Abstract<\/em><\/span><\/h5>\nThis text summarizes how a new approach to the Universe based on the existence of a “crystalline ether”<\/em>, which has recently been detailed in the third versions of two books [1]<\/em>, makes it possible to find a simple, unified and coherent explanation of all the theories of modern physics and of the Universe.<\/p>\nThe basic concepts of this approach can be summarized as follows: (i)<\/em> the support of the Universe is a form of “crystalline ether”<\/em> which consists of a solid and massive lattice, with the simplest possible elasticity, and in which matter is represented by the set of topological singularities of this lattice (loops of dislocations, disclinations and dispirations), and (ii)<\/em> this lattice exclusively satisfies, in absolute space, the basic classical physical concepts of Newton’s law and the two principles of thermodynamics.<\/p>\nWith these basic classical concepts alone, we show that it is possible to find all the modern theories of physics, namely that the behaviors of this lattice (the Universe)<\/em> and its topological singularities (the Matter)<\/em> satisfy electromagnetism, special relativity, general relativity, gravitation, quantum physics, cosmology and even the standard model of elementary particles.<\/p>\nThe Quest for a Theory of Everything<\/em><\/span><\/h5>\nModern theories of physics are based on mathematical relationships postulated to explain observed phenomena<\/em>, and not on an inference of these mathematical relationships from an understandable first principle. Electromagnetism is based on Maxwell’s equations<\/em>, without simple explanations of what electric and magnetic fields really are, what electric charge is, and how electromagnetic waves can propagate in a vacuum. Special relativity is based on Lorentz transformations<\/em>, without any explanation of the root causes why time expands and lengths contract when an object moves at high speed, or in relation to what the object is moving. General relativity is based on Einstein’s famous equation<\/em> that relates the curvature of space-time to the mass and energy of matter in space, without any real explanation of why matter “curves” space-time, and even what space-time is exactly. Quantum physics is based on Schr\u00f6dinger’s equation<\/em>, without any explanation of the deep reason for this relationship, what the wave function really is, and what defines the boundary between a classical and a quantum behavior of an object (quantum decoherence). Cosmology<\/em> is based on general relativity<\/em>, and it tries to describe the observed behaviors of the universe by injecting concepts, such as dark matter<\/em> and dark energy<\/em>, which have no underlying physical explanation for the moment, and which are introduced arbitrarily to make the theory fit the experiment. The Standard Model of Elementary Particles<\/em> is constructed from numerous experimental observations, but without any explanation of what an elementary particle really is, why it has mass and electric charge, what its spin really is, what differentiates leptons and quarks, why there are three families of leptons and quarks, what weak and strong forces really are, and what explains the confinement and asymptotic behavior of the strong force.<\/p>\nIn addition, these various theories do not have a common origin, and it seems very difficult, if not impossible, to unify them. The search for a theory of everything capable of explaining the nature of space-time, what matter is and how matter interacts, is in fact one of the fundamental problems of modern physics.<\/p>\n
Since the 19th century, physicists have sought to develop unified field theories, which should consist of a coherent theoretical framework capable of taking into account the different fundamental forces of nature. Recent attempts to search for a unified theory include the following: the “Great Unification”<\/em> which brings together the electromagnetic force, the weak interaction force and the strong interaction force, the “Quantum Gravity”<\/em> and the \u00abLooped Quantum Gravitation\u00bb<\/em> which seek to describe the quantum properties of gravity, the “Supersymmetry”<\/em> which proposes an extension of space-time symmetry linking the two classes of elementary particles, bosons and fermions, the “String and Superstring Theories”<\/em>, which are theoretical structures integrating gravity, in which point particles are replaced by one-dimensional strings whose quantum states describe all types of observed elementary particles, and finally the “M-Theory”<\/em>, which is supposed to unify five different versions of string theories, with the surprising property that extra-dimensions are necessary to ensure its coherence.<\/p>\nHowever, none of these approaches is currently able to consistently explain at the same time electromagnetism, relativity, gravitation, quantum physics and observed elementary particles. Many physicists believe that the 11-dimensional M-Theory is the Theory of Everything. However, there is no broad consensus on this and there is currently no candidate theory able to calculate known experimental quantities such as for example the mass of the particles. Particle physicists hope that future results from current experiments – the search for new particles in large accelerators and the search for dark matter – will still be needed to define a Theory of Everything.<\/p>\n
