The existence of singularities and the origin of space-time
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Published:
Dec 3, 2008
Keywords:
noncommutative geometry singularities space-time von Neumann algebras
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Abstract
Methods of noncommutative geometry are applied to deal with singular space-times in general relativity. Such space-times are modeled by noncommutative von Neumann algebras of random operators. Even the strongest singularities turn out to be probabilistically irrelevant. Only when one goes to the usual (commutative) regime, via a suitable transition process, space-time emerges and singularities become significant.
Article Details
How to Cite
Heller, M. (2008). The existence of singularities and the origin of space-time. Philosophical Problems in Science (Zagadnienia Filozoficzne W Nauce), (43), 35–43. Retrieved from https://zfn.edu.pl/index.php/zfn/article/view/232
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Templeton Prize
References
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Heller, M., Odrzygóźdź, Z., Pysiak, L. and Sasin, W., “Observables in a Noncommutative Approach to the Unification of Quanta and Gravity: A Finite Model”, Gen. Relat. Grav. 37, 541–555 (2005).
Heller, M., Odrzygóźdź, Z., Pysiak, L. and Sasin, W., “Anatomy of Malicious Singularities”, J. Math. Phys. 48, 092504–12 (2007).
Heller, M., Pysiak, L. and Sasin, W., “Noncommutative Unification of General Relativity and Quantum Mechanics”, J. Math. Phys. 46, 122501–122515 (2005).
Heller, M., Pysiak, L. and Sasin, W., “Noncommutative Dynamics of Random Operators”, Int. J. Theor. Phys. 44, 619–628 (2005).
Heller, M., Pysiak, L. and Sasin, W., “Conceptual Unification of Gravity and Quanta”, Int. J. Theor. Phys. 46, 2494–2512 (2007).
Heller, M. and Sasin, W., “Structured Spaces and Their Application to Relativistic Physics”, J. Math. Phys. 36, 3644–3662 (1995).
Johnson, R. A., “The Bundle Boundary in Some Special Cases”, J. Math. Phys. 18, 898–902 (1977).
Pysiak, L., “Time Flow in Noncommutative Regime”, Int. J. Theor. Phys. 46, 16–30 (2007).
Schmidt, B.G., “A New Definition of Singular Points in General Relativity”, Gen. Relat. Grav. 1, 269–280 (1971).
Tipler, F.J., Clarke, C.J.S. and Ellis, G.F.R., “Singularities and Horizons — A Review Article”, in: General Relativity and Gravitation. One Hundred Years after the Birth of Albert Einstein, vol. 2, (ed. by) A. Held (Plenum, New York — London, 1980), pp. 97–206.
Clarke, C.J.S., The Analysis of Space-Time Singularities (Cambridge University Press, Cambridge, 1993).
Connes, A., Noncommutative Geometry (Academic, New York, 1994).
Dodson, C.T.J., “Spacetime Edge Geometry”, Int. J. Theor. Phys. 17, 389–504 (1978).
Hawking, S.W. and Ellis, G.F.R., The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, 1973).
Heller, M., Odrzygóźdź, Z., Pysiak, L. and Sasin, W., “Observables in a Noncommutative Approach to the Unification of Quanta and Gravity: A Finite Model”, Gen. Relat. Grav. 37, 541–555 (2005).
Heller, M., Odrzygóźdź, Z., Pysiak, L. and Sasin, W., “Anatomy of Malicious Singularities”, J. Math. Phys. 48, 092504–12 (2007).
Heller, M., Pysiak, L. and Sasin, W., “Noncommutative Unification of General Relativity and Quantum Mechanics”, J. Math. Phys. 46, 122501–122515 (2005).
Heller, M., Pysiak, L. and Sasin, W., “Noncommutative Dynamics of Random Operators”, Int. J. Theor. Phys. 44, 619–628 (2005).
Heller, M., Pysiak, L. and Sasin, W., “Conceptual Unification of Gravity and Quanta”, Int. J. Theor. Phys. 46, 2494–2512 (2007).
Heller, M. and Sasin, W., “Structured Spaces and Their Application to Relativistic Physics”, J. Math. Phys. 36, 3644–3662 (1995).
Johnson, R. A., “The Bundle Boundary in Some Special Cases”, J. Math. Phys. 18, 898–902 (1977).
Pysiak, L., “Time Flow in Noncommutative Regime”, Int. J. Theor. Phys. 46, 16–30 (2007).
Schmidt, B.G., “A New Definition of Singular Points in General Relativity”, Gen. Relat. Grav. 1, 269–280 (1971).
Tipler, F.J., Clarke, C.J.S. and Ellis, G.F.R., “Singularities and Horizons — A Review Article”, in: General Relativity and Gravitation. One Hundred Years after the Birth of Albert Einstein, vol. 2, (ed. by) A. Held (Plenum, New York — London, 1980), pp. 97–206.