, the intersection does not imply a superposition but a partial fusion that creates a dual «entangled» system with four new subfields created and shared by them in that intersection.

On the above picture, the intersecting fields are A and B, and the subfields they create in their intersection are the fields «c», «d», «e» and «f». We name + to the fields placed at the right side of the centre of symmetry and – to the fields placed at its left side.

If the two intersecting fields A and B vary (or vibrate) periodically, expanding and contracting, the behaviour of the subfields will be different depending on whether the phases of variation are equal or opposite.

1. When the phases of variation are opposite, when A contracts B expands and vice versa, the subfield «d» will oscillate in a pendular way moving towards left and right; it will move towards the side of the intersecting field A or B that contracts.

So when the left intersecting field -A contracts the field «d» will move towards the left and we attribute to d, to the pushing force that creates such a displacement and to its inner orbital motion, a negative sign.

At that moment, we can say the «d» field also exists «virtually» with a + sign at the right side of the centre of symmetry of the system: it actually does not exist currently there, but it will exist a moment later when the A- intersecting field is going to expand and the B+ one is going to contract.

On the below picture, the negative «d» field moving towards left is coloured in yellow; it represents an electron field:

On the below picture, the «d» field coloured in yellow moves towards right getting a positive sign; it represents a positron field.

So, if we think about the + – b field as an electron/positron field, we can say that the electron is its own antimatter (as the positron will be its own antimatter too) because electron and positron will be the same field existing at different times in different, mirror symmetric, places. In that sense, electron and positron will be Majorana antiparticles.

(At this respect I would say that – because between each expansion and contraction of the two intersecting AB fields there will be a moment of no variation, (when a field reaches its maximum rate of expansion or contraction until it starts to getting contracted or expanded again), between each pendular oscillation of the «d» subfield there would be a precession; so, that oscillation of – + d will be describing periodically a circle. So, when the  – d moves toward left for the first time, when later it moves towards right becoming + d, they both will not be exactly the mirror symmetric particles,  to find the mirror symmetric particles it would be necessary to wait until the circular oscillation reaches  the – X  and  + X coordinates).

On this view it’s clear that the electron subfield is not «attracted» towards the left, its displacement towards left (the electronegativity) comes as a mechanical consequence of the variation of the intersecting fields that create it varying with opposite phases.

On the other hand, following this hypothetical model, the subfields – c and + e, that exist in opposite places at the same time, will experience a periodical expansion and contraction: -c will contract when -A contracts while +e will expand when +B expands.

When – c  (or + e) contracts, there would be an increment of the velocity of its inner orbits because of the pushing force caused by such a contraction inside of those fields. They will experience an opposite decompression when expanding.

I consider the contracted – c subfield as a neutron and the expanding + e subfield is an antineutrino; I consider the expanded – c subfield as a neutrino and the expanding + e subfield as a proton.

Neutron and proton will be Dirac antiparticles (because they are different fields) existing at different consecutive times in mirror symmetric locations.

When the contracted neutron – c actually exists at the left side of the dual system, the contracted + e proton will only exist at the right side in a virtual way because at that moment, in the right-handed side, it will exist an expanded  + e antineutrino.

Because of the above mentioned, those electron/positron, neutron/proton, neutrino/antineutrino subfields, will respect the Pauly Exclusion Principle with respect their own antimatter. To me, the PEP is not related to two sub-particles existing in the same place at the same time because that would be impossible, I think the PEP is only related to the existence of a sub-particle and its sub-antiparticle in two mirror symmetric places at the same time. (To speak about electronic shells in this context means that the electron subfield will be placed at a different location while moving in a pendular way).

So, when it comes to opposite phases of variations of the two intersecting fields, we will be speaking about the created subfields as «fermions» because they will respect the PEP.

2. When the intersecting fields A and B have the same phase of variation (A and B contract or expand at the same time), the mechanical behaviour of the mentioned subfields will be different:

Now there will be an up/down (instead of left/right) displacement of the d field, and the Pauly Exclusion Principle will not avoid the coexistent existence of two exactly mirror symmetric subfields, c and e, at the left and right sides of the centre of symmetry of the system.

So here we will speak about the created subfields as «bosons» that will not respect the PEP:

When  – A and + B contract at the same time, the d subfield will experience an upward displacement and a high contraction. That will imply the creation of a pushing force that can be considered a polarized «photon».

When – A  and + B expand at the same time, the d subfield will experience a downward displacement and an expansion. That expansion will imply a decay of the orbital energy inside of the d field, and that downward displacement will imply a temporary interruption of the upward source which before had created the photon. That interruption is the quanta phenomenon. But that interrupted photonic pushing force has its continuity in the convex side of the intersection of A and B where now there will be an inverted contracted e field causing an inverted pushing force that will be now creating an anti-photon.

