A Theory of Space, Time and Matter

arXiv (Cornell University), 2010

We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, abandoning the usual requirement of a Ricci-flat five dimensional space-time, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing, at least at this stage, new physics, we get a very aesthetic presentation of classical physics in the spirit of general relativity. The usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are shown to be only various aspects of the geometry, for example curvature, of space-time considered as a Lorentzian manifold; that is no physical objects are introduced in space-time, no laws are given, everything is only geometry! This work is therefore in the continuation of the various attempts made since Einstein, Weyl, Nordstrom, Kaluza, Klein, Rainich, Wheeler.

Newton considered three-dimensional universe endowed with flat space Euclidean geometry, and treated the time as anoutside parameter and established his dynamics of the universe. Einstein along with space, considered time, and gener-ated a four-dimensional universe endowed with non-Euclidean curved space-time geometry with time as its fourth di-mension, and set up his field equations. Schwarzschild solved Einstein’s field equations around a star in space, which is,otherwise, flat, and obtained a solution. We, along with space and time, considered mass which also included energy ac-cording to Einstein’s mass-energy equivalence relation: E=mc2 , and generated a five-dimensional universe with themass as its fifth dimension, and solved the Einstein’s field equations, in some simple cases, and obtained solutionsaround a star in space, which is otherwise, flat.

arXiv (Cornell University), 2010

We consider in this paper, the geometrization of classical physics, i.e gravitation and electromagnetism. The goal is therefore to show that all the usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are only various aspects of the geometry, for exemple curvature, of spacetime considered as a Lorentzian manifold; that is no object is "put" in spacetime, no laws are given, everything is only geometry. We show why this goal is probably inaccessible in dimension 4, and put forward, while studying this case, the concepts leading to a solution in a five-dimensional spacetime. The solution we propose does not use truly new mathematics, but more a different view of the classical axiomatism of the classical theories, and in particular the suppression of an hypothesis usually made about the Ricci curvature, unjustified from our point of view. This work is therefore in the continuation of the various attempts made since Einstein, Weyl, Nordstrom, Kaluza, Klein, Rainich, Wheeler.

Pier Sandro Scano, 2024

The topic is whether the 4-dimensional structure constitutes a proven theory and whether it completely and effectively describes space-time phenomena. Spacetime is almost universally assumed as the basic structure for physical and cosmological thinking. Its meaning lies in the fusion of time and space into a unified entity. In the article, the theoretical foundation and mathematical formalism are analysed. The theory is confirmed by an incontrovertible quantity of experimental verifications. However reasons for reflection emerge, starting from the one-way character of time. The conclusion is that on space and time we know little, in the state, to be able to affirm a definitive and testable theory. Further research is necessary on what is assumed to be indisputable. Finally, it doesn't seem sustainable that Special Relativity, supplemented by General Relativity, constitutes a complete theory of spatiotemporal relations.

International Journal of Astronomy and Astrophysics, 2013

Newton considered three-dimensional universe endowed with flat space Euclidean geometry, and treated the time as an outside parameter and established his dynamics of the universe. Einstein along with space, considered time, and generated a four-dimensional universe endowed with non-Euclidean curved space-time geometry with time as its fourth dimension, and set up his field equations. Schwarzschild solved Einstein's field equations around a star in space, which is, otherwise, flat, and obtained a solution. We, along with space and time, considered mass which also included energy according to Einstein's mass-energy equivalence relation: E = mc 2 , and generated a five-dimensional universe with the mass as its fifth dimension, and solved the Einstein's field equations, in some simple cases, and obtained solutions around a star in space, which is otherwise, flat.

