Effective Topology from Spacetime Tomography

Abstract

We recover the effective topology of spacetime using the notion of record from the decoherent histories approach to Quantum Theory. From a series of (gedanken) experiments, we obtain the set of possible events, grouped into sub-sets that corresponds to histories, but with no other information such as (causal) order or any notion of proximity. This corresponds to tomography of the "effective" spacetime, that is done in an operational way. Making certain assumptions about these records, and using the existence of upper bound in the speed of transfer of matter and information, we recover the full partial (causal) order up to certain ambiguities. The partially ordered set of events corresponds to an "effective" causal set which is a discretized version of spacetime with the causal relation as defining feature. We conclude with a derivation of the topology of this effective discretized spacetime.