A new way towards the Theory of Everything: Universe conjectured as a 3D Newtonian lattice and Matter conjectured as topological singularities of this lattice
One fundamental problem of modern physics is the search for a theory of everything able to explain the nature of space-time, what matter is and how matter interacts. There are various propositions, as Grand Unified Theory, Quantum Gravity, Supersymmetry, String and Superstring Theories, and M-Theory. However, none of them is able to consistently explain at the present and same time electromagnetism, relativity, gravitation, quantum physics and observed elementary particles.
By developing a complete theory of the deformation of solid lattices using Euler’s coordinates, one finds that this one can be used for the description of the spatiotemporal evolution of the Universe instead of the general relativity. In this way, it is suggested that the Universe could be a massive elastic three-dimensional lattice described in the absolute space by using Euler’s coordinates, and that fundamental building blocks of Ordinary Matter could consist of topological singularities of this lattice, namely diverse dislocation loops, disclination loops and dispiration loops. One finds then, for an isotropic elastic lattice obeying Newton’s law, with specific assumptions on its elastic properties, that the behaviors of this lattice and of its topological defects display “all” known physics, including electromagnetism, special relativity, general relativity, gravitation and quantum physics. It allows also one to resolve some longstanding questions of modern cosmology, as the universe expansion, the big-bang and the dark energy. It appears above all a completely new scalar charge, the curvature charge, which has no equivalence in the modern physical theories, which creates a very small deviation to the equivalence principle of Einstein between inertial mass and gravitational mass, and which allows one to give very simple explanations of the weak asymmetry observed between matter and anti-matter, the weak interaction force, the formation of galaxies, the disappearance of antimatter, the formation of gigantic black holes in the heart of the galaxies and the famous dark matter. Moreover, studying lattices with axial symmetries, one can identify a lattice structure whose topological defect loops coincide exactly with the complex zoology of elementary particles, and which allows one to explain quite simply the asymptotical nature of the strong interaction force.
In 2013, a theory was proposed [1,2], which lays methodically the foundations of an original approach by Euler coordinates of the solid lattices deformations, using only the Newton’s law and the two first principles of the thermodynamics as fundamental physical principles.
The concept of tensor dislocation charges and tensor disclination charges within a lattice was also introduced in details. This new charge concept allows one to quantify the linear topological singularities, which can appear at the microscopic scale of a solid lattice, such as dislocations and disclinations. But localized topological singularities have also been described, such as twist disclination closed loops presenting a scalar charge of rotation, responsible for a divergent field of rotation vectors, analogous to the electrical charge responsible for a divergent electrical field, or edge dislocation closed loops presenting a scalar charge of curvature, responsible for a divergent field of curvature vectors presenting some analogy with the space curvature of general relativity.
Numerous analogies appeared between this eulerian theory of deformable media and the theories of electromagnetism, gravitation, special relativity and general relativity, reinforced by a possible solution of the famous paradox of electron field energy. These analogies were surprising and remarkable but, by far, not perfect. It was then tantalizing to analyze much more carefully these analogies and to try to find how to perfect them. The purely qualitative description, step by step, of the main results recently obtained [3,4,5] in this search is the subject of this page.
Cosmic lattice and cosmological expansion
By choosing a particular imaginary lattice with a free energy per unit volume which depends linearly and quadratically on its volume expansion, and quadratically on its shears and on its local rotations, this lattice presents a pure transversal waves propagation only if these waves are circularly polarized, and does not present longitudinal waves when the volume expansion of the lattice is smaller than a critical value. In this case, the longitudinal waves propagation is replaced by the appearance of non-propagating local modes of longitudinal vibrations of the volume expansion of the lattice.
In the presence of a gradient of the scalar expansion field with a spherical symmetry, the transversal wave rays are bended, and this curvature can reach a point of no return if the gradient is sufficient, leading to a surprising analogy with the photons sphere of a black hole.
Adding an initial expansion kinetic energy to this lattice, it can expand from a singular point in space. This phenomenon presents first a very quick expansion, which is followed by a slowing down, then a re-acceleration of the expansion. Under certain conditions on the elastic free energy of the lattice, this expansion can be followed by a reverse cycle of contraction. These behaviors present a disturbing similarity with the cosmological theories of Big Bang and Big Crunch and, in the case of this lattice one finds a very simple explanation of the dark energy of the astrophysicists.
From these analogies with the non-propagation of longitudinal waves and the wave rays curvature of general relativity, as well as with the cosmological expansion of universe, this lattice has been called the Cosmic Lattice.
Maxwell’s equations and special relativity
The evolution equations of such a lattice when the field of expansion is homogeneous and constant are absolutely similar to the Maxwell’s equations of electromagnetism . This analogy includes not only the two Maxwell’s equation couples, but also all the electromagnetism phenomenologies, such as the dielectric properties of matter, the diamagnetic, paramagnetic and ferromagnetic properties of matter, as well as the electric charges and currents. And all these phenomenologies are associated with topological singularities moving inside the lattice. In particular, the rotation charge of a twist disclination loop is the perfect analogy of the electrical charge.
The localized topological singularities (for example the closed loops of edge dislocation and twist disclination) meet a relativistic dynamics inside the lattice, which results in the appearance of the Lorentz transformation. The twist disclination loops presenting a scalar rotation charge are also submitted to a force, which is perfectly analogous to the Lorentz force acting on the electrical charges.
In fact, the cosmic lattice behaves as the ether with regard to moving clusters of topological singularities. These moving clusters present a contraction of length and a time dilation, which depend on their velocity with regard to the lattice, similar to the effects of the special relativity, but which are perfectly real and measurable by an observer situated outside the lattice. This allows this external observer to explain very simply the famous twin paradox of the special relativity.
Local observers, which would be constituted from moving clusters of topological singularities, have no physical way to measure their own velocity with regard to the lattice, which leads them to postulate the classical special relativity in their reference frame, with all the paradoxes which are associated with its use.
Newton’s gravitation and general relativity
The presence of a localized cluster of topological singularities leads to a divergent perturbation of the scalar volume expansion in its vicinity, which depends at the same time on the lattice distortion energy induced by the cluster, on its scalar curvature charge and on its scalar rotation charge.
One can also imagine macroscopic topological defects of the lattice, as a hole in the lattice with a vacancy nature or a lattice portion inclusion with an interstitial nature. These two defects are topologically perfectly symmetrical, but their properties are very different inside the lattice. They present in fact very interesting analogies, respectively with the black holes and the neutron stars of the astrophysics.
It appears several interaction properties between the various topological defects of the lattice through their own expansion field, but with a large domination of the effects due to the distortion energy of the singularities. This leads to the existence of a dominant interaction force between two topological singularities, which presents, at great distances, a perfect similarity with the Newton’s gravitational interaction force between two massive bodies.
The measuring rods and clocks peculiar to the reference frame of a local observer (himself constituted of a cluster of lattice topological singularities) seem always to him as perfectly immutable, which leads him to postulate the invariance of the transversal waves propagation velocity in his frame, when an observer situated outside the lattice can measure enormous variations of the length of the measuring rods, of the time measured by the local clock and of the wave propagation celerity in the frame of the local observer as a function of the local variations of the scalar expansion of the lattice.
It is possible to find a metric translating the behaviors of the measurement rods and the clocks in the vicinity of a spherical cluster of topological singularities, which becomes perfectly identical to the Schwarzschild metric of general relativity at sufficient distance of the cluster. As a consequence, the curvature of transversal wave rays in the vicinity of a cluster are qualitatively and quantitatively identical to the light rays curvature calculated by general relativity in the vicinity of massive celestial objects.
