Spacetime granularity from finite-dimensionality of local observable algebras
arXiv:1908.09293 · doi:10.1088/1361-6382/ab5eb0
Abstract
There are important indications that nature may be locally finite-dimensional, i.e., that any spatially bounded subsystem can be described by a finite-dimensional local observable algebra. Motivated by these ideas, we show that operational spacetime topology is described by an atomistic Boolean algebra if (i) local observable algebras are finite-dimensional factors, (ii) the intersection of two local algebras is also local, and (iii) the commutant of a local algebra is also local. Thus, in this case, spacetime has a point-free granular behavior at small scales.
16 pages; changes to v3: title modified, multiple references added, minor changes to the text
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