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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.
In this book, it is suggested that Universe could be a massive elastic 3D-lattice, and that fundamental building blocks of Ordinary Matter could consist of topological singularities of this lattice, namely diverse dislocation loops and disclination loops. We find, 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, unifying electromagnetism, relativity, gravitation and quantum physics, and resolving some longstanding questions of modern cosmology and particle physics.

Content uploaded by G. Gremaud

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All content in this area was uploaded by G. Gremaud on Jun 24, 2018

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... One can also introduce in (20) (23) so that (20) can be written ...

... -on the generalization of the analogy to other modern physics theories: the theory of solid lattice deformation developed here in Euler's coordinates is actually a much more complex theory than the classical electromagnetism, since it stems from a tensor theory, which can be reduced to a vector theory by contraction on the tensor indices. Considering the tensor aspect of solid lattice deformation theory, and by relaxing the more restrictive hypothesis (the nondivergent deformations), the analogy could become particularly interesting and fruitful [22,23]. ...

... Concerning the curvature charge q θ of a prismatic dislocation loop, it has without doubt a role to play in an analogy with the gravitation theory [22,23], even if such a charge does not exist in the modern physics theories as gravitation, quantum physics or particles physics. In the case of the solid lattice deformation in Euler's coordinates, the divergence of relation (64) furnishes the following equation ...

It is shown that the set of equations known as “Maxwell’s equations” perfectly describe
two very different systems: (1) the usual electromagnetic phenomena in
vacuum or in the matter and (2) the deformation of isotropic solid lattices, containing
topological defects as dislocations and disclinations, in the case of constant
and homogenous expansion. The analogy between these two physical systems is
complete, as it is not restricted to one of the two Maxwell’s equation couples in the
vacuum, but generalized to the two equation couples as well as to the diverse phenomena
of dielectric polarization and magnetization of matter, just as to the electrical
charges and the electrical currents. The eulerian approach of the solid lattice
developed here includes Maxwell’s equations as a special case, since it stems
from a tensor theory, which is reduced to a vector one by contraction on the tensor
indices. Considering the tensor aspect of the eulerian solid lattice deformation theory,
the analogy can be extended to other physical phenomena than electromagnetism,
a point which is shortly discussed at the end of the paper.

... This paper presents a theory recently developed [1] and published in a book [2] [3] , which shows that an Eulerian approach of the deformation of a Newtonian lattice in an absolute space can furnish an investigation frame extremely rich and interesting for physics, if judicious elastic and structural properties of the considered lattice are postulated. Indeed, it shows very strong and often perfect analogies with all the modern physics theories of the macrocosm and microcosm, as the Maxwell equations, the special relativity, the Newtonian gravitation, the general relativity, the modern cosmology, the quantum physics and the standard model of elementary particles. ...

... Particle physicists expect that the outcome of the ongoing experiments-search for new particles at the large particle accelerators and search for dark matter-are needed to provide further input for a theory of everything. In the recent theoretical work presented in the book [2] [3], it is suggested that Universe could be a massive elastic 3D-lattice, and that fundamental building blocks of Ordinary Matter could consist of topological singularities of this lattice, namely diverse dislocation loops and disclination loops. We find, 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, unifying electromagnetism, relativity, gravitation and quantum physics, and resolving some longstanding questions of modern cosmology. ...

... Moreover, studying lattices with axial symmetries, represented by " colored " cubic 3D-lattices, one can identify a lattice structure whose topological defect loops coincide with the complex zoology of elementary particles, which could open a promising field of research. In this paper, motivations, main steps and principal results of the new theories presented in the two parts of book [2] [3] are summarized as succinctly as possible, without showing the mathematical concepts and developments contained in the book. ...

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. In
this paper, one summarizes the content of a new book, published in English [2] and in French [3],
in which it is suggested that Universe could be a massive elastic 3D-lattice, and that fundamental
building blocks of Ordinary Matter could consist of topological singularities of this lattice, namely
diverse dislocation loops and disclination loops. For an isotropic elastic lattice obeying Newton’s
law, with specific assumptions on its elastic properties, one obtains the result that the behaviours
of this lattice and of its topological defects display “all” known physics, unifying electromagnetism,
relativity, gravitation and quantum physics, and resolving some longstanding questions of modern
cosmology. Moreover, studying lattices with axial symmetries, represented by “colored” cubic
3D-lattices, one has identified a lattice structure whose topological defect loops coincide with the
complex zoology of elementary particles, which could open a very promising field of research.
Here, only main steps and principal results of the new theory are presented and discussed, without
showing the mathematical concepts and developments contained in the book.

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