caa a22 4500 463195469 CHVBK 20180406164921.0 cr unu---uuuuu 170326e20070101xx s 000 0 eng 10.1007/s10773-006-9078-3 doi (NATIONALLICENCE)springer-10.1007/s10773-006-9078-3 Pysiak Leszek Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland aut Time Flow in a Noncommutative Regime [Elektronische Daten] [Leszek Pysiak] We develop an approach to dynamical and probabilistic properties of the model unifying general relativity and quantum mechanics, initiated in the paper (Heller et al. (2005) International Journal Theoretical Physics 44, 671). We construct the von Neumann algebra $${\cal M}$$ of random operators on a groupoid, which now is not related to a finite group G, but is the pair groupoid of the Lorentzian frame bundle E over spacetime M. We consider the time flow on $${\cal M}$$ depending on the state $$\phi $$ . The state $$\phi $$ defining the noncommutative dynamics is assumed to be normal and faithful. Then the pair $$({\cal M}, \phi) $$ is a noncommutative probabilistic space and $$\phi$$ can also be interpreted as an equilibrium thermal state, satisfying the Kubo-Martin-Schwinger condition. We argue that both the "time flow” and thermodynamics have their common roots in the noncommutative unification of dynamics and probability. Springer Science+Business Media, Inc., 2006 unification theory nationallicence quantum mechanics nationallicence noncommutative dynamics nationallicence noncommutative probability nationallicence random operators nationallicence von Neumann algebra nationallicence International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/1(2007-01-01), 16-30 0020-7748 46:1<16 2007 46 10773 https://doi.org/10.1007/s10773-006-9078-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10773-006-9078-3 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Pysiak Leszek Department of Mathematics and Information Science, Warsaw University of Technology, Plac Politechniki 1, 00-661, Warsaw, Poland aut NATIONALLICENCE 773 0- International Journal of Theoretical Physics Springer US; http://www.springer-ny.com 46/1(2007-01-01), 16-30 0020-7748 46:1<16 2007 46 10773 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer