A 2D model of Causal Set Quantum Gravity: The emergence of the continuum

Classical and Quantum Gravity (Impact Factor: 3.56). 07/2007; DOI: 10.1088/0264-9381/25/10/105025
Source: arXiv

ABSTRACT Non-perturbative theories of quantum gravity inevitably include configurations that fail to resemble physically reasonable spacetimes at large scales. Often, these configurations are entropically dominant and pose an obstacle to obtaining the desired classical limit. We examine this "entropy problem" in a model of causal set quantum gravity corresponding to a discretisation of 2D spacetimes. Using results from the theory of partial orders we show that, in the large volume or continuum limit, its partition function is dominated by causal sets which approximate to a region of 2D Minkowski space. This model of causal set quantum gravity thus overcomes the entropy problem and predicts the emergence of a physically reasonable geometry.

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    ABSTRACT: This paper presents an brief review of some recent work on the causal set approach to quantum gravity. Causal sets are a discretisation of spacetime that allow the symmetries of GR to be preserved in the continuum approximation. One proposed application of causal sets is to use them as the histories in a quantum sum-over-histories, i.e. to construct a quantum theory of spacetime. It is expected by many that quantum gravity will introduce some kind of "fuzziness", uncertainty and perhaps discreteness into spacetime, and generic effects of this fuzziness are currently being sought. Applied as a model of discrete spacetime, causal sets can be used to construct simple phenomenological models which allow us to understand some of the consequences of this general expectation. Comment: 24 pages, 4 figures. Based on a proceedings article for the "Foundations of Space and Time" conference, Cape Town, August 2009, in honour of George Ellis' 70th birthday.
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    ABSTRACT: There are several indications (from different approaches) that Spacetime at the Plank Scale could be discrete. One approach to Quantum Gravity that takes this most seriously is the Causal Sets Approach. In this approach spacetime is fundamentally a discrete, random, partially ordered set (where the partial order is the causal relation). In this contribution, we examine how timelike and spacelike distances arise from a causal set (in the case that the causal set is approximated by Minkowski spacetime), and how one can use this to obtain geometrical information (such as lengths of curves) for the general case, where the causal set could be approximated by some curved spacetime. Comment: 8 pages, 2 figures, based on talk by P. Wallden at the NEB XIII conference
    Journal of Physics Conference Series 11/2008;
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    ABSTRACT: A 2d model of causal set quantum gravity is constructed using a continuum-inspired dynamics. Apart from a restriction to causal set dimension and topology, the model is fully dynamical and includes all relevant 2d conformally flat degrees of freedom. Surprisingly, in the large N limit the partition function is dominated by causal sets that resemble 2d Minkowski spacetime. Thus, in this model the "entropy problem" of causal set theory is overcome and a sensible low energy limit is obtained.
    Journal of Physics Conference Series 06/2009; 174(1):2049-.


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