Macrocosm and microcosm: an unexpected bond between elasticity theory and electron charge

The hypothesis on which the elasticity theory relies is the well-known continuum hypothesis: after an arbitrary magnification of any sample of matter we assume that the same properties of continuity will be found always. In other terms we do not take into account the existence of the atomic lattice that forms the matter under study. On the contrary, starting from the simple Fermi-Pasta model, formed by a series of equidistant atomic masses mutually bonded by exchange electrons, we can find equations for the speed of sound and Youngʹs modulus where only the atomic properties of the matter under study are present. These relations give values of the same order of magnitude of the values measured experimentally. Thus it seems to be possible a complete description of elastic phenomena in terms of electric fields in the matter. This fact, among other things, could be used in the laboratory to design special materials that, in the macroscopic domain, shall exhibit a number of prefixed features. Said unification seems to be valid even for the properties of gases and liquids.