2013/10/31 by Nicolas Franco, Michał Eckstein
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Causal structure #Causality (physics) #Classical mechanics #Commutative property #Computer science #Degrees of freedom (physics and chemistry) #Epistemology #Law #Mathematics #Motion (physics) #Noncommutative and Quantum Gravity Theories #Physics #Political science #Pure mathematics #Quantum mechanics #Simple (philosophy) #Space (punctuation) #Theoretical physics #Unitary state #gr-qc #math-ph #math.MP #math.OA #msc:53C50 #msc:54F05 #msc:58B34
paper · pdf · doi:10.3842/sigma.2014.010
published as SIGMA 10 (2014), 010, 23 pages
arxiv created 2014/01/28 · openalex publication_date 2014/01/28 · arxiv updated 2014/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We investigate the causal relations in the space of states of almost commutative Lorentzian geometries. We fully describe the causal structure of a simple model based on the algebra S(R 1,1 ) M 2 (C), which has a non-trivial space of internal degrees of freedom. It turns out that the causality condition imposes restrictions on the motion in the internal space. Moreover, we show that the requirement of causality favours a unitary evolution in the internal space.