and because world lines are defined geometrically as trajectories of maximum proper time — it is only with an active diffeomorphism that the geometry is changed and trajectories altered.) This was the first clear statement of the principle of gauge invariance in physical law. Einstein believed that the hole argument implies that the only meaningful definition of location and time is through matter. A point in spacetime is meaningless in itself, because the label which one gives to such a point is undetermined. Spacetime points only acquire their physical significance because matter is moving through them. In his words: "All our space-time verifications invariably amount to a determination of space-time coincidences. If, for example, events consisted merely in the motion of material points, then ultimately nothing would be observable but the meeting of two or more of these points." He considered this the deepest insight of general relativity. According to this insight, the physical content of any theory is exhausted by the catalog of the spacetime coincidences it licenses. John Stachel called this principle, the point-coincidence argument. Generally what is invariant under active diffeomorphisms, and hence gauge invariant, are the coincidences between the value the gravitational field and the value the matter field have at the same 'place' because the gravitational field and the matter field get dragged across together with each other under an active diffeomorphism. From these coincidences one can form a notion of matter being located with respect to the gravitational field. As Carlo Rovelli puts it: "No more fields on spacetime: just fields on fields." This is the true meaning of the saying "The stage disappears and becomes one of the actors"; space-time as a 'container' over which physics takes place has no objective physical meaning and instead the gravitational interaction is represented as just one of the fields forming the world. Einstein referred to his resolution as "beyond my wildest expectations." Implications of background independence for some theories of quantum gravity Loop quantum gravity (LQG) is an approach to quantum gravity which attempts to marry the fundamental principles of classical GR with the minimal essential features of quantum mechanics and without demanding any new hypotheses. Loop quantum gravity physicists regard background independence as a central tenet in their approach to quantizing gravity – a classical symmetry that ought to be preserved by the quantum theory if we are to be truly quantizing geometry (=gravity). One