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…


  • Tell All the Truth but Tell it Slant

    «Tell all the Truth but tell it slant – Success in Circuit lies Too bright for our infirm Delight The Truth’s superb surprise. As Lightning to the Children eased With explanation Kind The Truth must dazzle gradually Or every man be blind.» Yo will know this poem of Emily Dickinson. I find it very interesting,…


  • The original «Auld Lang Syne» Song

    This blog is devoted to the comprehension of the physical mechanisms that explain the anomalous cell division and differentiation. In the beginning of this new year 2015 I am going to make an exception for celebrating the new year with you. As English Second Language learner, this past New Year’s eve I tried to understand the…


  • Our Tilted Universe

    The thesis presented on this blog is that gravitational fields vary periodically, they expand and contract, with the same or opposite phases. Two intersected gravitational fields varying periodically create in their mutual intersection four new fields which vary periodically too. I consider that our known universe is one of the fields created by and in the…


  • About Many Interacting Worlds (MIW) Theory

    The authors of the article «Quantum Phenomena Modeled by Interactions between Many Classical Worlds» published on Physical Review X, have presented a rational model of (at least) two parallel universes that interact between them. With a simple model of their theory they could calculate quantum ground states and to reproduce the double-slit interference phenomenon. «probabilities…


  • CPT Violations

    Consider two intersecting (or overlapping) concave fields A and B that vary periodically, expanding and contracting, with equal or opposite phases. When A and B vary with opposite phases their different rhythms of variation can be considered two different temporal dimensions, T1 and T2. I assign T1 to A, placed in the left side of…


  • Six Quarks Atomic Model

    (At least) two intersecting gravitational fields that vary periodically with equal (Figure A) or opposite (Figure B) phases create in their mutual intersection four new fields that are the subatomic particles of the central atomic nucleus. Following the Pauli exclusion principle, the subatomic particles of figure A will be fermions that obey the exclusion principle.…


  • Prime and Irrational Numbers

    Summary: I think 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 think that there is also a similarity between prime numbers and subatomic…


  • Prime Numbers Distribution

    I have reviewed this post with the next one about Prime and Irrational Numbers I did not delete this post because I think it’s good to show that making mistakes is a part of the though process. Ideas come gradually and they need to be reviewed constantly. Etymologically “Prime” comes from the Latin “Primus” which…


  • Complex Prime Numbers and the Riemann Hypothesis

    Summarize: I consider that composite odd numbers formed by the multiplication of a prime number by itself n times, by example 9, 27, 81, etc (for the prime number 3), are imaginary prime numbers that reflect the real prime number 3; but the imaginary plane that reflects the real is interdimensional, by example a spiral…


  • 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…


  • Mass Gap Problem and Hodge Conjecture

    Summarize: It is well known that neutrinos have mass. But quantum field theories cannot demonstrate mathematically they have a mass bigger than zero. I think it could be demonstrated that neutrinos have positive mass working with a non conventional atomic model of two entangled – I use the term “entanglement” in the sense of physical…


  • Mass Gap Problem Solution

    M = D x V M = Mass D = Density V = Volume N = Neutron Ve+ = Anti neutrino P = Proton Ve- = Neutrino MN = (VN) (-a x -b x +c) MVe+ = (VVe+) / (-d x -e x +f) MP= (VP) (a x b x -c) MVe- = (VVe-) /…


  • Recap. The Next Copernican Revolution

    I’m going to summarize in this post, in a general and disordered way, the ideas that I have written on this blog until now. I consider that all are aplicable at atomic and astrophysical level: – Gravity is a force, but it’s not a force of attraction, it’s a force of pressure. – There is…


  • Física para gente de letras. (I)

    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…


  • Ciencia , Revolución y Sociedad

    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…


  • ¿Qué es la energía y para qué la necesitamos?

