Beyond the quantum by Theo M. Nieuwenhuizen

By Theo M. Nieuwenhuizen

Already Einstein might by no means see quantum mechanics as a whole conception. these days, many researchers, together with 't Hooft, view quantum mechanics as a statistical description of a few underlying fact. The workshop "Beyond the Quantum", equipped in Spring 2006 on the Lorentz middle in Leiden, The Netherlands, used to be one of many first conferences thoroughly dedicated to physics that may wish a proof past quantum mechanics. A large number of topics was once coated. the current ebook displays this.

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The SU(2) gravitational spin connection Aia used in LQG has only one component c which furthermore depends only on time; Aia = c ωai . Similarly, the triad Eia (of density weight 1) has a single component p; Eia = p (det ω) εai . p is related to the scale factor a via a2 = |p|. However, p is not restricted to be positive; under p → −p the metric remains unchanged but the spatial triad flips the orientation. The pair (c, p) is ‘canonically conjugate’ in the sense that the only non-zero Poisson bracket is given by: {c, p} = 8πGγ , 3 (1) where as before γ is the Barbero-Immirzi parameter.

These functions were studied exhaustively by the mathematician Harold Bohr, Niels’ brother. In quantum geometry, the N(µ) are the LQC analogs of the spin-network functions of full LQG. In ˆ(µ) and quantum theory, then, we are led to a representation in which operators N pˆ are well-defined, but there is no operator corresponding to the connection component c. This seems surprising because our experience with quantum mechanics suggests that one should be able to obtain the operator analog of c by differentiating N (µ) with respect to the parameter µ.

After a general introduction, for concreteness I focus on a specific approach which goes under the name loop quantum gravity. The underlying ideas are first summarized and recent advances are then illustrated by applying these ideas to cosmology. Quantum effects of geometry resolve the big-bang singularity of classical general relativity. Quantum physics does not break down at the big-bang. In simple models where details have been fully worked out, there is a pre-big-bang branch joined to the current post-big-bang branch by well-defined quantum evolution.

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