*(English)*Zbl 1116.83013

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.

##### MSC:

83C45 | Quantization of the gravitational field |

83C30 | Asymptotic procedures (general relativity) |

83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |

83-03 | Historical (relativity) |

01A50 | Mathematics in the 18th century |

01A55 | Mathematics in the 19th century |

01A60 | Mathematics in the 20th century |