    Desde que los seres humanos descubrimos cómo obtener luz y calor del fuego, allá en la época de las cavernas, la búsqueda de nuevos y más efectivos combustibles ha sido constante en nuestra historia. La máquina de vapor permitió además obtener del fuego una fuerza mecánica. El motor de explosión que aún hoy usamos mayoritariamente…


  • What Gravitational Waves Are

    We think that our Universe is a gravitational field that expands and contract periodically. It is entangled to (intersected with) at least another universe. For us the known as «Big Bang» is the consequence of the simultaneous contraction of two entangled universes (or the contraction of one of them and the expansion of the other…


  • Subatomic Particles as Imaginary Numbers Update

    In this post there is not any new idea, I have only tried to put clearly the pictures of the previous post, although probably here there are some formal mistakes too. I think that because we are working with nonconmutative dimensions that are real and imaginary at the same time, this ideas could be placed…


  • Subatomic Particles Are Imaginary Numbers

    We think it is possible to unify quantum mechanics, relativity, and gravity, with a model of (at least) two entangled gravitational fields that vary – expand and contract – periodically with different or opposite phases, and 4 imaginary numbers that exist simultaneously in 4 mirror reflected – inverted – dimensions created by the gravitational intersection.…


  • Alfa, Beta and Gamma Radiations and Decays

    Dipolos

    In this picture I have drawn the pendulum motion, from right to left, and from left to right, of field number 3 that exists at the intersection of two other fields, number 1 and number 2. These two fields are varying with opposite phases: in the “posición 1” in the picture, the field 1 expands and the field 2 contracts, and in the “posición 2” the field 1 contracts and the field 2 expands.

    I indicated “fields 1 and 2” but I was referring to the gravitational fields 1 and 2 that are curved by the matters 1 and 2. In this blog we argue that all gravitational fields vary cyclically, and they expand and contract with their specific frequencies depending on the opposition that matter presents to be passed through by the gravitational flux, therefore creating the variable gravitational curvature.

    When those two intersecting gravitational fields (I would have used the word “entangled” but I think that “entanglement” has a different meaning for mainstream physics), have an opposite phase of variation, the new field created in their intersection, the field 3 in the picture, experiences a pendulum displacement that is currently known as an “electric stream” or an “electron.” (At the end of the article I’m going to put a picture with intersecting gravitational fields that vary with the same phase of variation, causing different consequences).

    When the phases of variation are opposites, the “electron” or field 3 moves toward the side of the matter in which the gravitational field is contracted.

    Mainstream physics explains the movement of shared electrons toward an atomic matter because of its “electronegativity.” Electronegativity is for current science an intrinsic property or tendency of matter that allows this matter to attract electrons. If in a molecule one matter has a bigger electronegativity than the other one, that matter will attract the shared electrons in a stronger way than the other one. It produces an electronic asymmetry.

    “Electrons” are considered by the currently accepted atomic model as “subparticles” with a negative electrical charge.

    But for us, the “electron” is not a subatomic particle, it is a space that is created and exists by and at the intersection of two gravitational fields that vary with opposites (or equal) phases.

    For us, this field 3, the “electron,” could have or not have some material mass inside it. (Here we have drawn a mass “3”).

    When this “electron” with negative charge that has moved toward the matter 2, in the “posición 1” of the picture, currently accepted physics would say that matter 1 would have lost an electron because it has acquired a “proton,” which has a positive charge by opposition with the negative charge of the “electron.”

    When those two gravitational fields vary again, at the “posición 2” of the picture, the intersected space, our “electron” (or “shared electrons”) will have moved again toward the matter 2 because its gravitational field 2 will be again contracted. And the gravitational field 1 will be expanded, so it will have lost an electron and gained a “proton.”

    This is a cyclical and dipolar situation. Here there are two poles, the positive one and the negative one, that cyclically change their location.

    But for us “proton” doesn’t exist as a sub particle either, for us a proton is the absence of an electron, so a proton exists when the gravitational field of its matter is expanded.

    When the electron moves in a contrary direction, it is currently known as “positron”, which is considered an electron with a positive charge, an “anti-electron.” This name for us is only for distinguishing it from the electron that traveled previously and will travel again later in the opposite direction. The signs of “electrical charges” are only an accepted convention.

    But the intersection of two cyclically variable gravitational fields creates two other fields that I have drawn in this picture as two horizontal cones located in both gravitational fields 1 and 2. Those new spaces do not move as the field 3, but they experience some transformations while the intersected 1 and 2 gravitational fields vary (expand and contract) and the field 3 (the electron) moves toward one side or another.

    So those two conic spaces open or close and move their orbital planes toward one side or another in an inverse way with respect to the field that produces pressure over them from above, and in an equal way with respect to the field that creates pressure from below.

    In the “posición 1” the field 1 is expanded and the field 2 is contracted. The left cone, which is placed in the gravitational field 1, has longer orbits that are inclined toward the right side. It doesn’t suffer the pressure of the expanded gravitational field 1 or the contracted gravitational field 2.

