The Spacetime Picture in Quantum Gravity

We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry \`a la Connes, and spacetime relationalism, provides fertile ground for the search of adequate picture in Gravity. With this approach, we obtain a novel way deducing quantization possible values area surface. One gets same than those operator standard LQG, but our makes further prediction: some smaller sub-divisions are also allowed. In addition, arises as noncommutative distance between two points, thus they should be interpreted irreducible string-like objects at physical level (where interpretation holds).