Strain Energy Density in the Elastodynamics of the Spacetime Continuum and the Electromagnetic Field

We investigate the strain energy density of the spacetime continuum in the Elastodynamics of the Spacetime Continuum by applying continuum mechanical results to strained spacetime. The strain energy density is a scalar. We nd that it is separated into two terms: the rst one expresses the dilatation energy density (the “mass” longitudinal term) while the second one expresses the distortion energy density (the “massless” transverse term). The quadratic structure of the energy relation of Special Relativity is found to be present in the theory. In addition, we nd that the kinetic energy pc is carried by the distortion part of the deformation, while the dilatation part carries only the rest-mass energy. The strain energy density of the electromagnetic energy-momentum stress tensor is calculated. The dilatation energy density (the rest-mass energy density of the photon) is found to be 0 as expected. The transverse distortion energy density is found to include a longitudinal electromagnetic energy ux term, from the Poynting vector, that is massless as it is due to distortion, not dilatation, of the spacetime continuum. However, because this energy ux is along the direction of propagation (i.e. longitudinal), it gives rise to the particle aspect of the electromagnetic eld, the photon.