2025/12/01 by Chenyang Amy Hu, Chenyang (Amy) Hu, David Meyer +2 · 1 voice
Mathematics · Physics and Astronomy · #Causal sets #Causal structure #Conformal map #Dimension (graph theory) #Homotopy and Cohomology in Algebraic Topology #Manifold (fluid mechanics) #Minkowski space #Minkowski's theorem #Minkowski–Bouligand dimension #Noncommutative and Quantum Gravity Theories #Point processes and geometric inequalities #Space (punctuation) #gr-qc #math-ph
paper · pdf · doi:10.1063/5.0290407
openalex publication_date 2025/12/01 · openalex created_date 2025/12/30 · arxiv published 2025/12/31 · arxiv updated 2025/12/31 · openalex updated_date 2026/08/05
Aleksandrov, and then Zeeman, showed that the causal relations among the set of points in a Minkowski space of dimension greater than 2 determine the Minkowski space structure of the set up to a global conformal factor. We show that in any dimension the distances between causally related pairs of points determine the distances between spatially related pairs of points, and thus completely determine the Minkowski space structure of the set. This is a step in the direction of proving that causal sets arising from a Poisson process in a Lorentzian manifold determine that manifold up to the degree of approximation inherent in the intensity of the Poisson process—the Hauptvermutung of causal set theory.