Hypothesis on the Unity of Spacetime, A Medium Under Tension

This manuscript proposes a unifying framework in which matter, light, and gravity are no longer distinct entities but geometric states of a single spacetime fabric endowed with internal tension. This hypothesis connects the equations of general relativity and quantum mechanics by viewing them as two limiting regimes of one and the same dynamics. Particles are interpreted as stable tension knots, light as a free oscillation of the fabric, and gravity as a slow variation of its tension density. The aim of this work is to lay the conceptual and mathematical groundwork for a material, continuous, and causal spacetime medium, and then to deduce falsifiable experimental signatures. A number of earlier and recent works have argued that space – or the “vacuum” – should be understood as a physical medium with mechanical properties (density, elasticity, wave-supporting behaviour), often within explicitly Newtonian frameworks featuring three-dimensional space, absolute time, a non-expanding universe, and gravity interpreted as mere compression of the medium around compact objects [Ref. X–Y]. The present hypothesis belongs to this broad family of “space-as-medium” ideas, but departs from them in several crucial respects: (i) the medium is not added on top of space-time, it is space-time itself, modelled as a four-dimensional geometric fabric with metric that preserves special and general relativity; (ii) gravity arises jointly from geometric curvature and from an internal tension field , endowed with a potential and its own stress–energy tensor, which allows for a reinterpretation of dark matter and dark energy without abandoning the framework of an expanding Friedmann–Lemaître universe; (iii) rather than proposing a purely phenomenological mechanism, the present approach is built on an explicit variational formalism (action, field equations, and an observational testing programme) designed to connect the ontological picture and quantitative predictions in a coherent way.