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The case for background independence. (English) Zbl 1116.83013
Rickles, Dean (ed.) et al., The structural foundations of quantum gravity. Oxford: Clarendon Press (ISBN 0-19-926969-6/hbk). 196-239 (2006).
One of the problems both of quantum gravity and string theory is the fact that several useful theories start by a 3+1-decomposition of space-time into space and time. At the end, it is not clear in which sense the result depends on the fact, how this 3+1-decomposition has been done; this is the rough description of the problem of background independence. In a more detailed sense, one argues, that space-time is dynamical, i.e., the background for the motion of physical fields is itself a field in motion. Lee Smolin gives a presentation about this problem and puts it into a historical context, starting from Newton’s absolute space via Leibniz’s relationalism to Mach and Einstein. He discusses several variants of the notion of background independence. Then he argues why a correct quantum theory of gravity must be background independent. Loop quantum gravity and dynamical triangulations are discussed, too. For the entire collection see [Zbl 1104.83013].

83C45Quantization of the gravitational field
83C30Asymptotic procedures (general relativity)
83C05Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83-03Historical (relativity)
01A50Mathematics in the 18th century
01A55Mathematics in the 19th century
01A60Mathematics in the 20th century