Some of Topological and Methodological Aspects of Quantum Cosmology Models
Abstract
In this paper we address some critical remarks to two leading models quantum cosmology – Hawking-Hartle model and Vilenkin model. Both models appeal to different mathematical frameworks to reconstract of first moments of Universe ewolution. The first one presents wave function of the Universe using Feynman’s formalism of quantum mechanics — path integrals. The other one shows the beginnig of the Universe as quantum tunneling process. The authors of above mentioned approaches to quantum cosmology claims, that these mechanisms describe creation of the Universe ex nihilo. The main aim of tis paper is to show a weakness of such interpretations. Firstly, Gordon McCabe’s criticism is presented. His analyses are based on topological concept of cobordism. In the second step, we show that the concept of ex nihilo should be rather understood as “zero – point – geometry” with a material field.
References
Harrison E., Cosmology – the science of the Universe, 2nd edition Cambridge 2000.
Hartle J., Hawking S., (1983), Wave Function of the Universe, “Physical Review” D 28, s. 2960 – 2975.
Vilenkin A., (1984), Quantum Creation of Uniwerses, “Physical Review” D 30, s. 509-511.
Hawking S., A brief history of time, New York 1988.
Hawking S., Mlodinov L., Jeszcze krótsza historia czasu, Poznań, 2007.
McCabe G., (2004), The structure and interpretation of cosmology, Part I, “Studies in History and Philosophy of Modern Physics”, 35, s. 549-595.
McCabe G., (2005), The structure and interpretation of cosmology, Part II, “Studies in History and Philosophy of Modern Physics” 36, s. 67-102.
Milnor J. W., Topologia z różniczkowego punktu widzenia, PWN, Warszawa 1969.
Lickorish W. B. R., (1963), Homeomorphisms of non – orientable two – manifolds, “Proceedings of the Cambridge Philosophical Society”, vol. 59, s. 307-317.
Reinhart B. L., (1963), Cobordism and the Euler number, “Topolgy” 2, s. 173-177.
Włodarczyk J., Birational cobordisms and factorization of birational maps, J. Alg. Geom., 9 (2000), s. 425 – 449.
Życiński J., (1996), Methaphysics and Epistemology in Stephen Hawking’s Theory of the Creation of the Universe, “Zygon”, vol. 31, nr 2, s. 269 – 284.
Ashtekar A., Bojowald M., Lewandowski J., Mathematical structure of loop quantum cosmology, arxiv: gr-qc/0304074.
Heller M., Filozofia przyrody. Zarys historyczny, Znak 2004.
Trautman A., Differential Geometry for Physicists, Bibliopolis, Neapol 1984.
Bojowald M., (2001), Absence of a Singularity in Loop Quantum Cosmology, “Physical Review Letters” vol. 86 , s. 5227-5230.
Bojowald M., (2001), Dynamical Initial Conditions in Quantum Cosmology, “Physical Review Letters” vol. 87 (121301).
Bojowald M., (2002), Inflation from Quantum Geometry, “Physical Review Letters” Vol. 89 (261301).
Kolb E., Turner M., The early Universe, Redwood City 1990.
Tryon E. P., (1973), Is the Universe vacuum fluctuation?, “Nature” 246 (5433), s. 396 – 397.
Restivo S., The Social Relations of Physics, Mysticism and Mathematics, Dordrecht 1984.
Barrow J., Początek Wszechświata, CIS Warszawa 1995.
Drees W. B., (1987), Interpreting of the Wave function of the Universe, “International Journal of Theoretical Physics”, vol. 26 nr 10, s. 939-942.
Ambjorn J., Janik R., Westra W., Zohren S., (2006), The emergrnce of background geometry from quantum fluctuactions, arXiv: gr-qc/0607013.
Zeldovich Y. B., Starobinski A. A., (1984), Quantum creation of the Universe with nontrivial topology, “Soviet Astronomy Letters” vol. 10, s.135-137.
Grygiel W., „Wspaniały Projekt” – Boga czy człowieka?, Urania, nr 3, tom 82, s. 100-105.
Staruszkiewicz A., Koncepcja multiverse zamachem na tradycyjne pojmowanie praw przyrody, [w:] M. Heller, J. Mączka, P. Polak, M. Szczerbińska – Polak, Prawa Przyrody, Kraków – Tarnów, 2008, s. 13 – 19.
Hartle J. B., Scientific Knowledge from the Perspective of Quantum Cosmology, [w]: Boundaries and Barriers: On the Limits to Scientific Knowledge, red. Casti J. L. Karlqvist A., Addison-Wesley, Reading, MA 1996.
Heller M., (1989), Kwantowa kosmologia i ostateczne rozumienie Wszechświata, „Problemy”, Nr.2, s. 7.
Wrochna G., Agnostycyzm a metoda naukowa, [w]: „Questiones ad disputandum 6 (Między wiarą i niewiarą. Oblicza agnostycyzmu), (red.) Wójcik B., Biblos Tarnów 2005, s. 17-44.
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