From the Maxwell’s Equations of Lattice Deformations to the Description of the Universe by a « Crystalline Ether »

Abstract:

Using Eulerian coordinates to describe solid lattice deformations, it has been shown that the set of equations known as Maxwell’s equations—typically applied to electromagnetic phenomena in vacuum or matter—can also describe the elastic, anelastic, and plastic deformations of isotropic solid lattices containing topological defects such as dislocations and disclinations, under conditions of constant and homogeneous expansion. The analogy between the two physical systems is complete: it extends beyond one of the two Maxwell equation pairs in vacuum to both pairs, and includes analogues to dielectric polarization, magnetization, electric charges, and currents. In the Eulerian approach, Maxwell’s equations emerge as a special case derived from a tensor theory of lattice deformation, reducible to a vector formulation only for constant and homogeneous expansion. When dynamic and non-homogeneous expansions are considered, the tensorial nature of the theory becomes essential. This generalization naturally leads to a new conceptual framework for the Universe based on the existence of a crystalline ether. This framework offers a simple, unified, and coherent description of all major theories of modern physics—including electromagnetism, relativity, gravitation, quantum physics, cosmology, and the Standard Model of particle physics.

• Periodical: Key Engineering Materials (Volume 1062)
• Pages: 81-132
• DOI: https://doi.org/10.4028/p-O5VgC0
• Online since: August 2026
• Authors: Gerard Gremaud*
• Keywords: Cosmology, Crystalline Ether, General Relativity, Maxwell’s Equations, Quantum Physics, Special, Standard Model, Theory Of Everything

References

[1] G. Ross, Grand Unified Theories. Westview Press, 1984, ISBN 978-0-8053-6968-7.

[2] C. Kiefer, Quantum gravity, International series of monographs on physics (3rd ed.), Oxford University Press, 2012, p.1–4, ISBN 978-0-19-958520-5.

[3] M. Dine, Supersymmetry and String Theory: Beyond the Standard Model, Cambridge University Press, 2007, p.169, ISBN 978-0-521-[3] 85841-0

[4] K. Becker, M. Becker, J. Schwarz, (2007). String theory and M-theory: A modern introduction. Cambridge University Press, 2007, ISBN 978-0-521-86069-7.

[5] D. Rickles, (2014). A Brief History of String Theory: From Dual Models to M-Theory, Springer, 2014, p.104, ISBN 978-3-642-45128-7

[6] Alexander Unzicker and Sheilla Jones, «Bankrupting Physics», Palgrave McMillan, New York, 2013, ISBN 978-1-137-27823-4. Alexander Unzicker, «The Higgs Fake», amazon.co.uk, 2013, ISBN 978-1492176244

[7] Lee Smolin, «The trouble with Physics», Penguin Books 2008, London, ISBN 978-1-137-27823-4. Lee Smolin, «La révolution inachevée d'Einstein, au-delà du quantique», Dunod 2019, ISBN 978-2-10-079553-6. Lee Smolin, «Rien ne va plus en physique., L'échec de la théorie des cordes», Dunod 2007, ISBN 978-2-7578-1278-5

DOI: 10.3917/etu.4267.0115b

[8] Peter Woit, «Not Even Wrong, the failure of String Theory and the continuing challenge to unify the laws of physics», Vintage Books 2007, ISBN 9780099488644

[9] Sabine Hossenfelder, «Lost in Maths», Les Belles Lettres 2019, ISBN978-2-251-44931-9

[10] G. Gremaud, Theory of The Crystalline Ether — Universe and Matter conjectured as a 3-dimensional Lattice with Topological Singularities, Amazon, Charleston (USA), 2025, 662 pages, ISBN 979-8883393982. G. Gremaud, Théorie de l'Ether Cristallin — Univers et Matière conjecturés comme un Réseau Tridimensionel avec des Singularités Topologiques, Amazon, Charleston (USA), 2025, 642 pages, ISBN 979-8880376872

