Title:	Spacelike distance from discrete causal order
Authors:	Rideout, David Wallden, Petros
Issue Date:	Jul-2009
Publisher:	The IOP Publishing Ltd.
Citation:	Classical and Quantum Gravity, 2009, Vol.26, p155013
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 some evidence in support of the 'Hauptvermutung' of causal sets.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/3887
ISSN:	0264-9381 1361-6382 (Online)
Alternative Location:	http://fr.arxiv.org/abs/0810.1768 http://dx.doi.org/10.1088/0264-9381/26/15/155013
Copyright:	(2009) by the IOP Publishing Ltd.
Appears in Collections:	Research Papers (TP)

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