But this research seems to have really stagnated for about 40 years. Since the 1980s, thousands of theoretical physicists have published thousands of generally accepted scientific papers in peer-reviewed journals, even though these papers have contributed absolutely nothing new to the explanation of the Universe and solve none of the current mysteries of physics. An enormous amount of energy has been put into developing these theories, in a race to publish increasingly esoteric articles, in search of a form of “mathematical beauty” that is ever more distant from the “physical reality” of our world. Moreover, enormous sums have been invested in this research, to the detriment of fundamental research in other areas of physics, in the form of the construction of ever more complex and expensive machines. And, to the great despair of experimental physicists, the results obtained have brought practically nothing new to high energy physics, contrary to the “visionary” and optimistic predictions of the theorists.<\/p>\n
Many physicists now have serious doubts about the relevance of these theories of unification. On this subject, I strongly advise readers to consult, among others, the books by Unzicker and Jones [2]<\/em>, Smolin [3]<\/em>, Woit [4]<\/em> and Hossenfelder [5].<\/em><\/p>\nWhat if the Universe was a lattice?
<\/em><\/span><\/h5>\nIn the approach we will present here [1,6]<\/em>, the problem of the unification of physical theories is treated in a radically different way. Instead of trying to build a unified theory by tinkering with an assemblage of existing theories, making them more and more complex and esoteric, even adding strange symmetries and extra dimensions for their “mathematical beauty\u00bb, we start exclusively from the most fundamental classical concepts of physics<\/em>, which are Newton’s equation<\/em> and the first two principles of thermodynamics<\/em>. And using these fundamental principles, and developing an original geometry based on Euler coordinates to describe the topology of the Universe, we come, by a purely logical and deductive path, to suggest that the Universe could be a finite, elastic and massive solid, a “cosmological lattice”<\/em>, which would move and deform in an infinite absolute vacuum. In this a priori strange concept, it is assumed that the Universe is a lattice of simple cubic crystalline structure, whose basic cells have a mass of inertia that satisfies Newtonian dynamics in absolute space, and whose isotropic elasticity is controlled by the existence of an internal energy of deformation as simple as possible.<\/p>\nBy introducing into infinite absolute space a purely imaginary observer called the Great Observer GO<\/em>, and by equipping this observer with a reference system composed of an orthonormal absolute Euclidean reference frame to locate the points of the solid lattice and an absolute clock to measure the temporal evolution of the solid lattice in absolute space, a very detailed description of the spatio-temporal evolution of the lattice can be elaborated on the basis of the Euler coordinate system [7]<\/em>. In this coordinate system of the Great Observer GO, one can then describe in a very detailed way the distortions (rotation and deformation)<\/em> and the contortions (bending and torsion)<\/em> of the lattice. And one can also introduce topological singularities (dislocations, disclinations and dispirations) in this lattice in the form of closed loops [8]<\/em>, as constitutive elements of Ordinary Matter.<\/p>\nIf this original concept is developed in detail using an approach similar to the one used in solid state physics, it can be demonstrated by a purely logical and deductive mathematical path that the behaviors of this lattice and its topological singularities satisfy “all” the physics currently known, by spontaneously bringing out very strong and often perfect analogies with all the current major physical theories of the macrocosm and the microcosm, such as the Maxwell equations [9], special relativity, Newtonian gravitation, general relativity, modern cosmology and quantum physics.