Can we estimate the Young's modulus of the space-time from simple analogies based on the concepts of the strength of materials? Reflection and proposals

Overview & Synopsis

Einstein has shown that the matter curves the space-time. In its model, the space-time is a mathematical conceptualization unifying the space and the time that accounts for measured physical phenomena (delay of the perihelion of Mercury, deviation, curvature of light by a large mass, relativity of length and time, propagation of gravitational waves, caused in particular by coalescence of black holes, which materialize by infinitesimal deformations DL / L of space-time (10-21)), etc. The question that then comes to mind is whether the mathematical conceptualization of space-time has a physical reality? In this case, what is the material of the fabric of the space-time that undulates or bends under gigantic masses in motion? Where, from a mechanical point of view, can we find an equivalent Young's modulus E to the fabric of the space-time? A first clue is the Casimir's force, which tells us that the vacuum of space is not empty ... From recent publications on the subject and simple analogies based on the strength of materials, we will show that if the E-module of space-time exists, it seems incommensurably large whatever the approach considered (elastic plates in 2 dimensions, plates analyzed by a tensor calculation in 4 dimensions, strings, Casimir force). In any case, only a measure of the latter would make it possible to decide definitively.