Spacetime granularity from finite-dimensionality of local observable algebras

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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.
Original languageEnglish
Article number045014
Number of pages16
JournalClassical and Quantum Gravity
Issue number4
Publication statusPublished - 27 Jan 2020
MoE publication typeA1 Journal article-refereed


  • spacetime topology
  • quantum gravity
  • local finite-dimensionality


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