Abstract
The recent surge of interest in the origin of the temporal asymmetry of thermodynamical systems (including the accessible part of the universe itself) has put forward two possible explanatory approaches to this age-old problem. Hereby we show that there is a third possible alternative, based on the generalization of the classical (“Boltzmann–Schuetz”) anthropic fluctuation picture of the origin of the perceived entropy gradient. This alternative (which we dub the Acausal-Anthropic approach) is based on accepting Boltzmann's statistical measure at its face value, and accomodating it within the quantum cosmological concept of the multiverse. We argue that conventional objections raised against the Boltzmann–Schuetz view are less forceful and serious than it is usually assumed. A fortiori, they are incapable of rendering the generalized theory untenable. On the contrary, this analysis highlights some of the other advantages of the multiverse approach to the thermodynamical arrow of time.
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References
L. Boltzmann, Lectures on Gas Theory, translated by S. G. Brush (University of California Press, Berkeley, 1964).
H. D. Zeh, The Physical Basis of the Direction of Time (Springer, New York, 1992).
H. Price, Time's Arrow and Archimedes' Point (Oxford University Press, Oxford, 1996).
E. Lieb and J. Yngvason, “The physics and mathematics of the second law of thermodynamics, ” Phys. Rep. 310, 1(1999).
D. Albert, “The foundations of quantum mechanics and the approach to thermodynamic equilibrium, ” Brit. J. Phil. Sci. 45, 669(1994);Time and Chance (Harvard University Press, Cambridge, 2000).
J. Uffink, “Bluff your way in the second law of thermodynamics, ” Stud. Hist. Philos. Modern Phys. B 32, 305(2001).
H. R. Brown and J. Uffink, “The origins of time-asymmetry in thermodynamics: the minus first law, ” Stud. Hist. Philos. Modern Phys. B 32, 525(2001).
H. Price, “Boltzmann's time bomb, ” British J. Philos. Sci. 53, 83(2002).
H. Price, “Burbury's last case: The mystery of the entropic arrow, ” forthcoming in Time, Reality and Experience, Craig Callender, ed. (Cambridge University Press, Cambridge, 2002).
H. Bondi, Cosmology, 2nd edn. (Cambridge University Press, London, 1961).
P. A. M. Dirac, “The cosmological constants, ” Nature 139, 323(1937);“Cosmological models and the large numbers hypothesis, ” Proc. R. Soc. A 338, 439(1974).
W. Davidson, “Some cosmological implications of Dirac's large numbers hypothesis, ” Mon. Not. R. astr. Soc. 200, 645(1982).
R. H. Dicke, “Dirac's cosmology and Mach's principle, ” Nature 192, 440(1961).
R. W. Hellings et al., “Experimental test of the variability of G using Viking lander ranging data, ” Phys. Rev. Lett. 51, 1609(1983).
T. Damour, G. W. Gibbons, and J. H. Taylor, “Limits on the variability of G using binary-pulsar data, ” Phys. Rev. Lett. 61, 1151(1988).
P. A. M. Dirac, “Dirac replies [to Dicke's letter, Ref. 13], ” Nature 192, 441(1961).
H. R. Pagels, “Cozy cosmology, ” in Modern Cosmology and Philosophy, J. Leslie, ed. (Prometheus Books, New York, 1998), p. 180.
A. S. Eddington, “The end of the world: from the standpoint of mathematical physics, ” Nature 127, 447(1931).
G. Kutrovátz, “Heat death in ancient and modern thermodynamics, ” Open Sys. & Information Dyn. 8, 349(2001).
L. Boltzmann, “On certain questions of the theory of gases, ” Nature 51, 413(1895).
J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford University Press, New York, 1986).
J. Bekenstein, “Black holes and entropy, ” Phys. Rev. D 7, 2333(1973).
S. W. Hawking, “Black hole explosions?” Nature 248, 30(1974).
L. M. Krauss and M. S. Turner, “Geometry and destiny, ” Gen. Relativity Gravitation 31, 1453(1999).
M. M. Ćirković and N. Bostrom, “Cosmological constant and the final anthropic hypothesis, ” Astrophys. Space Sci. 274, 675(2000).
G. W. Gibbons and S. W. Hawking, “Cosmological event horizons, thermodynamics, and particle creation, ” Phys. Rev. D 15, 2738(1977).
