Title:	Towards a definition of locality in a manifoldlike causal set
Authors:	Glaser, Lisa Surya, Sumati
Issue Date:	15-Dec-2013
Publisher:	American Physical Society
Citation:	Physical Review D, 2013, Vol.88, p124026
Abstract:	It is a common misconception that spacetime discreteness necessarily implies a violation of local Lorentz invariance. In fact, in the causal set approach to quantum gravity, Lorentz invariance follows from the specific implementation of the discreteness hypothesis. However, this comes at the cost of locality. In particular, it is difficult to define a “local” region in a manifoldlike causal set, i.e., one that corresponds to an approximately flat spacetime region. Following up on suggestions from previous work, we bridge this lacuna by proposing a definition of locality based on the abundance of m-element order-intervals as a function of m in a causal set. We obtain analytic expressions for the expectation value of this function for an ensemble of causal set that faithfully embeds into an Alexandrov interval in d-dimensional Minkowski spacetime and use it to define local regions in a manifoldlike causal set. We use this to argue that evidence of local regions is a necessary condition for manifoldlikeness in a causal set. This in addition provides a new continuum dimension estimator. We perform extensive simulations which support our claims.
Description:	Open Access.
URI:	http://hdl.handle.net/2289/5899
ISSN:	1550-7998 1550-2368(Online)
Alternative Location:	http://arxiv.org/abs/1309.3403 http://dx.doi.org/10.1103/PhysRevD.88.124026
Copyright:	2013 American Physical Society
Appears in Collections:	Research Papers (TP)

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