YGGDRASIL: The Journal of Paraphysics, Volume 1, Issue 2, Summer 1997: 128-157, 1997

The first two attempts to derive a unified field theory as an extension to general relativity were made by Weyl and Kaluza. The main idea was to develop a geometrical model whereby both gravity and electromagnetism emerged naturally from the same curved space-time continuum. Over the years, each of these attempts has engendered one of the main groupings of classical (non-quantum) unified field theories. Weyl sought to alter the geometry of the continuum while maintaining the number of dimensions at four. Kaluza sought to maintain the geometry of the continuum, but account for electromagnetism by altering the number of dimensions to five. It is generally believed that Kaluza’s was the first five-dimensional model of material reality and that it was largely ignored by the scientific community except for Klein’s attempt to use the model as a basis for quantizing relativity, but the model does have a separate history independent of Klein’s modification. The mere assumption of a five-dimensional space-time structure can take two basic forms, both of which are not as independent of the other as one would expect or hope. First of all, the five-dimensional space-time may be used as a mathematical formalism alone, which has no more meaning than to allow for the extra variables needed to incorporate the electromagnetic field into a single space-time structure. In this manner, the fifth dimension is assumed to have no physical meaning. It was this form that Kaluza’s theory assumed so Kaluza’s original model merely duplicated Maxwell’s electromagnetic model without adding any new physics. In the second type of these theories, the fifth dimension is given an actual physical reality. It is a basic necessity of this type of theory to explain why the fifth dimension seems to be beyond the natural experience of human perception.

2021

This last essay explains what is the 5th dimension necessary to explain Inertia, Gravity, and the paradoxes of Quantum Mechanics. We must distinguish between Einstein's Space-Time and that of Spinoza, which does not contain Time while filling all infinite space without leaving gaps. The substance is Existence, therefore it is at the same time Thought and Infinite Extension, without distinction, since thought and extension exist. The substance is the fifth dimension.

arXiv (Cornell University), 2010

We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism, and extension to higher-dimensional space-time. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, abandoning the usual requirement of a Ricci-flat five dimensional space-time, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing, at least at this stage, new physics, we get a very aesthetic presentation of classical physics in the spirit of general relativity. The usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are shown to be only various aspects of the geometry, for example curvature, of space-time considered as a Lorentzian manifold; that is no physical objects are introduced in space-time, no laws are given, everything is only geometry. We will then extend this setting to more than 5 dimensions, giving a precise mathematical frame for possible additional physical effects, preserving gravitation and electromagnetism. Version 22 04 2013. 1

Gravity and space-time are relative to each other because gravity or more precisely a gravitational wave is the only candidate responsible for empty-space around a mass and empty-space is the only candidate responsible for the mass of an object. It is true that a gravitational wave is a ripple in space-time but space-time is a result of a web of gravitational waves is also true and hence it is more appropriate to call space-time as gravitational-space-time and its known word to us is empty-space. Smallest unit of this web of gravitational waves is known as kaushal constant (K) [1]. Gravity is a result of the force of attraction in between two adjacent kaushal constants of the adjacent planes at a relative point in gravitational-space-time and hence this can be nicknamed as a web of gravity. The slower you move through space, the smaller your gravity web (or weaker the relative gravity) and hence the faster you move through time and vice versa. This paper is a solution to both mathem...

2013

We propose in this paper a mathematicians' view of the Kaluza-Klein idea of a five dimensional space-time unifying gravitation and electromagnetism. By considering the classification of positive Einstein curvature tensors and the classical Cauchy-Choquet-Bruhat theorems in general relativity, we introduce concepts of types and rigidity. Then, abandoning the usual requirement of a Ricci-flat five dimensional spacetime, we show that a unified geometrical frame can be set for gravitation and electromagnetism, giving, by projection on the classical 4-dimensional space-time, the known Einstein-Maxwell-Lorentz equations for charged fluids. Thus, although not introducing, at least at this stage, new physics, we get a very aesthetic presentation of classical physics in the spirit of general relativity. The usual physical concepts, such as mass, energy, charge, trajectory, Maxwell-Lorentz law, are shown to be only various aspects of the geometry, for example curvature, of space-time considered as a Lorentzian manifold; that is no physical objects are introduced in space-time, no laws are given, everything is only geometry ! This work is therefore in the continuation of the various attempts made since Einstein,