This chapter is a technical introduction to CST. It begins with a review of the causal structureCausal structure for causal spacetimes, which is a poset, and leads up to a set of theorems in Lorentzian geometry which we collectively refer to as the HKMMKP theoremHKMMKP theorem. A discrete version of this theorem provides the primary motivation for the CST hypothesis and helps shape its continuum approximationContinuum approximation, which is conjectured to be unique. This approximation exhibits several interesting features, including Lorentz invarianceLorentz invariance  (despite discreteness), and a certain characteristic nonlocality. This chapter also contains definitions and notations which will be used in the remainder of the book.

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The Causal Set Hypothesis

  • Sumati Surya

摘要

This chapter is a technical introduction to CST. It begins with a review of the causal structureCausal structure for causal spacetimes, which is a poset, and leads up to a set of theorems in Lorentzian geometry which we collectively refer to as the HKMMKP theoremHKMMKP theorem. A discrete version of this theorem provides the primary motivation for the CST hypothesis and helps shape its continuum approximationContinuum approximation, which is conjectured to be unique. This approximation exhibits several interesting features, including Lorentz invarianceLorentz invariance  (despite discreteness), and a certain characteristic nonlocality. This chapter also contains definitions and notations which will be used in the remainder of the book.