Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-10T01:54:40.288Z Has data issue: false hasContentIssue false
  • English
  • Français

Combining Statistical-Thermodynamics and Relativity Theory: Methodological and Foundations Problems

Published online by Cambridge University Press:  31 January 2023

John Earman
John Earman*
Affiliation:
University of Minnesota
Get access Rights & Permissions [Opens in a new window]

Extract

Classical statistical mechanics has commanded a modest but steady amount of attention from philosophers of science. By contrast, there has been an almost total neglect of relativistic statistical mechanics, or more precisely, a neglect of the prospects and problems of producing a relativistic version of classical statistical mechanics. The neglect is undeserved, for this area offers a fascinating array of case studies for those concerned with the history and sociology of science, with the structure and dynamics of scientific theories, or with foundations problems in physics. This paper is dedicated to the goal of ending the neglect. Towards this end, I will survey some of the issues which arise in attempting to marry statistical-thermodynamics with relativity theory. The choice of the issues to be discussed and their treatment naturally reflect my own preferences and prejudices, and I cannot hope for the reader’s agreement on all points.

Type
Part V. Statistical Mechanics
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1978 , Issue 2: Volume Two: Symposia and Invited Papers 1978 , 1978 , pp. 156 - 185
Copyright
Copyright © 1981 Philosophy of Science Association

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

1

There are many people whom I would like to thank for help and encouragement on this project; but so far, they have not given any.