    And the conic horizontal space located in the contracted gravitational field 2, has smaller orbits because it is experiencing the pressure from below by the contracted field 2 and from above by the expanded gravitational field 1. It is inclined toward the right side too.

    In the “posición 2” it occurs the opposite: the conic space of the left side, in the contracted gravitational field 1 has the pressure of both gravitational fields 1 and 2. So it has smaller orbits and now it is inclined toward the left. And the conic horizontal space located at the right in the expanded gravitational field 2 does not have as much pressure, then it has bigger orbits now and it is inclined toward the left too.

    As mentioned earlier, these conic spaces do not have the motion force that has the space that exists in the intersection of the gravitational fields, the “shared electron,” when it moves toward the matter that has its gravitational field contracted. So they do not have any electrical charge, positive or negative. This is because we think it is possible to say that they have a neutral charge. In fact we think that those two conic fields are currently known as “neutrons.” Neutrons have a neutral charge but it is known that they have mass.  How can we explain that these spaces that we think are neutrons could have any mass? We will see this later.

    We are seeing that all fields that we are describing correspond with different subatomic particles of the currently accepted atomic model, protons and neutrons in a nucleus inside the matter and electrons outside it.

    Current physics considers that in the “Beta negative radiation” a “neutron” “transforms” into an “electron” and a “proton”. The proton is preserved in the nucleus, and two particles are emitted: an electron and a beta negative particle.

    In the “Beta positive radiation” current science affirms that a “proton” transforms into a “neutron” and a “positron” (the electron with negative charge). And the positron is called the “beta positive particle.”

    For us, in the “Beta negative radiation,” the field 1 expands and gains a + proton (because the shared electron “3” moves towards the field 2); the field 2 contracts and gains the shared electron field “3.”  The neutron (the horizontal conic space) of the field 1 has lost the pressure and has increased its volume; and the neutron of the gravitational field 2 has reduced its volume because it is now suffering the pressure of both gravitational fields 1 and 2.

    So it could be said that when a matter gains an electron because its gravitational field contracts, it obtains a neutron too; and when a matter loses an electron and gains a proton it loses a neutron too. (We are thinking here only about intersected gravitational fields that have opposite or clearly different phases of variation).

    It will occur for example in Redox reactions, when a matter gains an electron being reduced, it loses a proton and it will gain a neutron. And the matter that is oxidized, losing an electron and gaining a proton, will lose a neutron too.

    We said that neutrons are gained or lost. But for us, the field that is the electron continues being there. But they have been modified. Because current physics thinks about neutrons in terms of mass, we think that maybe they are measuring the loss of pressure and they are misidentifying pressure with mass, and losses of pressure with losses of mass. But this “loses of mass” necessary, we think, appear in the exact same proportion in the neutron located at the other gravitational field, which previously would have “lost its own mass”, its pressure.

    It could be accepted for us too that inside of these fields that are neutrons for us, could exist a material mass too. But neutrons and neutrinos would be the same material mass; it only would change the pressure on it, its own weight.

    In the case of “”posición 2,” the opposite occurs. Matter 1 gains the “positron” and gains a “neutron.”  And matter 2 loses its “electron” and its “neutron” and gains a “proton.”

    So, what could be the beta positive and beta negative radiations? We guess that these radiations are created by the transformations of the fields that are currently known as neutrons.

    For us, the neutron placed in the contracted gravitational field that has near it the shared electrons, produces the beta negative radiation because its pressure (the pressure on the neutron field) is increased; and the beta positive radiation will be created by the neutron located in the other gravitational field when it becomes contracted, so it will have near it a positron, losing its previous “proton”.

    So it could be said that in beta negative radiation matter gains a neutron and an electron and loses a proton; and in beta positive radiation matter gains a neutron and a positron and loses a proton.

    The same could be said about beta positive and beta negative decays, they will be opposite to beta negative and beta positive radiations emitted by the neutron of the matter that has its gravitational field intersected with other, and both vary with opposite phases of variation.

    In this sense, when the neutron of the matter 2 gains pressure (at the “posición 1” of the picture), it will emit beta negative radiation and its matter 2 will gain an electron at the same time; at the same time, the neutron of matter 1 will have a beta negative decay and its matter will gain a proton. And when the matter 1 gains pressure  (at the “posición 2” of the picture), it will emit beta positive radiation and its matter 1 will gain a positron at the same time, while the neutron of the matter 2 has a beta negative decay and its matter gains a proton.