DOI: 10.4236/jmp.2016.712126

[11] G. Gremaud, The Crystalline Ether — What if the Universe was a lattice and we were its topological singularities?, Amazon, Charleston (USA), 2025, 318 pages, ISBN 979-8883536273. G. Gremaud, L'Ether Cristallin — Et si l'Univers était un réseau et que nous en étions des singularités topologiques?, Amazon, Charleston (USA), 2025, ISBN 979-8883513656

[12] G. Gremaud, Théorie eulérienne des milieux déformables — charges de dislocation et désinclinaison dans les solides, Presses polytechniques et universitaires romandes (PPUR), Lausanne (Switzerland), 2013, 751 pages, ISBN 978-2-88074-964-4

DOI: 10.1016/s0151-9107(01)80092-1

[13] 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

[14] G. Gremaud, "On local space-time of loop topological defects in a newtonian lattice", arXiv:1407.1227( 2014)

[15] G. Gremaud, "Maxwell's equations as a special case of deformation of a solid lattice in Euler's coordinates", arXiv :1610.00753 (2016)

[16] G. Gremaud, "Universe and Matter conjectured as a 3-dimensional Lattice with Topological Singularities", Journal of Modern Physics, 7, 1389-1399 (2016)

DOI: 10.4236/jmp.2016.712126

[17] G. Gremaud, "In Search of a Theory of Everything — What if the Universe was an elastic and massive lattice and we were its topological singularities?", Journal of Advances in Physics, 17, 282-285 (2020)

DOI: 10.24297/jap.v17i.8726

[18] G. Gremaud, "The Crystalline Ether", European Journal of Applied Sciences, Vol.11, No.3 (2023)

[19] J.F. Nye, Acta Metall.,vol. 1, p.153, (1953)

[20] K. Kondo, RAAG Memoirs of the unifying study of the basic problems in physics and engeneering science by means of geometry, volume 1. Gakujutsu Bunken Fukyu- Kay, Tokyo, (1952)

[21] B.A. Bilby, R. Bullough and E. Smith, «Continous distributions of dislocations: a new application of the methods of non-riemanian geometry», Proc. Roy. Soc. London, Ser. A 231, p.263–273, (1955)

DOI: 10.1098/rspa.1955.0171

[22] E. Cartan, C.R. Akad. Sci., 174, p.593, 1922 & C.R. Akad. Sci., 174, p.734, (1922)

[23] E. Kröner, «Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen», Arch. Rat. Mech. Anal., 4, pp.273-313, (1960)

DOI: 10.1007/bf00281393

[24] E. Kröner, «Continuum theory of defects», in «physics of defects», ed. by R. Balian et al., Les Houches, Session 35, p.215–315. North Holland, Amsterdam, 1980.

[25] M. Zorawski, «Théorie mathématique des dislocations», Dunod, Paris, 1967.

[26] J.-P. Hirth, «A Brief History of Dislocation Theory», Metallurgical Transactions A, vol. 16A, p.2085, (1985)

[27] V. Volterra, «L'équilibre des corps élastiques», Ann. Ec. Norm. (3), XXIV, Paris, (1907)

[28] E. Orowan, Z. Phys., vol. 89, p.605,614 et 634, (1934)

[29] M. Polanyi, Z. Phys., vol.89, p.660, (1934)

[30] G. I. Taylor, Proc. Roy. Soc. London, vol. A145, p.362, (1934)

[31] J. M. Burgers, Proc. Kon. Ned. Akad. Weten schap., vol.42, p.293, 378, (1939)

[32] P. B. Hirsch, R. W. Horne, M. J. Whelan, Phil. Mag., vol. 1, p.667, (1956)

[33] W. Bollmann, Phys. Rev., vol. 103, p.1588, (1956)

[34] O. Lehmann, «Flussige Kristalle», Engelman, Leibzig, (1904)

[35] G. Friedel, Ann. Physique, vol. 18, p.273, (1922)

[36] S.E. Whittaker, «A History of the Theory of Aether and Electricity», Dover reprint, vol. 1, p.142, 1951.

[37] A. Unzicker, «What can Physics learn from Continuum Mechanics?», arXiv:gr-qc/0011064, (2000)

[38] S. J. Brodky, A. Deur, C. D. Roberts, «The Secret to the Strongest Force in the Universe», Scientific American Magazine, Vol.330, No.5, May (2024)