Emergence of spatial structure from causal sets

Abstract

There are numerous indications that a discrete substratum underlies continuum spacetime. Any fundamentally discrete approach to quantum gravity must provide some prescription for how continuum properties emerge from the underlying discreteness. The causal set approach, in which the fundamental relation is based upon causality, finds it easy to reproduce timelike distances, but has a more difficult time with spatial distance, due to the unique combination of Lorentz invariance and discreteness within that approach. We describe a method to deduce spatial distances from a causal set. In addition, we sketch how one might use an important ingredient in deducing spatial distance, the `$n$-link', to deduce whether a given causal set is likely to faithfully embed into a continuum spacetime.

21 pages, 21 figures; proceedings contribution for DICE 2008, to appear in Journal of Physics: Conference Series

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Cited by in corpus (6)

• Problem of Time in Quantum Gravity
• The structure of causal sets
• Causal Set Generator and Action Computer
• A renormalization procedure for tensor models and scalar-tensor theories of gravity
• Inference of Boundaries in Causal Sets
• Manifold Properties from Causal Sets using Chains