Physics from geometry

The invariance of the speed of light is taken as the fundamental of modern physics. But, in recent, the faster-than-light was observed. It requires that the fundamental of the whole physics be reassessed. In this paper, in the mathematics, the definitions in Euclidean Elements are stressed. It is pointed out that these definitions are only the concepts. They are not related to a certain real object or body. In physics, the Newtonian framework is stressed. It is pointed out that, in Newtonian theory, the abstract concepts are used as the definitions in Euclidean Elements. For example, the Sun is treated just as a point particle. And the initial law only is an abstracted concept which cannot be checked with experiment while it can be understood by our brain. According to the Euclidean Elements and Newtonian theory, some of the mathematical and physical concepts in modern physics are discussed. For example, it is pointed out that the extra dimension in modern physics is not a mathematical concept of Euclidean geometry as it is related to a real pillar. It is stressed that high and fractional coordinate systems are used to describe the object that can be described with the Cartesian one. And, the equations of physics in different coordinate systems and the transformation of the equations among different coordinate systems are discussed.

International Journal of Modern Physics A, 1996

We unify the gravitational field with its source by considering a new type of 5D manifold in which space and time are augmented by an extra dimension which induces 4D matter. The classical tests of relativity are satisfied, and for solitons we obtain new effects which can be tested astrophysically. The canonical cosmological models are in agreement with observations, and we gain new insight into the nature of the big bang. Our inference is that the world may be pure geometry in 5D.

viXra, 2016

This book proposes a review and, on some important points, a new interpretation of the main concepts of Theoretical Physics. Rather than offering an interpretation based on exotic physical assumptions (additional dimension, new particle, cosmological phenomenon,.. .) or a brand new abstract mathematical formalism, it proceeds to a systematic review of the main concepts of Physics, as Physicists have always understood them : space, time, material body, force fields, momentum, energy.. . and propose the right mathematical tools to deal with them, chosen among well known mathematical theories. After a short introduction about the place of Mathematics in Physics, a new interpretation of the main axioms of Quantum Mechanics is proposed. It is proven that these axioms come actually from the way mathematical models are expressed, and this leads to theorems which validate most of the usual computations and provide safe and clear conditions for their use, as it is shown in the rest of the book. Relativity is introduced through the construct of the Geometry of General Relativity, based on 5 propositions and the use of tetrads and fiber bundles, which provide tools to deal with practical problems, such as deformable solids. A review of the concept of momenta leads to the introduction of spinors in the framework of Clifford algebras. It gives a clear understanding of spin and antiparticles. The force fields are introduced through connections, in the, now well known, framework of gauge theories, which is here extended to the gravitational field. It shows that this field has actually a rotational and a transversal component, which are masked under the usual treatment by the metric and the Levy-Civita connection. A thorough attention is given to the topic of the propagation of fields with interesting results, notably to explore gravitation. The general theory of lagrangians in the application of the Principle of Least Action is reviewed, and two general models, incorporating all particles and fields are explored, and used for the introduction of the concepts of currents and energy-momentum tensor. Precise guidelines are given to find operational solutions of the equations of the gravitational field in the most general case. The last chapter shows that bosons can be understood as discontinuities in the fields. In this 4th version of this book, changes have been made :-in Relativist Geometry : the ideas are the same, but the chapter has been rewritten, notably to introduce the causal structure and explain the link with the practical measures of time and space;-in Spinors : the relation with momenta has been introduced explicitly-in Force fields : the section dedicated to the propagation of fields is new, and is an important addition.-in Continuous Models : the section about currents and energy-momentum tensor are new.-in Discontinuous Processes : the section about bosons has been rewritten and the model improved. 1 To be precise : assumptions are labeled "propositions", and the results which can be proven from these propositions are labeled "theorems". xi open, but I hope that their meaning will be clearer, leading the way to a better and stronger understanding of the real world. The first chapter is devoted to a bit of philosophy. From many discussions with scientists I felt that it is appropriate. Because the book is centered on the relation between Mathematics and Physics, it is necessary to have a good understanding of what is meant by physical laws, theories, validation by experiments, models, representations,...Philosophy has a large scope, so it deals also with knowledge : epistemology helps us to sort out the different meanings of what we call knowledge, the status of Science and Mathematics, how the Sciences improve and theories are replaced by new ones. This chapter will not introduce any new Philosophy, just provide a summary of what scientists should know from the works of professional philosophers. The second chapter is dedicated to Quantum Mechanics (QM). This is mandatory, because QM has dominated theoretical Physics for almost a century, with many disturbing and confusing issues. It is at the beginning of the book because, as we will see, actually QM is not a physical theory per se, it does not require any assumption about how Nature works. QM is a theory which deals with the way one represents the world : its axioms, which appear as physical laws, are actually mathematical theorems, which are the consequences of the use by Physicists of mathematical models to make their computations and collect their data from experiments. This is not surprising that measure has such a prominent place in QM : it is all about the measures, that is the image of the world that physicists build, and not about the world itself. And this is the first, and newest, example of how the use of Mathematics can be misleading. The third chapter is dedicated to the Geometry of the Universe. By this we do not mean how the whole universe is, which is the topic of Cosmology. Cosmology is a branch of Physics of its own, which raises issues of an epistemological nature, and is, from my point of view, speculative, even if it is grounded in Astrophysics. We will only evoke some points of Cosmology in passing in this book. By Geometry of the Universe I mean here the way we represent locations of points, components of vectors and tensors, and the consequences which follow for the rules in a change of representation. This will be done in the relativist framework, and more precisely in the framework of General Relativity. It is less known, seen usually as a difficult topic, but, as we will see, some of the basic concepts of Relativity are easier to understand when we quit the usual, and misleading, representations, and are not very complicated when one uses the right mathematical tools. We show that the concept of deformable solid can be transposed in GR and can be used practically in elaborate models. such as those necessary in Astrophysics. The fourth chapter addresses Kinematics, which, by the concept of moment, is the gate between forces and geometry. Relativity requires a brand new vision of these concepts, which has been engaged, but neither fully or consistently. Rotation in particular has a different meaning in the 4 dimensional space than in the usual euclidean space, and a revision of rotational moment requires the introduction of a new framework. Spinors are not new in Physics, we will see what they mean, in Physics and in Mathematics, with Clifford algebras. This leads naturally to the introduction of the spin, which has a clear and simple interpretation, and to the representation of particles by fields of spinors, which incorporates in a single quantity the motion, translational and rotational, and the kinematics characteristics of material objects, including deformable solids. The fifth chapter addresses Force Fields. After a short reminder of the Standard Model we will see how charges of particles and force fields can be represented, with the concept of connections on fiber bundles. We will not deal with all the intricacies of the Standard Model, but focus on the principles and main mechanisms. The integration of Gravity, not in a Great Unification Theory, but with tools similar to the other forces and in parallel with them, opens a fresh vision on important issues in General Relativity. In particular it appears that the common and exclusive use of the Levi-Civita connection and scalar curvature introduces useless complications xii INTRODUCTION but, more importantly, misses important features of the gravitational field. One of the basic properties of fields is that they propagate. This phenomenon is more subtle than it is commonly accepted. In a realist view of fields, that is the acceptance that a field is a physical entity which occupies a definite area in the universe, and experimentally checked assumptions, we deduce fundamental equations which can be used to explore the fields which are less well known, and notably gravitation. The sixth chapter is dedicated to lagrangians. They are the work horses of Theoretical Physics, and we will review the problems, physical and mathematical, that they involve, and how to deal with them. We will see why a lagrangian cannot incorporate explicitly some variables, and build a simple lagrangian with 6 variables, which can be used in most of the problems. The seventh chapter is dedicated to continuous models. Continuous processes are not the rule in the physical world, but are the simplest to represent and understand. We will see how the material introduced in the previous chapters can be used, how the methods of Variational Calculus, and its extension to functional derivatives, can be used in solving two models, for a field of particles and for a single particle. In this chapter we introduce the concept of currents and Energy-Momentum tensor and prove some important theorems. We give guidelines which can solve the equations for the gravitational field in the vacuum in the most general concept. The eighth chapter is dedicated to discontinuous processes. They are common in the real world but their study is difficult. From the concept of propagation of fields, we shall accept that this is not always a continuous process. Discontinuities of fields then appear as particles, which can be assimilated to bosons. We show how their known properties can be deduced from this representation.

