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

Classical and Quantum Gravity (Impact Factor: 3.1). 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: 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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    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; DOI:10.1088/0264-9381/26/15/155013 · 3.10 Impact Factor
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    ABSTRACT: Why are "analogue spacetimes'' interesting? For the purposes of this workshop the answer is simple: Analogue spacetimes provide one with physically well-defined and physically well-understood concrete models of many of the phenomena that seem to be part of the yet incomplete theory of "quantum gravity'', or more accessibly, "quantum gravity phenomenology''. Indeed "analogue spacetimes'' provide one with concrete models of "emergence'' (whereby the effective low-energy theory can be radically different from the high-energy microphysics). They also provide many concrete and controlled models of "Lorentz symmetry breaking'', and extensions of the usual notions of pseudo-Riemannian geometry such as "rainbow spacetimes'', and pseudo-Finsler geometries, and more. I will provide an overview of the key items of "unusual physics'' that arise in analogue spacetimes, and argue that they provide us with hints of what we should be looking for in any putative theory of "quantum gravity''. For example: The dispersion relations that naturally arise in the known emergent/analogue spacetimes typically violate analogue Lorentz invariance at high energy, but do not do so in completely arbitrary manner. This suggests that a search for arbitrary violations of Lorentz invariance is possibly overkill: There are a number of natural and physically well-motivated restrictions one can put on emergent/ analogue dispersion relations, considerably reducing the plausible parameter space.


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