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All of modern physics is based on General Relativity (GR) and Quantum Theory (QT). GR is a geometrical interpretation of gravity as curvature of space and time. QT removes the determinism from classical physics; it is only possible to calculate probabilities for the outcomes of experiments.
Unfortunately both theories, as presently formulated, contradict each other. On the one hand, QT assumes that physics takes place on a fixed, prescribed geometry. This is inconsistent with Einstein’s equations of GR according to which space and time there and then get curved the more matter is present there and then. Dynamical matter is therefore incompatible with a fixed geometry. On the other hand, GR is a classical theory. This leads to a contradiction because the probabilities for the matter densities will leave an undeterministic imprint on the curvature of geometry.
Moreover, both theories are also incomplete within themselves: GR predicts its own failure in terms of so called curvature singularities, that is, points in spacetime where curvature and thus the „gravitational force“ diverges, becomes infinite. These occur, for instance, at the big bang or in the centers of black holes. QT in turn fails when applied to gravity where it predicts meaningless probabilities above hundred per cent.
Obviously we need a better, consistent theory which unifies GR and QT. One candidate for such a theory is Loop Quantum Gravity (LQG). LQG has a built-in regulator which avoids the aforementioned curvature singularities: Space and time are granular, get chopped up into smallest quanta of 10-33 cm and 10-43 s respectively which are known as Planck length and Planck time respectively. LQG derives its name from a formulation of the theory in terms of so called Wilson loops, familiar from (Lattice) QCD. This means that geometry and matter are excited on one dimensional closed paths or loops. Zillions of these elementary, mutually intersecting and linked loops then form the spacetime continuum at large scales. For instance, one would need an order of 1068 such loops in order to „weave“ a sheet of paper of size A4. The granular structure of spacetime, sometimes termed spacetime foam, becomes visible only under high resolution, see figure. A recent review of LQG can be found in [1]. The MPI for gravitational physics, Golm, is internationally leading in the analysis of the „Quantum - Einstein Equations“ that one derives from LQG.
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