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It is a common misconception that spacetime discreteness necessarily impliesa violation of local Lorentz invariance. In fact, in the causal set approach toquantum gravity, Lorentz invariance follows from the specific implementation ofthe discreteness hypothesis. However, this comes at the cost of locality. Inparticular, it is difficult to define a "local" region in a manifoldlike causalset, i.e., one that corresponds to an approximately flat spacetime region.Following up on suggestions from previous work, we bridge this lacuna byproposing a definition of locality based on the abundance of m-elementorder-intervals as a function of m in a causal set. We obtain analyticexpressions for the expectation value of this function for an ensemble ofcausal set that faithfully embeds into an Alexandrov interval in d-dimensionalMinkowski spacetime and use it to define local regions in a manifoldlike causalset. We use this to argue that evidence of local regions is a necessarycondition for manifoldlikeness in a causal set. This in addition provides a newcontinuum dimension estimator. We perform extensive simulations which supportour claims.

Towards a Definition of Locality in a Manifoldlike Causal Set