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Exact description of rotational waves in an elastic solid. (English) Zbl 1247.74008

Summary: Conventional descriptions of transverse waves in an elastic solid are limited by an assumption of infinitesimally small gradients of rotation. By assuming a linear response to variations in orientation, we derive an exact description of a restricted class of rotational waves in an ideal isotropic elastic solid. The result is a nonlinear equation expressed in terms of Dirac bispinors. This result provides a simple classical interpretation of relativistic quantum mechanical dynamics.We construct a Lagrangian of the form \({\mathcal{L}} = -{\mathcal{E}} + U + K = 0\), where \({\mathcal{E}}\) is the total energy, \(U\) is the potential energy, and \(K\) is the kinetic energy.

MSC:

74B05 Classical linear elasticity
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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[1] Bell J.S.: On the Einstein Podolsky Rosen Paradox. Phys. 1, 195–200 (1964)
[2] L. de Broglie, Recherches sur la Théorie des Quanta. PhD Thesis, University of Sorbonne, Paris, 1924.
[3] Close R.A.: Torsion waves in three dimensions: quantum mechanics with a twist. Found. Phys. Lett. 15, 71–83 (2002) · doi:10.1023/A:1015847426800
[4] R. A. Close, A Classical Dirac Equation. In: Ether Space-time & Cosmology, Vol 3. (Physical vacuum, relativity, and quantum physics) eds. M.C. Duffy and J. Levy, Apeiron, Montreal 2009, 49-73.
[5] Hestenes D.: Local observables in the Dirac theory. J. Math. Phys. 14(7), 893–905 (1973) · doi:10.1063/1.1666413
[6] H. Kleinert, Gauge Fields in Condensed Matter. vol II. World Scientific, Singapore, 1989, 1240-64. · Zbl 0785.53061
[7] S. Matsutani and H. Tsuru, Physical relation between quantum mechanics and solitons on a thin elastic rod. Phys. Rev. A 46 (1992), 1144-7.
[8] A. A. Michelson and E. W. Morley, On the relative motion of the earth and the luminiferous ether. Am. J. Sci. (3rd series) 34 (1887), 333-45. · JFM 19.1084.01
[9] P. Rowlands, The physical consequences of a new version of the Dirac equation. In: Causality and Locality in Modern Physics and Astronomy: Open Questions and Possible Solutions (Fundamental Theories of Physics, vol 97) eds G. Hunter, S. Jeffers, and J-P. Vigier, Kluwer Academic Publishers, Dordrecht, 1998, 397-402.
[10] Rowlands P., Cullerne J.P.: The connection between the Han-Nambu quark theory, the Dirac equation and fundamental symmetries. Nuclear Phys. A 684, 713–715 (2001) · Zbl 01609320 · doi:10.1016/S0375-9474(01)00470-5
[11] P. Rowlands, Removing redundancy in relativistic quantum mechanics. Preprint: arXiv:physics/0507188 (2005).
[12] Schmelzer I.: A condensed matter interpretation of SM fermions and gauge fields. Found. Phys. 39(1), 73–107 (2009) · Zbl 1161.81441 · doi:10.1007/s10701-008-9262-9
[13] Takabayashi Y.: Relativistic hydrodynamics of the Dirac matter. Suppl. Prog. Theor. Phys. 4(1), 1–80 (1957)
[14] E. Whittaker, A History of the Theories of Aether and Electricity. Vol 1. Thomas Nelson and Sons Ltd., Edinburgh, 1951, 128-69. · Zbl 0043.24503
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