References

[1] Bel, L. “Formes hamiltoniennes et systems conservatifs.” Annales de l’Institut Henri Poincaré 22(1975): 173–199.Google Scholar
[2] Carter, B. “Black Hole Equilibrium States.” In Black Holes. Edited by DeWitt, C. and DeWitt, B.S. New York: Gordon and Breach, 1973. Pages 57–214.Google Scholar
[3] Cattaneo, C. “Sur une forme de l’equation de la chaleur eliminante la paradoxe d’une propagation instantanee.” Comptes Rendus 247(1958): 431–433.Google Scholar
[4] Currie, D.G., Jordan, T.F., and Sudarshan, E.C.G. “Relativistic Invariance and Hamiltonian Theories of Interacting Particles.” Reviews of Modern Physics 35(1963): 350–375.CrossRefGoogle Scholar
[5] Danzig, D. van. “On the Phenomenological Thermodynamics of Moving Water.” Physica 6(1939): 673–704.CrossRefGoogle Scholar
[6] Danzig, D. van. “On Relativistic Thermodynamics.” Koninklijke Nederlansche Akademie van Wetenschappen 42(1939): 601–607.Google Scholar
[7] Danzig, D. van. “On Relativistic Gas Theory.” Koninklijke Nederlansche Akademie van Wetenschappen 42(1939): 608–625.Google Scholar
[8] Droz-Vincent, P. “Hamiltonian Systems in Relativistic Dynamics.” Nuovo Cimento B 12(1972): 1–9.CrossRefGoogle Scholar
[9] Eckart, C. “Thermodynamics of Irreversible Processes III.” Physical Review 58(1940): 919–924.CrossRefGoogle Scholar
[10] Ehlers, J. “General Relativity and Kinetic Theory.” In General Relativity and Cosmology. Edited by Sachs, R.K. New York: Academic Press, 1971. Pages 1–70.Google Scholar
[11] Ehlers, J. “General-Relativistic Kinetic Theory of Gases.” In Relativistic Fluid Dynamics. Edited by Cattaneo, C. Rome: Edizioni Cremonese, 1971. Pages 301–388.Google Scholar
[12] Ehlers, J. “Survey of General Relativity Theory.” In Relativity, Astrophysics, and Cosmology. Edited by Israel, W. Dordrecht-Holland: D. Reidel, 1973. Pages 1–125.Google Scholar
[13] Ehlers, J. “Progress in Relativistic Statistical Mechanics, Thermodynamics and Continuum Mechanics.” In General Relativity and Gravitation. Edited by Shaviv, G. and Rosen, J. Pages 213–232.Google Scholar
[14] Einstein, A. “Über das Relätivitatsprinzip und die aus demselben gezogenen Folgerungen.” Jahrbuch der Radioaktivitat und Electronik 4(1907): 411–462.Google Scholar
[15] Havas, P. “Some Basic Problems in the Formulation of Relativistic Statistical Mechanics of Interacting Particles.” In Statistical Mechanics of Equilibrium and Non-Equilibrium. Edited by Meixner, J. Amsterdam: North-Holland, 1965. Pages 1–19.Google Scholar
[16] Hughes, W.F. “Relativistic Magnetohydrodynamics and Irreversible Thermodynamics.” Proceedings of the Cambridge Philosophical Society 57(1961): 878–889.CrossRefGoogle Scholar
[17] Israel, W. “Nonstationary Irreversible Thermodynamics: A Causal Relativistic Theory.” Annals of Physics 100(1976): 310–331.CrossRefGoogle Scholar
[18] Jüttner, F. “Das Maxwellsche Gesetz der Geschwindigkeitverteilung in der Relativtheorie.” Annalen der Physik 34(1911): 856–882.CrossRefGoogle Scholar
[19] Kranyš, M. “Relativistic Hydrodynamics with Irreversible Thermodynamics without the Paradox of Infinite Velocity of Heat Conduction.” Nuovo Cimento B 41(1966): 51–70.CrossRefGoogle Scholar
[20] Künzle, H.P. “Galilei and Lorentz Invariance of Classical Particle Interactions.” Symposia Mathematica 14(1974): 53–84.Google Scholar
[21] Landau, L.D. and Lifshitz, E.M. Fluid Mechanics. New York: Pergamon Press, 1975.Google Scholar
[22] Leutwyler, H. “A No-Interaction Theorem in Classical Relativistic Hamiltonian Particle Mechanics.” Nuovo Cimento 37 (1965): 556–567.CrossRefGoogle Scholar
[23] Lichnerowicz, A. Theories Relativistes de la Gravitation et de L’Électromagnétisme. Paris: Masson et Cie, 1955.CrossRefGoogle Scholar
[24] Møller, C. The Theory of Relativity. Oxford: Clarendon Press, 1962.Google Scholar
[25] Møller, C. The Theory of Relativity, 2nd ed. Oxford: Clarendon Press, 1972.Google Scholar
[26] Ott, H. “Lorentz Transformation der Wärme und der Temperature.” Zeitschrift fur Physik 175(1963): 70–104.CrossRefGoogle Scholar
[27] Planck, M. “Zur Dynamik Bewegter System.” Annalen der Physik 26 (1908): 1–34.CrossRefGoogle Scholar
[28] Schouten, J.A. Tensor Analysis for Physicists. Oxford: Oxford University Press, 1959.Google Scholar
[29] Schucking, E.L. and Spiegel, E.A. “Thermodynamics and Cosmology.” Comments on Astrophysics and Space Scienoe. 2(1970): 121–125.Google Scholar
[30] Stewart, J.M. Non-Equilibrium Relativistic Kinetic Theory. New York: Springer-Verlag, 1971.CrossRefGoogle Scholar
[31] Stewart, J.M. “On Transient Relativistic Thermodynamics and Kinetic Theory.” Proceedings of the Roval Society of London A 357(1977): 59–75.Google Scholar
[32] Synge, J.L. “The Energy Tensor of a Continuous Medium.” Proceedings of the Royal Society of Canada 28(1934): 127–171.Google Scholar
[33] Synge, J.L. The Relativistic Gas. Amsterdam: North Holland, 1957.Google Scholar
[34] Synge, J.L. Relativity: The General Theory. Amsterdam: North Holland, 1964.Google Scholar
[35] Tolman, R.C. “Relativity Theory: The Equipartition Law in a System of Particles.” Philosophical Magazine 28(1914): 583–600.Google Scholar
[36] Tolman, R.C. “On the Extension of Thermodynamics to General Relativity.” Proceedings of the National Academy of Sciences 14 (1928): 268–272.CrossRefGoogle ScholarPubMed
[37] Tolman, R.C. “Further Remarks on the Second Law of Thermodynamics in General Relativity.” Proceedings of the National Academy of Sciences 14(1928): 701–706.CrossRefGoogle ScholarPubMed
[38] Tolman, R.C. Relativity. Thermodynamics, and Cosmology. Oxford: Clarendon Press, 1934.Google Scholar
[39] Zumino, B. “Some Questions in Relativistic Hydrodynamics.” Physical Review 108(1957): 1116–1121.CrossRefGoogle Scholar