R. Penrose, The Emperor's New Mind (Oxford University Press, Oxford, 1989).
G. F. R. Ellis and G. B. Brundrit, “Life in the infinite universe, ” Q. J. Roy. Astron. Soc. 20, 37(1979).
N. Bostrom, Anthropic Bias: Observation Selection Effects in Science and Philosophy (Routledge, New York, 2002).
H. Poincaré, The Foundations of Science (Science Press, Lancaster, 1946).
N. Wiener, Cybernetics (Wiley, New York, 1961).
L. Brillouin, Science and Information Theory (Academic, New York, 1962).
S. Lloyd and H. Pagels, “Complexity as thermodynamical depth, ” Ann. Phys. 188, 186(1988).
R. A. Treumann, “Evolution of the information in the universe, ” Astrophys. Space Sci. 201, 135(1993).
M. Tegmark, “Does the universe in fact contain almost no information?” Found. Phys. Lett. 9, 25(1996).
J. Collier, “Intrinsic information, ” in Information, Language and Cognition: Vancouver Studies in Cognitive Science, P. P. Hanson, ed. (Oxford University Press, Oxford, 1990), p. 390.
S. C. Shapiro, “Computationalism, ” Minds and Machines 5, 517(1995).
S. W. Hawking, “Arrow of time in cosmology, ” Phys. Rev. D 32, 2489(1985).
J. Earman, “An attempt to add a little direction to ‘the problem of the direction of time,’ ” Phil. Sci. 41, 15(1974).
A. D. Linde, Inflation and Quantum Cosmology (Academic, San Diego, 1990).
A. Albrecht, in The Birth of the Universe and Fundamental Physics, F. Occhionero, ed. (Springer, New York, 1994), preprint gr-qc/9408023.
M. Tegmark, “Is ‘the Theory of Everything’ merely the ultimate ensemble theory?” Ann. Phys. 270, 1(1998).
R. Nozick, Philosophical Explanations (Harvard University Press, Cambridge, 1981).
J. Rosen, “Self-generating universe and many worlds, ” Found. Phys. 21, 977(1991).
J. J. C. Smart, Our Place in the Universe: A Metaphysical Discussion (Blackwell, Oxford, 1989).
A. D. Linde, “Eternally existing self-reproducing chaotic inflationary universe, ” Phys. Lett. B 175, 395(1986).
M. Clutton-Brock, “Entropy per baryon in a ‘many-worlds’ cosmology, ” Astrophys. Space Sci. 47, 423(1977).
M. Clutton-Brock, “The arrow of time in a bouncing universe, ” Observatory 102, 147(1982).
M. Tegmark and M. J. Rees, “Why is the cosmic microwave background fluctuation level 10−5?” Astrophys. J. 499, 526(1998).
R. P. Feynman, The Character of Physical Law (Cox and Wyman, London, 1965).
C. von Weizsäcker, “Der zweite Hauptsatz und der Unterschied von der Vergangenheit und Zukunft, ” Ann. Phys. 36, 275(1939).
E. Wilson, The Diversity of Life (Harvard University Press, Cambridge, 1992).
H. P. Yockey, “A calculation of the probability of spontaneous biogenesis by information theory, ” J. Theor. Biol. 67, 377(1977).
H. P. Yockey, “Self-organization origin of life scenarios and information theory, ” J. Theor. Biol. 91, 13(1981).
F. Hoyle, “The universe—past and present reflections, ” Ann. Rev. Astron. Astrophys. 20, 1(1982).
F. H. Crick and L. E. Orgel, “Directed panspermia, ” Icarus 19, 341(1973).
F. Raulin-Cerceau, M.-C. Maurel, and J. Schneider, “From panspermia to bioastronomy, the evolution of the hypothesis of universal life, ” Orig. Life Evol. Biosph. 28, 597(1998).
F. Hoyle and N. C. Wickramasinghe, “Comets–a vehicle for panspermia, ” Astrophys. Space Sci. 268, 333(1999).
D. N. F. Dunbar, W. A. Wensel, and W. Whaling, “The 7.68-Mev State in C12, ” Phys. Rev. 92, 649(1953).
C. B. Collins and S. W. Hawking, “Why is the universe isotropic?” Astrophys. J. 180, 317(1973).
C. B. Collins, “The postulate of uniform thermal histories—a new formulation and its application to a special class of spacetimes, ” Classical Quantum Gravity 7, 1983(1990).
H. Kragh, Cosmology and Controversy (Princeton University Press, Princeton, 1996).
J. Collier, “Information originates in symmetry breaking, ” Symmetry: Science and Culture 7, 247(1996).
J. L. Borges, Collected Fictions(Penguin, New York, 1999).
G. Oppy, “Physical eschatology, ” Philo 4(2)(2001).
F. C. Adams and G. Laughlin, “A dying universe: the long-term fate and evolution of astrophysical objects, ” Rev. Mod. Phys. 69, 337(1997).
L. P. Horwitz, R. T. Arshansky, and A. C. Elitzur, “On the two aspects of time: the distinction and its implications, ” Found. Phys. 18, 1159(1988).
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Ćirković, M.M. The Thermodynamical Arrow of Time: Reinterpreting the Boltzmann–Schuetz Argument. Foundations of Physics 33, 467–490 (2003). https://doi.org/10.1023/A:1023715732166
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DOI: https://doi.org/10.1023/A:1023715732166