Approaches to Quantum Gravity

110 O. DreyerIn addition to the proposals presented at the workshop we have also discusseda novel approach which differs from the computational universe mainly in that itdoes not use the Einstein equations. We instead argued that they are a result of theinternal and background independent approach.The main ingredient are coherent degrees of freedom. These play the role ofmatter but they are also used to define notions of space and time. It is because theyplay this dual role that the equivalence principle and also the Einstein equationsare true.In this approach there is no notion of spacetime without matter. Tearing apartspacetime and matter by viewing the latter as living on the former creates deepproblems like the cosmological constant problem and the problem of time. Herewe avoid these problems.This view also goes well with a new view of quantum mechanics [7]. In thisview of quantum mechanics a notion like position is only applicable to large quantumsystems and is not fundamental. Given such a view, it is only natural that aspacetime emerges and is not included as a basic building block.In recent years we have seen a number of new approaches to the problem ofQuantum Gravity come very close to the stated goal. Using methods and ideasforeign to the more traditional approaches they were able to make progress whereothers got stuck. Maybe we will soon have not just one quantum theory of gravitybut several to choose from. To decide which one is the right one will then requirerecourse to experiment. What an exciting possibility.References[1] G. Volovik, The Universe in a Helium Droplet (Oxford University Press, 2003).[2] P. Horava, Phys. Rev. Lett. 95, 016405 (2005).[3] S. Lloyd, quant-ph/0501135.[4] P. Jordan and E. Wigner, Z. Phys. 47 (1928) 631.[5] X.-G. Wen, Quantum Field Theory of Many-Body Systems (Oxford University Press,2004).[6] E. Mach, Science of Mechanics (Open Court Publishing Company, 1960).[7] O. Dreyer, quant-ph/0603202.