<\/em><\/p>\nBut this approach does not only find analogies with other theories of physics, it also offers original, new and simple explanations to many physical phenomena that are still quite obscure and poorly understood at present by modern physics, such as the deep meaning and physical interpretation of cosmological expansion, electromagnetism, special relativity, general relativity, quantum physics and particle spin<\/em>. It also offers new and simple explanations of quantum decoherence<\/em> (the boundary between classical and quantum behavior of an object), dark energy, dark matter, black holes<\/em>, and many other phenomena.<\/p>\nThe detailed development of this approach also leads to some very innovative ideas and predictions, among which the most important is the appearance, alongside the electrical charge<\/em>, of a new charge characterizing the properties of topological singularities, the curvature charge<\/strong><\/em>, which is an inevitable consequence of the treatment of a solid lattice and its topological singularities in Euler coordinates. This concept of curvature charge has very important consequences and provides new explanations for many obscure points in modern physics, such as weak force, matter-antimatter asymmetry, galaxy formation, segregation between matter and antimatter within galaxies, the formation of gigantic black holes in the heart of galaxies, the apparent disappearance of antimatter in the Universe, the formation of neutron stars, the concept of dark matter, the bosonic or fermionic nature of particles<\/em>, etc.<\/p>\nFinally, the study of lattices with special symmetries called axial symmetries, symbolically represented by “colored” 3D lattices of face-centered cubic structure<\/em>, allows us to identify an astonishing lattice structure whose looped topological singularities coincide perfectly with the complex zoology of all elementary particles of the Standard Model,<\/em> and which also allows us to find simple physical explanations for the weak and strong forces<\/em> of the Standard Model, including the confinement and asymptotic freedom phenomena associated with the strong force<\/em>, and also the existence of three families of elementary particles of very different energies.<\/em><\/p>\nIt is this concept of “cosmological lattice”<\/em>, that we will qualify as “crystalline ether”<\/em> that we will detail in the continuation of this paper, and we will show how this concept allows to bring a simple and unified explanation of the modern theories of physics and the Universe.<\/p>\nThe formulation of the deformation of a solid lattice
in Euler coordinates<\/em><\/span><\/h5>\nWhen one wants to study the deformation of solid lattices, it is common practice to describe the evolution of their deformation using a Lagrange coordinate system<\/em> and to use various differential geometries to describe the topological defects they contain.<\/p>\nThe use of Lagrange coordinates<\/em> to describe deformable solids presents a number of inherent difficulties. From a mathematical point of view, the tensors describing the deformations of a continuous solid in Lagrange coordinates are always of a higher order than one in the spatial derivatives of the components of the displacement field, which leads to a very complicated mathematical formalism when a solid presents strong distortions (deformations and rotations). To these difficulties of a mathematical order are added difficulties of a physical order when it is a question of introducing certain known properties of solids. Indeed, the Lagrange coordinate system becomes practically unusable, for example when it is necessary to describe the temporal evolution of the microscopic structure of a solid lattice (phase transitions) and its structural defects (point defects, dislocations, disclinations, joints, etc.), or if it is necessary to introduce certain physical properties of the medium (thermal, electrical, magnetic, chemical, etc.) resulting in the existence in real space of scalar, vector or tensor fields.<\/p>\nThe use of differential geometries<\/em> to introduce topological defects such as dislocations in deformable continuous media was initiated by the work of Nye (1953) [10]<\/em>, who for the first time established the relationship between the dislocation density tensor and the curvature of the lattice. On the other hand, Kondo (1952) [11]<\/em> and Bilby (1954) [12]<\/em> have independently shown that dislocations can be identified with a crystalline version of Cartan’s (1922) [13]<\/em> concept of continuum torsion. This approach was formalized in great detail by Kr\u00f6ner (1960) [14].