The Spacetime Picture in Quantum Gravity
arXiv:2012.03994 · doi:10.1088/1361-6382/abcbde
Abstract
We propose an approach which, by combining insights from Loop Quantum Gravity (LQG), Topos theory, Non-commutative Geometry à la Connes, and spacetime relationalism, provides fertile ground for the search of an adequate spacetime picture in Quantum Gravity. With this approach, we obtain a novel way of deducing the quantization of the possible values for the area of a surface. One gets the same area values than those from the area operator in standard LQG, but our approach makes a further prediction: some smaller values and sub-divisions are also allowed. In addition, the area arises as a noncommutative distance between two noncommutative points, and thus they should be interpreted as irreducible string-like objects at the physical level (where the area interpretation for the noncommutative distance holds).
20 pages, accepted for publication in Class. Quantum Grav