immediate consequence is that LQG is UV-finite because small and large distances are gauge equivalent as one can replace one metric function for another related to the first by an active diffeomorphism. A more precise argument can be given. The direct proof of finiteness of canonical LQG in the presence of all forms of matter has been provided by Thiemann. However, it has been suggested that loop quantum gravity violates background independence by introducing a preferred frame of reference ('spin foams'). Perturbative string theory (in addition to a number of non-perturbative formulations) is not 'obviously' background independent, because it depends on boundary conditions at infinity, similarly to how perturbative general relativity is not 'obviously' background dependent. However some sectors of string theory admit formulations in which background independence is manifest, including most notably the AdS/CFT. It is believed that string theory is background independent in general, even if many useful formulations do not make it manifest. For a contrary view see Smolin. See also Erich Kretschmann Philosophy of space and time References Sources Albert Einstein, H. A. Lorentz, H. Weyl, and H. Minkowski, The Principle of Relativity (1952): Einstein, Albert (1916) "The Foundation of the General Theory of Relativity," pp. 111–164. Carlo Rovelli, Quantum Gravity, published by Cambridge University Press (2004) . A preliminary version can be downloaded for free at http://www.cpt.univ-mrs.fr/~rovelli/book.pdf. Norton, John, The Hole Argument, The Stanford Encyclopedia of Philosophy (Spring 2004 Edition), Edward N. Zalta (ed.) See section 13.6. Physics Meets Philosophy at the Planck Scale (Cambridge University Press). Joy Christian, Why the Quantum Must Yield to Gravity, e-print available as gr-qc/9810078. Appears in Physics Meets Philosophy at the Planck Scale (Cambridge University Press). Carlo Rovelli and Marcus Gaul, Loop Quantum Gravity and the Meaning of Diffeomorphism Invariance, e-print available as gr-qc/9910079. Robert Rynasiewicz: The lessons of the hole argument, Brit.J.Phil.Sci. vol. 45, no. 2 (1994), pp. 407–437. Alan Macdonald, Einstein's hole argument American Journal of Physics (Feb 2001) Vol 69, Issue 2, pp. 223–225. External links Stachel, John, "The Hole Argument and Some Physical and Philosophical Implications", Living Rev. Relativ. 17(1) (2014). General relativity Obsolete theories in physics