Time and Physics — a Noncommutative Revolution

  • Michał Heller
Part of the Synthese Library book series (SYLI, volume 309)


Basic ideas of noncommutative geometry are briefly presented. This mathematical theory, being global from the very beginning, can be used to model physics in which local concepts, such as those of time instant and space point, are meaningless. In spite of the lack of the standard time concept a “noncommutative dynamics” can be defined. Noncommutative generalizations of causality, probability and chance are discussed.


Noncommutative Geometry Leibniz Rule Noncommutative Space Local Concept Noncommutative Algebra 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Connes, A. (1994). Noncommutative Geometry. New York-London: Academic Press.Google Scholar
  2. Connes, A and Rovelli, C. (1994). Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in Generally Covariant Quantum Theories, Classical and Quantum Gravity 11, 2899–2917.CrossRefGoogle Scholar
  3. Heller, M. and Sasin, W. (1999). Noncommutative Unification of General Relativity and Quantum Mechanics, International Journal of Theoretical Physics 38, 1619–1622.CrossRefGoogle Scholar
  4. Heller, M. and Sasin, W. (1998). Emergence of Time, Physics Utters A250, 48–54.Google Scholar
  5. Heller, M., Sasin, W. and Lambert, D. (1997). Groupoid Approach to Noncommutative Quantization of Gravity, Journal of Mathematical Physics 38, 5840–5855.CrossRefGoogle Scholar
  6. Heller, M, Sasin, W. and Odrzygóźdź, Z. (2000). State Vector Reduction as a Shadow of Noncommutative Dynamics, Journal of Mathematical Physics 41, 5168–5179.CrossRefGoogle Scholar
  7. Landi, G. (1997). An Introduction to Noncommutative Spaces and Their Geometries. Berlin-Heidelberg: Springer.Google Scholar
  8. Madore, J. (1999). An Introduction to Noncommutative Differential Geometry and Its Physical Applications. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  9. Manin, Y. I. (1991). Topics in Noncommutative Geometry. Princeton: Princeton University Press.Google Scholar
  10. Masson, T. (1996). Géométrie non commutative et applications à la théorie des champs, Vienna, Preprint of the Erwin Schrödinger International Institute for Mathematical Physics, no 296.Google Scholar
  11. Smolin, L. (1997). The Life of the Cosmos, New York-Oxford: Oxford University Press.Google Scholar
  12. Sunder, V. S. (1987). An Invitation to von Neumann Algebras. New York-Berlin: Springer.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Michał Heller
    • 1
  1. 1.Faculty of PhilosophyPontifical Academy of TheologyCracowPoland

Personalised recommendations