<\/em> However, the use of differential geometries to describe deformable media very quickly comes up against difficulties quite similar to those of the Lagrange coordinate system. A first difficulty is linked to the fact that the mathematical formalism is very complex, since it is similar to the formalism of general relativity, which consequently makes it very difficult to manipulate and interpret the general field equations thus obtained. A second difficulty appears with differential geometries when it is a question of introducing into the environment topological defects of other types than dislocations. For example, Kr\u00f6ner (1980) [15]<\/em> proposed that the existence of extrinsic point defects, which can be considered as extra-matter, could be identified with the presence of matter in the universe and therefore introduced in the form of Einstein’s equations, which would lead to a purely Riemannian differential geometry in the absence of dislocations. He also proposed that intrinsic point defects (vacancies, interstitials) could be approached by a non-metric part of an affine connection. Finally, he also considered that the introduction of other topological defects such as disclinations could call upon even more complex higher order geometries, such as Finsler or Kawaguchi geometries. In fact, the introduction of differential geometries generally gives rise to a very heavy mathematical artillery (metric tensor and Christoffel symbols) in order to describe spatio-temporal evolution in infinitesimal local reference points, as shown for example by Zorawski’s mathematical theory of dislocations (1967) [16].<\/em><\/p>\nGiven the complexity of the calculations thus obtained, whether in the case of the Lagrange coordinate system or in that of differential geometries, it had long seemed desirable to me to try to develop a much simpler approach to deformable solids, but nevertheless just as rigorous, which was finally published in 2013 and 2016 in two first books [7]<\/em> entitled \u00abEulerian Theory of newtonian deformable lattices – dislocation and disclination charges in solids\u00bb.<\/em><\/p>\nThese books describe how the deformation of a lattice can be characterized by distortions and contortions. For this purpose, a vector representation of tensors<\/em> is used, which has undeniable advantages over the purely tensor representation, if only because of the possibility of using the powerful formalism of vector analysis, which makes it possible to easily obtain the geometrocompatibility equations<\/em>, which ensure the solidity of the lattice, and the geometrokinetic equations<\/em>, which make it possible to describe the kinetics of the deformation. Then, physics is introduced in this topological context, namely Newtonian dynamics<\/em> and Eulerian thermokinetics<\/em>. With all these ingredients, it becomes possible to describe the particular behaviors of solid lattices, such as elasticity, anelasticity, plasticity and self-diffusion,<\/em> and to write the complete set of evolution equations of a lattice<\/em> in the Euler coordinate system.<\/p>\nOn the basis of this Eulerian description of solids, it is possible to describe the various phenomenologies observed on usual solids.<\/em> Among others, we can find out how to obtain the functions and equations of state of an isotropic solid, what are the elastic and thermal behaviors that can appear, how waves propagate and why there are thermoelastic relaxations, what are the phenomena of mass transport and why inertial relaxations can appear, what are the usual phenomena of anelasticity and plasticity, and finally how it can appear structural transitions of 2nd and 1st species in a solid lattice.<\/p>\nThe concepts of dislocation and disclination charges in lattices
<\/em><\/span><\/h5>\n The description of defects (topological singularities)<\/em> that can appear within a solid, such as dislocations and disclinations, is a field of physics, initiated mainly by the idea of the macroscopic defects of Volterra (1907) [17],<\/em> which has undergone a dazzling development during its century of very rich history, as illustrated very well by Hirth (1985) [18]<\/em>. It was in 1934 that the theory of lattice dislocations really began, following the papers by Orowan [19],<\/em> Polanyi [20]<\/em> and Taylor [21]<\/em>, who independently described the edge dislocation. Then it was in 1939 that Burgers [22]<\/em> described screw and mixed dislocations. And it is finally in 1956 that the first experimental observations of dislocations are reported, simultaneously by Hirsch, Horne and Whelan [23]<\/em> and by Bollmann [24]<\/em>, thanks to the electron microscope. As for disclinations, it was in 1904 that Lehmann [25]<\/em> observed them for the first time in molecular crystals, and it was in 1922 that Friedel [26]<\/em> gave a first physical description of them. Then, from the middle of the twentieth century, the physics of defects in solids took a considerable extent.