This metric becomes somewhat different from the Schwarzschild metric in closed proximity of the cluster of topological singularities. In the case of a black hole, if the radius of the Schwarzschild sphere (the point of no return) remains the same as the radius of Schwarzschild in general relativity, the radius of the photon sphere becomes identical to the radius of the Schwarzschild sphere and the radius of infinite time dilation becomes null in the case of the cosmic lattice, which is much more satisfactory to the spirit than a photon sphere radius corresponding to 3/2 of the Schwarzschild radius and an infinite time dilation radius corresponding to ½ of the Schwarzschild radius as calculated by the Schwarzschild metric in general relativity.
This metric leads also the external observer to formulate simple and decoupled equations in order to describe the geometric curvature of the lattice and the time gap between the local clocks in the vicinity of a cluster of topological defects. For the local observers, the same physical quantities are described by the very complex equations of space-time curvature of the general relativity.
Weak interaction force and cosmological evolution of matter
It appears also a very short range interaction force, corresponding in fact to a capture potential, between the rotation charge of a twist disclination loop and the curvature charge of an edge dislocation loop, which leads to the formation of a stable topological loop of dispiration. This force presents a surprising similarity with the weak interaction force of the standard model of elementary particles, whereas there is no charge analogous to the curvature charge in all the modern physical theories.
The existence of this curvature charge which has no analogous in the modern physical theories leads to surprising effects. Indeed, the interstitial or vacancy nature of the topological loops of edge dislocation involved in the loops of composed topological singularities is associated to the nature of particle or antiparticle, with respectively a weak gravitational component of repulsion or attraction, which is subtracted or added to the main attractive gravitational component related to the distortion energy of the singularity. This effect creates a very small deviation to the equivalence principle of Einstein between inertial mass and gravitational mass, and it explains perfectly the weak asymmetry existing between matter and antimatter, with an attractive gravitational component very slightly higher for the antimatter. Moreover, only the pure interstitial edge dislocation loop, corresponding to the neutrino, presents really antigravity. This gravitational effect of the curvature charge allows one to explain very simply several phenomena which are badly or even not explained in the scenario of cosmological evolution of matter, as the precipitation of matter and anti-matter in the form of galaxies, the disappearance of anti-matter from the universe, the formation of gigantic black holes in the center of the galaxies, and the nature of the dark matter of the astrophysicists.
The formation and the cooling of the cosmic microwave background, the Hubble’s law and the redshift of the galaxies are also very well explained in this scenario of cosmological evolution of matter.
Quantum physics and particles spin
The existence of localized perturbations of the volume expansion instead of longitudinal waves propagation if the scalar expansion of the lattice is smaller than a critical value allows one to find mathematically and exactly the Schrödinger equation of the quantum physics for the description of the spatiotemporal behavior of the topological expansion perturbations associated to the moving topological singularities. As a consequence, one can explain the quantum wave function associated with a topological singularity as the local amplitude and phase of the volume expansion fluctuations, in other words as the gravitational fluctuations associated with this singularity.
This interpretation of the quantum wave function is perfectly matching the Bohm’s interpretation of quantum physics, and allows also one to give simple explanations to the superposition and the exclusion principles, as well as to the existence of bosons and fermions.
The loops of topological singularities do not admit a static solution for the field of gravitational perturbations (volume expansion perturbations) in their immediate vicinity. This means that the loops have to spin around one of their axes in order to find a dynamic solution of the expansion perturbation field. It appears then a compulsory quantification of their angular momentum, perfectly similar to the spin of elementary particles, and one shows that this rotation motion implies a magnetic momentum in the case of the twist disclination loop, analogous to the electrical charge, and that it does not violate the laws of special relativity.
On the other hand, there can exist transversal waves packets propagating inside the lattice, which are submitted to the condition that they present a non-null helicity so that their energy is conserved. These wave packets present a kind of “malleability”, a plasticity of their extension in space, without loss of their identity. This implies all the properties of non-locality, of linear momentum, of wave–particle duality, of entanglement and of decoherence of the photons of modern physics.
