The Geometry of Gravity

Massimo Melli

The Geometry of Gravity

2024

I received this email Re: Academia Quantum: Your Manuscript ID 4QBdzR Has Been Rejected. Thank you again for your submission to Academia Quantum. Unfortunately, we are not able to accept this particular paper for publication at this time. Your submission didn't include a references section. for lack of references. My reply was: In my essay I mentioned Newton, Spinoza, Maxwell, Einstein and my theory of the Logons, created by myself. My reference is me, Massimo Melli, the inventor of the Logons. I am referring to Massimo Melli's equation (i.e. myself): Infinity X 0 = 1, which explains my "logon theory". For that theory, although 0 indicates a lack of dimensions, it still constitutes a physical existence, the Logon. Such "Physical Zero" should essentially be the basis not only of the number 1 but of all numbers as a dimensional coordinate 0. And that is the Ether, which is the cause of Inertia and Gravity. As far as I know, nobody said that before me...

The Geometry of Gravity Introduction Maxwell, in his essay: Field and Ether of 1890, clearly states that Newton had never been convinced that bodies really act on each other at a distance, independently of something interposed. Newton was Maxwell's precursor, in thinking that there was "something" that makes possible the transmission of gravity from one body to another. Newton tried to explain gravity as a "pressure" of a medium existing between bodies in space, but never published anything for fear of not having enough data to document his hypothesis. It was Maxwell who finally invented the Ether, to explain Faraday's lines of force and to explain the function of the Ether for the propagation of radiation in space. Einstein was the one who introduced the concept of ether without admitting that it existed, until, overwhelmed by the evidence of scientific experiments, he finally had to admit its existence in 1924: Gravity had become a phenomenon due to the geometry of space-time. Nowadays, many people, including many scientists, still think that gravity is an attractive force that can be explained by Newton's equation of the inverse square of the distance. Easy to understand by thinking that bodies attract each other. The truth is different: Newton, Maxwell and Einstein were right. Gravity is a geometric phenomenon of space. The Cabalist Leon explains it with his concept of "cone of certainty" and with Spinoza's Substance. The Discovery of the Ether It was the great Maxwell who first gave scientific form to the idea of the ether, based on Faraday's experiments. In fact, he used the ether to transmit electromagnetic radiation and light through empty space, but the hypothesis of an ether had been supported by various thinkers in the past, for different reasons, since ancient times. First of all Newton. Maxwell in his famous essay: Field and Ether says: "When Newton demonstrated that the force acting on every heavy body depends on its relative position with respect to other bodies, the new theory met with violent opposition from the most illustrious scholars of the time who defined the theory of gravitation as a return to the discredited method of explaining everything by means of occult causes, attractive powers and the like..." But Newton was so far from affirming that bodies act on each other at a distance, independently of something interposed. Indeed, he wrote: “It is inconceivable that brute inanimate matter, without the medium of something else, nonmaterial, should act and influence other matter without mutual contact… To me the idea that gravity is innate, inherent and essential to matter, so that one body can act on another at a distance, through a vacuum, without the medium of something else which makes possible the transmission of action and force from one to the other, is such an absurdity that I am convinced no man with adequate capacity for thinking over scientific problems can ever accept it.” Newton, as Maxwell relates, made attempts to explain gravity by differences in pressure in an ether, but he never published his theory “because he had failed by experiment and observation to account satisfactorily for this medium (the ether) and the manner in which it produces the principal phenomena of nature.” For two centuries after Newton, people continued to talk about attraction between bodies, and gravity as an attractive force. The Earth attracts the Moon, the Sun attracts the Earth, these were ideas rooted in everyone's minds, until Einstein came along to explain that gravity was equivalent to inertia and was the consequence of the geometry of space-time, curved by the mass of bodies. Spinoza, who was a contemporary of Newton, however had intuited that there must exist a Substance that is equivalent to the Ether of Physics, predicted by Newton, later used by Maxwell in his equations and considered necessary by Einstein to explain the phenomena of his Theory of Relativity. What is Substance? It is a "physical medium", transparent, immaterial, continuous, that fills space-time, that is, a potential energy in its pure state. For Spinoza, Substance is everything that does not need anything else outside of itself to exist. It is clear to him that Substance also includes all Being, that is, everything that exists (Spinoza's Pantheism). The Substance exists, it is unique, and it is infinite because nothing can limit it and consequently it can occupy the entire available space which is infinite. Therefore for Spinoza there is only one Substance: God. Thanks to Newton, Spinoza, Maxwell and Einstein we are now beginning to understand too. The truth is that infinite space-time consists of a Substance, which reacts elastically to the presence of a mass