Spacetime, which consists of three dimensions of space and one time dimension, is such a large, abstract concept that scientists have a very difficult time understanding and defining it. Moreover, different theories offer different, contradictory insights on spacetime’s structure. While general relativity describes spacetime as a continuous manifold, quantum field theories require spacetime to be made of discrete points. Unifying these two theories into one theory of quantum gravity is currently one of the biggest unsolved problems in physics.
In an attempt to better understand spacetime, a new possible structure of spacetime has been proposed on the Planck scale. Spacetime could be both discrete and continuous at the same time, conceivably satisfying general relativity and quantum field theories simultaneously.
This theory is inspired by information theory, since information can also be simultaneously discrete and continuous, the underlying mathematical structure of information theory in this framework is sampling theory - that is, samples taken at a generic discrete set of points can be used to reconstruct the shape of the information (or spacetime) everywhere down to a specific cutoff point. In the case of spacetime, that cutoff would be the natural ultraviolet lower bound, if it exists. This lower bound can also be thought of as a minimum length uncertainty principle, beyond which structural properties cannot be precisely known.
In the study, a sampling theory that can be generalized to apply to spacetime was developped. In this it shows that a finite density of sample points obtained throughout spacetime’s structure can provide scientists with the shape of spacetime from large length scales all the way down to the natural ultraviolet cutoff. Further, it shows that this expression establishes an equivalence between discrete and continuous representations of spacetimes. As such, the new framework for the sampling and reconstruction of spacetime could be used in various approaches to quantum gravity by giving discrete structures a continuous representation.
But it is very hard to obtain experimental data that could guide the search for the theory that unifies quantum theory and general relativity.
