Hypersurface Tension: A Mechanical Model of Spacetime with Gravitation and Quantum Geometry

It is well known that a three-dimensional volume is a three-surface in four-dimensions. Statistical thermodynamics and the bounding of quantum states at any stable surface gives rise to negative stress-energy (surface tension) regardless of the dimensionality of the hypersurface. A mechanical model of spacetime with hypersurface tension was introduced at a prior conference. In the prior work, similarities between spacetime geometry and equations of quantum mechanics, namely Klein-Gordon, Schrödinger, Heisenberg, and Weyl, were identified. In this talk, the model is extended to include further comparisons with general relativity. A symmetric nondegenerate anisotropic elastic tensor is proposed as a constitutive relation between stress energy and curvature instead of the traditional Einstein constant. It is shown that such a relation provides a spatial geometry resembling quantum mechanics while temporal terms and the overall structure of tensor equations remain consistent with general relativity. Current efforts to test and validate the model are described.