Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Connes, A. (1994). Noncommutative Geometry. New York-London: Academic Press.
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.
Heller, M. and Sasin, W. (1999). Noncommutative Unification of General Relativity and Quantum Mechanics, International Journal of Theoretical Physics 38, 1619–1622.
Heller, M. and Sasin, W. (1998). Emergence of Time, Physics Utters A250, 48–54.
Heller, M., Sasin, W. and Lambert, D. (1997). Groupoid Approach to Noncommutative Quantization of Gravity, Journal of Mathematical Physics 38, 5840–5855.
Heller, M, Sasin, W. and Odrzygóźdź, Z. (2000). State Vector Reduction as a Shadow of Noncommutative Dynamics, Journal of Mathematical Physics 41, 5168–5179.
Landi, G. (1997). An Introduction to Noncommutative Spaces and Their Geometries. Berlin-Heidelberg: Springer.
Madore, J. (1999). An Introduction to Noncommutative Differential Geometry and Its Physical Applications. Cambridge: Cambridge University Press.
Manin, Y. I. (1991). Topics in Noncommutative Geometry. Princeton: Princeton University Press.
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.
Smolin, L. (1997). The Life of the Cosmos, New York-Oxford: Oxford University Press.
Sunder, V. S. (1987). An Invitation to von Neumann Algebras. New York-Berlin: Springer.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Heller, M. (2002). Time and Physics — a Noncommutative Revolution. In: Eilstein, H. (eds) A Collection of Polish Works on Philosophical Problems of Time and Spacetime. Synthese Library, vol 309. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0097-9_3
Download citation
DOI: https://doi.org/10.1007/978-94-017-0097-9_3
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6039-6
Online ISBN: 978-94-017-0097-9
eBook Packages: Springer Book Archive