<\/p>\nIn the Eulerian theory introduced here [7]<\/em>, dislocations and disclinations are approached by intuitively introducing the concept of dislocation charges<\/em>, using the famous “pipes” of Volterra (1907) [27]<\/em> and an analogy with electric charges. In Euler coordinates, the notion of charge density then appears in a geometrocompatibility equation<\/em> of the solid, while the notion of charge flux is introduced in a geometrokinetic equation<\/em> of the solid. The rigorous formulation of the concept of charges in solids makes the essential originality of this approach of topological singularities<\/em>. The thorough development of this concept reveals first-order tensor charges, dislocation charges<\/em>, associated with plastic distortions (plastic deformations and rotations)<\/em> of the solid, and second-order tensor charges, disclination charges<\/em>, associated with plastic contortions (plastic bending and torsion)<\/em> of the solid. It appears that these topological singularities are quantified in a solid lattice and that they can be topologically localized only in strings (thin tubes)<\/em>, which can be modeled as one-dimensional lines of dislocation or disclination<\/em>, or in membranes (thin plates)<\/em>, which can be modeled as two-dimensional joints of bending, torsion or accommodation<\/em>.<\/p>\nThe concept of dislocation and disclination charges allows us to rigorously retrieve the main results obtained by the classical dislocation theory. However, it allows us to define a tensor of linear dislocation charge<\/em>, from which we derive a scalar of linear rotation charge<\/em>, which is associated with the screw part of the dislocation, and a vector of linear bending charge<\/em>, which is associated with the edge part of the dislocation. For a given dislocation, the scalar charge of rotation and the vectorial charge of bending are then perfectly defined without having to use a convention to define them, contrary to the classical definition of a dislocation by its Burgers vector<\/em>. On the other hand, the description of dislocations in the Euler coordinate system<\/em> by the concept of dislocation charges allows to treat in an exact way the evolution of charges and deformations during very strong volume contractions or expansions of a solid medium.<\/em><\/p>\nBy analytically introducing the concepts of density and flux of dislocation and disclination charges in lattices<\/em>, it is possible to describe in detail the macroscopic and microscopic topological singularities of the lattice that can be associated with dislocation and disclination charges, and to describe the movement of dislocation charges within the lattice by introducing the fluxes of dislocation charges and the Orowan relationships<\/em>. The Peach and Koehler force<\/em> acting on dislocations is also deduced and a new complete set of lattice evolution equations<\/em> in the Euler coordinate system can be established, this time taking into account the existence of topological singularities within the lattice.<\/p>\nThe concept of charges within the Eulerian solid lattice allows the development of a very detailed dislocation theory in common solids<\/em>. It is also possible to calculate the fields and energies of screw and edge dislocations<\/em> in an isotropic solid lattice, as well as the interactions that can occur between dislocations<\/em>. One can also develop a model of dislocation string<\/em>, which is the fundamental model to explain most of the macroscopic behaviors of the anelasticity and plasticity of crystalline solids<\/p>\nThe premises of a possibility to describe the Universe
by a “crystalline ether”<\/em><\/span><\/h5>\nOn the basis of the Eulerian description of solid lattices, we show that it is possible to calculate the rest energy \u00a0 E<\/strong>0<\/sub>\u00a0 <\/em> of dislocations, which corresponds to the elastic energy<\/em> stored in the lattice by their presence, and their kinetic energy<\/em> \u00a0 E<\/strong>cin <\/sub><\/em>, which corresponds to the kinetic energy of the particles of the lattice mobilized by their motion<\/em>, which then allows to attribute to them a virtual mass of inertia\u00a0<\/em> M<\/strong>0<\/sub><\/em>\u00a0 which surprisingly satisfies relations similar to the Einstein’s famous equation\u00a0<\/em> E<\/strong>0 <\/sub><\/em>= M<\/strong>0<\/sub><\/em>c2<\/sup>\u00a0 of special relativity<\/em>, but which is obtained here in a quite classical way, i.e. without calling upon a principle of relativity. Moreover, at high speed, it is shown that dislocation dynamics also satisfies the principles of special relativity<\/em> and the Lorentz transformations. <\/em><\/p>\nIt can also be shown that, in the case of isotropic solid media having a homogeneous and constant volume expansion, thus deforming only by shear, a perfect and complete analogy with Maxwell’s equations of