that moves it from its equilibrium position. Each point of the Substance, being the centre of space-time, opposes the movement by exerting an inertial pressure on the body that moves it: and that is gravity, that is an inertial pressure due to infinite space-time. But what is the Substance made of? Every non-rigid body immersed in space takes on a spherical shape, so if the Substance is made up of very small spheres, all equal to each other, that fill it all up, without leaving any voids, that must have been a problem that had occupied the mind of the great Newton. The problem was to find the maximum number of identical spheres, tangent to a central sphere of the same size, and Newton correctly calculated that there must have been 12. The distance between the centres of those infinitesimal spheres turned out to be “ħ cut”, that is, the Planck distance. One thing is certain, Newton had intuited the problem, but the progress of human knowledge continues…who knows what will happen now? Below is the representation of the quantized and energetic “space-time atoms”, the “logons” according to a hexagonal symmetry in which each atom (logon) is in contact with 12 atoms, forming tetrahedra…The distance between the logons is always the same, equal to the Planck distance ħ. How are the quantized logons distributed in space-time? Here is the structure of the quantized logons predicted by Leon in his essay on the ether published on Academia Edu with the title:” The Mystery of the Continuum.” This is a compact distribution of logons that form a hexagonal lattice of tetrahedra in contact with each other. In reality, the logons interpenetrate each other to form Reuleaux tetrahedra. The Reuleaux tetrahedron The Geometry of the Reuleaux Tetrahedron The image above represents four interconnected spheres (light blue) of probability surrounding four quantized logons and nested in each other so that the center of each sphere is on the surface of the other three. At the center of the three spheres is a tetrahedron (dark green) that contains a space-time common to all four spheres. This central tetrahedron that I propose to call "Aleph", has some interesting properties: 1- Every point of its volume is common to the four quantized logons. 2- The distance between its vertices is assumed equal to " ħ cut”, the Planck constant. 3- Its total probability must be shared 1/4 between the four quantized logons. 4- Since logons (i.e. space-time atoms) are dimensionless, this central tetrahedron or Aleph, although limited in size, contains infinite space-time atoms and therefore its total probability is 1. 5- Every possible event that has a non-zero probability of occurring within the Aleph will be verified in it, as if its space-time were continuous. 6- The sum of infinite Alephs fills all the infinite space-time available. Below is a Reuleaux triangle, which forms a face of the Reuleaux Tetrahedron. At the vertices of the central tetrahedron are located the quantized logons. When displaced by a dense and compact mass, the logons move, to make room for the mass, but they react elastically, exerting an inertial pressure on the mass. Why? When they are pushed towards the inside of the tetrahedron by the elasticity of Inertia, the probability spheres create a void inside the blue triangle, because each logon is the center of the continuous Infinite, which is nothing other than Spinoza's Substance, and seeks to regain its rightful position at the center of spacetime. The displaced logons exert a pressure on the mass that moved them. This is gravity, due to the inertia of space-time. Let us now introduce the concept of “Cone of Certainty” of a Probability field. In a cone of certainty the probability that an event will occur inside the cone is 1, that is, certainty. At the zero point, the apex of the cone, the probability is very dense, but as one moves away from the origin, it becomes diluted, in a ratio inversely proportional to the square of the distance. This does not take away, however, the fact that the predicted event will occur inside the cone. Outside of it, it will not occur. If we apply the concept to the pressure exerted by the logons on the mass that moves them, since the logons are very small spheres of probability, we can apply the concept of a cone of certainty to the pressure they exert on the mass In yellow is indicated a cone of certainty, whose apex is found in the center of the mass. By eye we see that at a double distance from the center, the probability, like gravity, is diluted, not by half, but by the square of the distance. In fact, to obtain the area of the cone, the distance that from 1 becomes 2 must be multiplied by itself, then becomes the square of the distance: 2X2=4 If we now take two masses at a certain distance from each other, their cones of certainty cancel each other out, trying to create a vacuum, which attracts the two masses, until they fit together to eliminate the vacuum. Nature has a horror of the vacuum. Conclusion Everything that exists in space-time has its sphere of probability. Even logons have their very small spheres of probability whose radius is at Planck's distance from the contiguous quantized logons. But what is probability? It is a potential energy due to existence, and existence is Spinoza's Substance. And God said to Moses: I am He who is. I am existence. Probability creates Inertia, which in turn creates Gravity. Existence is the Unity of all that exists, and it abhors a vacuum, because there can be no vacuums in the Substance of God, who is All in All. So: Probability of Existence = Potential Energy = Inertia = Gravity

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The Geometry of Gravity

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