The Space-Time Continuum as a Transversely Isotropic Material and the Meaning of the Temporal Coordinate
- Dept. of Mathematics, University of Louisiana at Lafayette, LA 70504-1010 (United States)
A transversely isotropic elastic continuum is considered in four dimensions, three of which are isotropic, and the properties of the material change only related to the fourth dimension. The model employs two dilational and three shear Lame coefficients. The isotropic dilational coefficient is assumed to be much larger than the second dilational coefficient, and the three shear coefficients. This amounts to a material that is virtually incompressible in the three isotropic dimensions. The first and third shear coefficients are positive, while the second shear coefficient is assumed to be negative. As a result, in the equations of elastic equilibrium, the second derivatives of the displacement with respect to the fourth coordinate enter with negative sign. This makes the equations hyperbolic, with a fourth dimension opposing to the other three. The hyperbolic nature of the fourth dimension allows to be interpreted as time.
- OSTI ID:
- 21513128
- Journal Information:
- AIP Conference Proceedings, Vol. 1316, Issue 1; Conference: 7. Vigier symposium: International symposium honoring French mathematical physicist Jean-Pierre Vigier, London (United Kingdom), 12-14 Jul 2010; Other Information: DOI: 10.1063/1.3536442; (c) 2010 American Institute of Physics; ISSN 0094-243X
- Country of Publication:
- United States
- Language:
- English
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