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: We present evidence for a continuum phase in a theory of 2D causal set quantum gravity which contains a dimensionless non-locality parameter ϵ ∈ (0, 1]. We also find a phase transition between this continuum phase and a new crystalline phase which is characterized by a set of covariant observables. For a fixed size of the causal set, the transition temperature β−1c decreases monotonically with ϵ. The locus of the transition in the β2 versus ϵ plane asymptotically approaches to the infinite temperature axis, suggesting that the continuum phase survives the analytic continuation.
    Classical and Quantum Gravity 01/2012; 29(13). · 3.56 Impact Factor
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    ABSTRACT: Causal sets is an approach to quantum gravity, where spacetime is replaced by a causal set. It is fundamentally discrete, and the causal relations between spacetime elements is the only structure that remains. A complete theory should have (i) kinematics (ii) dynamics and (iii) phenomenology. In this contribution we will explore the dynamical part of the theory, focusing on recent developments. We will analyse (a) classical dynamics of the causal set, (b) quantum dynamics of matter and fields on a classical causal set and finally (c) quantum dynamics of the causal set.
    Journal of Physics Conference Series 08/2013; 453(1):2023-.


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