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

Classical and Quantum Gravity (Impact Factor: 3.17). 07/2007; 25(10). DOI: 10.1088/0264-9381/25/10/105025
Source: arXiv


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.


Available from: Joe Henson, Nov 29, 2015
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    • "The implications of this result for causal sets were explored by Brightwell, Henson and Surya [21]. The result of El-Zahar and Sauer implies that a 2-dimensional partial order chosen uniformly at random is (effectively) distributed as the partial order induced on a Poisson process in [0] [1] 2 (or, equivalently, an interval in M 2 ), and so such a random partial order can be embedded faithfully in an interval in M 2 . "
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    ABSTRACT: The causal set approach to quantum gravity is based on the hypothesis that the underlying structure of spacetime is that of a random partial order. We survey some of the interesting mathematics that has arisen in connection with the causal set hypothesis, and describe how the mathematical theory can be translated to the application area. We highlight a number of open problems of interest to those working in causal set theory.
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    • ". The uniform distribution over Ω 2d without restrictions on N f is dominated by random 2d orders which are approximated by 2d Minkowski spacetime [11] and we will see in what follows that fixing N f changes the associated partition function as a function of N f . "
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    ABSTRACT: We define the Hartle-Hawking no-boundary wave function for causal set quantum gravity over the discrete analogs of spacelike hypersurfaces. Using Markov Chain Monte Carlo and numerical integration methods we analyse this wave function in non perturbative 2d causal set quantum gravity. Our results provide new insights into the role of quantum gravity in the observable universe. We find that non-manifold contributions to the Hartle-Hawking wave function can play a significant role. These discrete geometries exhibit a rapid spatial expansion with respect to the proper time and also possess a spatial homogeneity consistent with our current understanding of the observable universe.
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    • "In a model of full 2-d quantum gravity of causal sets [16], the main contribution from the sum over histories comes from causets which correspond to an interval in M 2 . While this is a toy model, it provides another reason to be interested in causal sets which are approximated by Minkowski spacetime. "
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    ABSTRACT: Any discrete approach to quantum gravity must provide some prescription as to how to deduce continuum properties from the discrete substructure. In the causal set approach it is straightforward to deduce timelike distances, but surprisingly difficult to extract spacelike distances, because of the unique combination of discreteness with local Lorentz invariance in that approach. We propose a number of methods to overcome this difficulty, one of which reproduces the spatial distance between two points in a finite region of Minkowski space. We provide numerical evidence that this definition can be used to define a `spatial nearest neighbor' relation on a causal set, and conjecture that this can be exploited to define the length of `continuous curves' in causal sets which are approximated by curved spacetime. This provides evidence in support of the ``Hauptvermutung'' of causal sets. Comment: 32 pages, 16 figures, revtex4; journal version
    Classical and Quantum Gravity 10/2008; 26(15). DOI:10.1088/0264-9381/26/15/155013 · 3.17 Impact Factor
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