If we are observing the dual system from its concave side, we will have been able to detect the previously emitted photon, but we won’t detect the currently emitted antiphoton; so we will be speaking about a «dark» – not directly detected or visible for us – antiphoton.

(The same can be said when it comes to fermions about for example a «dark» positron if we were placed inside of the – c expanded neutrino trying to detect the electronic behaviour of the dual system, we won’t be able to detect it directly).

At the left and right sides, there would be – at the same time – two mirror symmetric c and e subfields that will contract when A and B contract and will expand when A and B expand.

Note that there is still another force of pressure (or lack of force or a decompression) I have not mentioned yet: it’s the pushing force created on those mentioned subfields by the side of the fields A and B that is not cobordian to those subfields when A and B (or A or B) contract, (such a force will come from outside of the shared nucleus to inside).

Considered in this way, the atom would be then a dual structure with a shared nucleus. Electromagnetic charges would be the consequences of the interaction of at least two intersecting fields varying with the same or opposite phase. Strong and weak interactions would depend on those phases of variation. The strongest interaction and the strongest «bond» takes place when A and B contract at the same time.

I think in this model «supersymmetry» means that fermions become bosons and bosons become fermions periodically, (the subfields are the same although their shape and their behaviour and consequences vary), because of the phases of variation of the two intersecting fields A and B synchronize and desynchronize periodically.

I think we also could translate this model to the quantum chromodynamic terminology speaking about «quarks» as the moving sides of A and B that are cobordian with the subfields (created in their intersection), acting as pushing forces. In this sense, for example when it comes to the electron, we can speak inside of the electronic subfield about an «up» negative quark that is the pushing force caused by the displacement of the right side of the – A field moving towards left when contracting; we can think also about a decay of that electronic quark, but it will be a different down quark created by the displacement of the + B field when expanding. That down quark will be acting as one of the quarks that create the neutron; the other neutronic quark will be another part of the contracting – A moving towards left.

The below animated gif would be an approximate representation of the motion of the system (it would be necessary to add the circular rotation of the whole system):

I write a kind of unconventional blog about physics and maths and I’m going to publish now this email there.

In case you found time to reply to my email I would like very much to get your permission to publish your answer there as well.

Best wishes and kind regards from Spain,

Alfonso De Miguel»
curvaturasvariables.wordpress.com

—————————————

With respect to the book «Lost in Math», I must say I’m enjoying it so far. I’ve read phrases and implicit point of views that I don’t share at all, but the book is easy to read and to understand. For example, look at this description of supersymmetry:

You can know more about the author on her blog: http://backreaction.blogspot.com/2018/10/string-theory-pros-and-cons-video-no.html

But the more interesting thing to me so far is this little paragraph I bolded in blue:

It says: «Aesthetic ideals also gave rise to what may be the strangest episode in the history of physics: the popularity of ‘vortex theory‘, whose purpose was to explain the variety of atoms by knots of a different type. Knot theory is an interesting area of mathematics that today indeed has applications in physics, but atomic structure isn’t one of them». Nevertheless, vortex theory, at its peak, collected about twenty-five scientists, mostly in Great Britain but also in the United States, who wrote several dozen papers in the period from 1870 to 1890.»

When I read this I got shocked. How the bloody hell nobody during the last 10 years told me anything about the «vortex theory»? And the «KNOT»????

By God Blessed, I’ve argued with a lot of people about that and nobody mentioned anything about it…

(It’s the same that already happened to me with the Pushing gravity theory I mentioned in this blog in previous posts. Since Michelson and Morley «demonstrated» the inexistence of the ether at the beginning of the XX century, the theoretical models based on the existence of such ether became forgotten for our science. And now we have an atomic model that no one understands built without the necessity of any ether but whose ultimate support is a vibrating field existing in the emptiness that permeates the whole space, that is to say, a new kind of ether with the unsuspicious name of «Higgs»…)

The below figures would be representations of intersecting vortices:

When I saw this picture I thought it was the intersecting vortices considered as longitudinal fields (not as tubular rings) when being observed from an above view as i represent them for example in this figure about the carbon atom:

But it seems that vortex for that theory were tubular rings.

Anyway, I’m now very interested in reading more about that atomic model – and the knot geometry – because of this is the first time I see the notion of vibrating fields (it seems that Kelvin’s vortices were thought to have an inner vibration) that actually INTERSECT to build an atomic model.

The vortex atom theory, originally an idea of William Thomson (Lord Kelvin for friends), was popular in England – and virtually ignored in Germany – from 1870 to 1890. (But as it required the existence of an aether – as the pushing gravity theory do – it was forgotten at the beginning of the XX century).

You can get a full information about the vortex theory in «The Vortex Theory of Atoms — Pinnacle of classical physics», by Steven van der Laan, (thesis for his master’s degree in History and Philosophy of Science in the Institute for History and Foundations of Science, Utrecht University. 2012)

https://dspace.library.uu.nl/handle/1874/260711

Have a great day.

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