A Theory of Space, Time, and Gravity, 2024

A unified field and gravity theory.

2021

In this paper, we investigate the ontological hypothesis, which implies that the spacetime is not the ultimate structure in our universe, and its existence emerges from a deeper physical entity. By using a very simple approach based on a classical problem, regarding the propagation of electromagnetic waves in empty vacuum. We were able to deduce that this deeper entity is just an omnipresent multi-rest states physical structure; aether. After that, we try to see how this ether fits in the universe that we exist in. The outcome is that its existence causes the emergence of some basic phenomena that our universe is built on. At the microscopic scale it turned out to be a source of the essential quantum phenomenon, which is currently known as the waveparticle duality. On the other hand, at the macroscopic scale it causes the emergence of spacetime curvature, around huge, massive objects like Earth. Finally, we consider a simple experiment that enables us to detect this ether, which is based on the concept of the conservation of linear momentum in nature, and the ontology of the inertial mass for the elementary particles.

Erkenntnis, 1995

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,

Cosmos and history: the journal of natural and social philosophy, 2015

We are drawn to physics by our desire to understand the most fundamental physical entities and processes of the Cosmos, from which all complexity evolves. However, the foundational models we are using, Relativity and Quantum Mechanics, were not created for this purpose. They confine inquiry to the description and prediction of the observer’s experiences and measurements. Not understanding these models’ limitations, physicists misinterpret and misapply them in their attempts to explain phenomena, producing confusion. The recent discoveries of black holes and the galaxial rotation and recession anomalies have highlighted the need for a new approach. Theoretical physics must become space physics—the study of space and its causal role in all fundamental phenomena including particle formation gravity, inertia, and electromagnetism. To replace Newtonian Mechanics and Relativity we need only identify the position and motion of the space that causes the effects that they describe. Gravity t...

2019

Journal of physics, 2022

Since it started about three centuries ago, theoretical physics went through a huge advancement and, particularly in the last century, the development was material. Its application to engineering brought a massive revolution in the way we humanity live now. Its interpretation opened up astoundingly deep understanding of our universe. One important research activity for the future is to further develop our theories and to further deepen our understanding of the universe. However, as Tomonaga said, when we are in a phase of looking for new paradigm, it is important to understand how our current theory was developed. The purpose of this paper is to present a logical and historic study of the conceptual development of theoretical physics. As the field of theoretical physics is so vast, we cannot cover all theories we have now. We will focus on the most fundamental theories of physics. As this field of physics is as deep and intricate as pure mathematics, if not more, it will be helpful to compare our challenge with that pure mathematicians are facing in the field of the foundations of mathematics. Such common ground will inevitably lead us to deeper philosophical issues. After all what we call physics started with Newton who developed both calculus and dynamics. He called it not physics but natural philosophy. So, it is naturally expected that philosophy, mathematics and theoretical physics develop hand in hand. It has been about a century since these fields started to develop separately and it is about time to restart the original interaction between these three intrinsic intellectual activities. Certainly this will help our timely search for a new paradigm. We must move forward.