Standard model of elementary particles and strong interaction force
One can imagine a “colored cubic lattice”, with specific properties of stacking and of rotation of three types of “colored” planes, which allows one to construct a set of topological singularities perfectly similar to the various elementary particles of the standard model, with singularities corresponding to the leptons and singularities corresponding to the quarks. The singularities corresponding to the quarks have mandatory, for topological reasons, to combine as pairs (baryons) or as triplets (mesons) of loops, bound by a force generated by a ribbon of “colored” stacking faults. This binding force presents in fact all the asymptotic properties of the strong force of the standard model.
In this colored lattice, one can also perfectly identify topological singularities corresponding to the W and Z bosons, as well as to the gluons.
On the other hand, the fact that it is possible to replace an edge dislocation loop by an edge disclination loop, with a rotation angle of 90° or 180°, inside a composed topological loop of dispiration allows one to explain simply the existence of three families of particles in the standard model.
Finally, the massive entity associated with each cell of the cosmic lattice could correspond to the Higgs particle of the standard model, with the consequence that the nature of this massive entity is completely different from the nature of the other particles, as these ones correspond to topological singularities of the lattice.
It is remarkable that the description, using Euler’s coordinates in an absolute space-time frame, of a massive “colored” cubic 3D-lattice containing loop topological singularities and having very particular elastic properties allows one to find analogies with all observed natural physical phenomena.
It appears that this theory is the first and only (i) to combine all known physics in a very simple manner, including electromagnetism, relativity, gravitation and quantum physics, (ii) to give a simple meaning to the local space-time and the quantum behavior of topological singularities, (iii) to find a completely new scalar curvature charge which creates a very small deviation to the equivalence principle of Einstein between inertial mass and gravitational mass, and which allows very simple explanations of the weak asymmetry observed between matter and anti-matter, the weak interaction force, the formation of galaxies, the disappearance of antimatter, the formation of gigantic black holes in the heart of the galaxies and the famous dark matter, (iv) to propose simple explanations to well-known problems of modern cosmology, as the universe expansion, the big-bang and the dark energy, and (v) to propose a model of “colored” cubic 3D-lattice whose diverse microscopic loop singularities correspond exactly to each of the elementary particles of the three families of particles of the standard model, and which allows to give a simple structural explanation to the strong interaction force.
 Livre: G. Gremaud, “Théorie eulérienne des milieux déformables – charges de dislocation et désinclinaison dans les solides”, Presses polytechniques et universitaires romandes (PPUR), Lausanne 2013, 751 pages
ISBN 978-2-88074-964-4, disponible sur PPUR
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 Book: G. Gremaud, “Eulerian theory of newtonian deformable lattices – dislocation and disclination charges in solids” , Amazon, Charleston (USA) 2016, 312 pages
ISBN 978-2-8399-1943-2, available on Amazon and CreateSpace
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 Livre: G. Gremaud, “Univers et Matière conjecturés comme un Réseau Tridimensionnel avec des Singularités Topologiques”, Amazon, Charleston (USA) 2016, 664 pages
ISBN 978-2-8399-1940-1, disponible sur Amazon, CreateSpace et Kindle
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 Book: G. Gremaud, “Universe and Matter conjectured as a 3-dimensional Lattice with Topological Singularities”, Amazon, Charleston (USA) 2016, 650 pages
ISBN 978-2-8399-1934-0, available on Amazon, Create Space and Kindle
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 Article: G. Gremaud, “Universe and Matter conjectured as a 3-dimensional Lattice with Topological Singularities”, July 2016, Journal of Modern Physics, 7, 1389-1399 , DOI 10.4236/jmp.2016.712126
 Article: G. Gremaud, “Maxwell’s equations as a special case of deformation of a solid lattice in Euler’s coordinates”, September 2016, arXiv :1610.00753 [physics.gen-ph]
 Illustrated summary (V10): “Universe and Matter conjectured as a 3-dimensional Lattice with Topological Singularities”, Lausanne, March 2017, 41 pages
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 Summary of the theory: “Could the Universe be a massive elastic 3D-lattice and ordinary matter consist of topological singularities?”, Lausanne, November 2014
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