Causal set Kinematics of CSTtheory posits that any continuum causal spacetimeCausal spacetime (M, g) is an approximation to an underlying discrete structure, namely, an ensembleEnsemble of causal sets  \(\mathfrak C_\rho (M,g)\) of causal sets generated via a generalised Poisson point processGeneralised Poisson point process (GPPP) or “Poisson sprinkling” Poisson sprinkling into (M, g) at fixed densityDensity  \(\rho \) . If this hypothesis is correct, \(\mathfrak C_\rho (M,g)\) should contain all the topological and geometric information in (M, g) at scales larger than the discreteness scaleDiscreteness scale  \(\rho ^{-1}\) . In this chapter we show several examples of the “reconstruction”Geometric reconstruction of continuum geometric and topological quantities from the underlying causal set ensembleEnsemble of causal sets. These are constructed from geometric order invariantsGeometric order invariantOrder invariant which are the discrete covariant observablesCovariant observables of the theory.

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Kinematics

  • Sumati Surya

摘要

Causal set Kinematics of CSTtheory posits that any continuum causal spacetimeCausal spacetime (M, g) is an approximation to an underlying discrete structure, namely, an ensembleEnsemble of causal sets  \(\mathfrak C_\rho (M,g)\) of causal sets generated via a generalised Poisson point processGeneralised Poisson point process (GPPP) or “Poisson sprinkling” Poisson sprinkling into (M, g) at fixed densityDensity  \(\rho \) . If this hypothesis is correct, \(\mathfrak C_\rho (M,g)\) should contain all the topological and geometric information in (M, g) at scales larger than the discreteness scaleDiscreteness scale  \(\rho ^{-1}\) . In this chapter we show several examples of the “reconstruction”Geometric reconstruction of continuum geometric and topological quantities from the underlying causal set ensembleEnsemble of causal sets. These are constructed from geometric order invariantsGeometric order invariantOrder invariant which are the discrete covariant observablesCovariant observables of the theory.