    Mainstream science considers that neutrons are inside of matter, in its nucleus. And because they need to justify the apparent losses of nuclear energy because it would be contrary to the principle of conservation of energy, they needed to invent a new sub particle below protons, neutrons and electrons, imagined by Pauli at XX century: the “neutrino.”

    For us, the neutrino is only the same neutron when it has lost its pressure, so when it is located in a gravitational field that is expanded when it  is intersected with another gravitational field that is contracted. We assume that recent measures of neutrinos must be measures of the consequences of the described variations in those fields.

    On the other hand, with respect to Alfa and Gamma radiation and decay, we think that the mechanism of explanation is the same that we have already proposed. But in these cases, the phases of variation of the intersected gravitational fields must be the same or similar. So here the two intersected gravitational fields expand and contract at the same time.

    When it comes to explaining Alfa radiation it is currently accepted that the nucleus loses two protons and two neutrons. And when the nuclear decay occurs, emitting electromagnetic waves, a new nucleus is formed with the same number of protons and neutrons. In the Gamma radiation it is said that there are not transformations of protons and neutrons but a photon is emitted because of the excess of energy that was accumulated there.

    For us there is not any difference on the mechanism that creates Alfa and Gamma radiation and produces their decays. It must be the same: two intersected gravitational fields are varying with the same frequency; when they contract at the same time the space created in their intersection increases its pressure moving up (it could be seen in the picture below). The ascending pressure creates a “photon.” And the two neutrons lose their pressure and increase their area.

    In this way, when the two gravitational fields are contracted at the same time, the “electron” increases its energy creating a photon, the two “neutrons” are lost and the two “protons” (the expanded gravitational fields) are lost too.

    Then, the energy created by the field that exists in the gravitational intersection, the electron for us, starts to experience a decay on its ascending energy because of the two intersected gravitational fields start two to become expanded. In this moment the expanding gravitational fields create a pressure on the two horizontal conic spaces that are for us “neutrons”. So, when nuclear decay occurs, the two “neutrons” appear again with their pressure, and the two “protons” are recovered too because of the gravitational fields 1 and 2 are now expanded.

    In this case it could be thought the losses of energy is motivated by the emission of the photon. But it could be thought using the current idea of “neutrinos,” that the energy was absorbed by the transformation of two neutrinos into two neutrons, because when the two gravitational fields were contracted and the coming up field, the electron, emitted the photon, the two neutrons did not have much more pressure; they would be neutrinos; and when the nuclear decay occurs, the two neutrons recover their pressure again (the pressure that is caused on them by the expanded gravitational fields).

    But four us the apparent losses of energy by the system when a photon is emitted must be found in the inverse side of the curvature that exists in the gravitation, at the convex side, of the gravitational fields. Because when the two gravitational fields expand the field that we identified as an “electron” (or shared electrons) comes down and losses its ascending pressure. But this pressure is not lost; it still exists in the field that is located in the convex side of those two intersected gravitational fields. This new field has its curvature inverted with respect to the curvature of the field that we identify as an electron.

    So the waves emitted by this inverted field will have an opposite direction with respect to the gravitational flux. It is because we thing they can be considered as an anti-photon and an anti-gravitational force.

    This process will be cyclical.

    * In the picture below there is a problem of weight distribution that we think explains the Mass Gap problem. We will try to explain it in the next post.

    * The fields that we have described in this article, are for us the currently known as «chemical bounds«. Two expanded gravitational fields represent a weaker interaction and two contracted gravitational fields represent a stronger interaction.

    * This presented model would be aplicable to any stelar system too. It could be interesting to think about if the orbit of the Earth were located in a field like the field «neutron», or if our Moon is located in a similar field too. Because then it would exist an Anti-earth (already known to Greeks as «Antichthon») located in the another gravitational field. In this cases the Earth would not orbit around the Sun, and the Moon would not orbit around the Earth.

    * The model would be aplicable to the intersection of two universes too. The cyclical «Big Bang» would occur when the two Universe gravitational fields were contracted creating a «Big bang photon».

    Here we have spoken only about the simplest possible system, with only two intersected gravitational fields.

    Symmetry1

    . . .