Abstract
Time-asymmetric spacetime structures, in particular those representing black holes and the expansion of the universe, are intimately related to other arrows of time, such as the second law and the retardation of radiation. The nature of the quantum arrow, often attributed to a collapse of the wave function, is also essential to understand the much discussed “black hole information loss paradox”. The master arrow that would combine all arrows of time does not have to be identified with the direction of a formal time parameter that would allow us to formulate the dynamics as a succession of global states (a trajectory in configuration space). It may even change direction with respect to a fundamental physical clock, such as the cosmic expansion parameter, if this were extrapolated to negative “pre-big-bang” values.
Dieser Beitrag wurde 2010 für das Oxford Handbook of Spacetime (Hrsg. Vesselin Petkov) geschrieben, dessen Erscheinen derzeit nicht absehbar ist. Aus diesem Grunde, und da er vorwie- gend an Physiker gerichtet ist, habe ich ihn hier nicht übersetzt. S. a. arxiv/1012.4708.
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Notes
- 1.
By “lead to” I mean here a (timeless) logical inference – not a causal relation that might already require an arrow of time.
References
H.D. Zeh, The Physical Basis of the Direction of Time, 5th edn. (Springer, 2007), Chap. 2.
dto., Chap. 5.
J.R. Oppenheimer and H. Snyder, Phys. Rev. 56, 455 (1939).
F.J. Dyson, Rev. Mod. Phys. 51, 447 (1979).
H.D. Zeh, The Physical Basis of the Direction of Time, 5th edn. (Springer, 2007c), Sect. 3.2.
J.D. Bekenstein, Phys. Rev. D7, 2333 (1973); S.W. Hawking, Comm. Math. Phys. 43, 199 (1975).
F.C. Adams and G. Laughlin, Rev. Mod. Phys. 69, 337 (1997).
D.N. Page, Phys. Lett. B95, 244 (1980); see also Ya.B. Zel’dovich, Usp. Fiz. Nauk 123, 487 (1977) [Sov. Phys. Usp. 20, 945 (1977)].
S.W. Hawking, Phys. Rev. D14, 2460 (1976); D.N. Page, in R.B. Mann and R.G. McLenaghan (edts.), Proc. 5th Can. Conf. Gen. Rel. and Relat. Astrophys. (World Scientific, Singapore, 1994), and Refs. therein; D. Gottesmann and J. Preskill, JHEP 0403, 026 (2004); S.W. Hawking, Phys. Rev. D72, 084013 (2005); S.D.H. Hsu and D. Reeb, Phys. Rev. D79, 124037 (2009); C. Barceló, S. Liberati, S. Sonego, and M. Visser, arXiv 1011.5911v1.
R. Penrose, in C.J. Isham, R. Penrose, and D.W. Sciama (edts.), Quantum Gravity II (Clarendon Press, Oxford, 1981); see also C. Kiefer, arXiv 0910.5836.
S.W. Hawking, Phys. Rev. D13, 191 (1976).
C. Kiefer, Class. Quant. Grav. 18, L151 (2001); in H.T. Elze (edt.), Decoherence and Entropy in Complex Systems (Springer, Berlin, 2004); H.D. Zeh, Phys. Lett. A347, 1 (2005).
L. Boltzmann, Berliner Berichte 1016 (1897).
A. Einstein and W. Ritz, Phys. Z. 10, 323 (1911).
T. Gold, Am. J. Phys. 30, 403 (1962).
H.D. Zeh, Entropy 8, 44 (2006).
C. Kiefer and H.D. Zeh, Phys. Rev. D51, 4145 (1995).
M. Bojowald, Gen. Rel. Grav. 35, 1877 (2003).
H.D. Conradi and H.D. Zeh, Phys. Lett. A151, 321 (1991); A. Ashtekar, M. Campiglia, and A. Henderson, Report arXiv 1011.1024v1.
R. Arnowitt, S. Deser, and C.W. Misner, in L. Witten (edt.) Gravitation: An Introduction to Current Research (Wiley, New York, 1962).
J. Barbour, in R. Penrose and C.J. Isham (edts.), Quantum Concepts in Space and Time (Cambridge Press, Cambridge, 1986); Class. Quant. Grav. 11, 2853 (1994); The End of Time (Weidenfeld and Nicolson, London, 1999).
See C. Kiefer, Quantum Gravity (Cambridge University Press, Cambridge, 2007), for a review.
K. Kuchar, in G. Kunstatter, D. Vincent, and J Williams (edts.), Proc. 4th Can. Conf. Gen. Rel. and Rel. Astrophys. (World Scientific, Singapore, 1992); C.J. Isham, in L.A. Ibort, and M.A. Rodriguez (edts.), Integrable Systems, Quantum Groups and Quantum Field Theory (Kluwer, Dordrecht, 1993).
H.D. Zeh, Die Physik der Zeitrichtung, Springer Lecture Notes. (Springer, Berlin, 1984), §6; Phys. Lett. A116, 9 (1986); A126, 311 (1988).
D.N. Page and W.K. Wootters, Phys. Rev. D27, 2885 (1983).
D. Giulini and C. Kiefer, Phys. Lett. A193, 21 (1994).
J.J. Halliwell and S.W. Hawking, Phys. Rev. D31, 1777 (1985); C. Kiefer, Class. Quant. Grav. 4, 1369 (1987).
C. Kiefer, Phys. Rev. D38, 1761 (1988).
A.O. Barvinsky, A. Yu. Kamenshchik, C. Kiefer, and I.V. Mishakov, Nucl. Phys. B551, 374 (1999).
V.G. Lapchinsky and V.A. Rubakov, Acta Phys. Polonica 10, 1041 (1979); T. Banks, Nucl. Phys. B249, 332 (1985); R. Brout and G. Venturi, Phys. Rev. D39, 2436 (1989); see also J.J. Halliwell and S.W. Hawking, Phys. Rev. D31, 1777 (1985); C. Kiefer, Class. Quant. Grav. 4, 1369 (1987).
Acknowledgement
I wish to thank Claus Kiefer for his comments on an early draft of this manuscript.
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Zeh, H.D. (2012). The Nature and Origin of Time-Asymmetric Spacetime Structures. In: Physik ohne Realität: Tiefsinn oder Wahnsinn?. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21890-3_22
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