electromagnetism<\/em> appears, thanks to the possible replacement of the shear tensor by the rotation vector. The existence of an analogy between electromagnetism and the theory of incompressible continuous media was already perceived a long time ago and developed by many authors, as Whittaker (1951) [28]<\/em> has shown. However, the analogy becomes much more complete by using the Euler coordinate approach [7]<\/em>, because it is not limited to an analogy with one of the two pairs of Maxwell equations in vacuum, but is generalized to the two pairs of Maxwell equations as well as to the various phenomenologies of dielectric polarization<\/em> and magnetization of matter<\/em>, and to the notions of electric charges and currents.<\/em> This analogy makes it possible to consider the cosmological lattice as a physical support for electromagnetic fields<\/em>, and to give physical interpretations to the various quantities of electromagnetism<\/em>. For example, the local rotation field of the lattice corresponds to the electric induction field of electromagnetism and the velocity field of the lattice to the magnetic field.<\/p>\nThe analogy with Maxwell’s equations is very astonishing by the simple fact that it is initially postulated that the solid lattice satisfies a very simple dynamic, purely Newtonian<\/em>, in the absolute reference frame of the external observer’s laboratory, which is equipped with orthonormal rules and a clock giving a universal time, whereas the topological singularities within the solid lattice, namely dislocations and disclinations with their respective charges, responsible for the distortions and plastic contortions of the solid, are subject to relativistic dynamics<\/em> within the solid, precisely due to the set of Maxwellian equations governing the shear forces in the medium. From this point of view, the relativistic dynamics of topological singularities is nothing else than a consequence of the perfectly classical Newtonian dynamics of the elastic solid lattice<\/em> in the frame of reference of the external observer.<\/p>\nFinally, it also appears in Euler coordinates that at long distance from a localized cluster<\/em> of topological singularities, formed for example by one or more dislocation loops or one or more disclination loops, the tensorial aspect of the distortion fields generated at short distance by this cluster may be neglected at long distance, so that lattice perturbations can be perfectly described at a large distance<\/em> by the only two vectorial fields of torsional rotation and bending curvature<\/em> associated with the only two scalar charges of the cluster, its scalar rotation charge\u00a0 Q<\/strong>\u03bb\u00a0<\/sub> and its scalar curvature charge<\/em> \u00a0<\/em> Q<\/strong>\u03b8<\/sub><\/em>. The rotation charge then becomes the perfect analogue of the electric charge<\/em> in Maxwell’s equations, whereas the curvature charge has some analogy with a gravitational mass<\/em> in gravitation theory.<\/p>\nThe existence of analogies between the mechanics of continuous media and the physics of defects<\/em> and the theories of electromagnetism, special relativity and gravitation<\/em> had already been the subject of numerous publications, the most famous of which are certainly those of Kr\u00f6ner [4,5]<\/em>. Excellent reviews in this field of physics have also been published, notably by Whittaker (1951) [20]<\/em> and by Unzicker (2000) [29]<\/em>. But none of these publications had gone as far in highlighting these analogies as the approach presented in my first books [7]<\/em>.<\/p>\nThe numerous analogies that appeared in the first books [7]<\/em> between the Eulerian theory of deformable media and the theories of electromagnetism, gravitation, special relativity, general relativity and even the Standard Model of elementary particles, reinforced by the absence of charges similar to magnetic monopoles, by a possible solution to the famous paradox of the electrical energy of an electron, and by the existence of a weak asymmetry between lacunar and interstitial charges of curvature, were sufficiently surprising and remarkable not to fail to titillate any open and somewhat curious scientific mind. But it is clear that these analogies were by no means perfect. It was therefore very tempting to analyze these analogies in greater depth and to try to find out how to perfect them, and this is what has led to the last books [1]<\/em>, which are devoted to the deepening, improvement and understanding of these analogies, and whose main steps are illustrated in the following.<\/p>\nSECOND PART – The “crystalline ether” and its Newton’s equation<\/span>
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<\/a><\/strong><\/em>From the Maxwell\u2019s equations of lattice deformations <\/strong><\/em>\u2026