Abstract
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell–Boltzmann statistics, it is not necessary to assume that the particles are distinguishable or individuals. In other words, Maxwell–Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. The main goal of this paper is to provide the mathematical grounds of a quasi-set theoretical framework for statistical mechanics.
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REFERENCES
D. Bouwmeester and A. Zeilinger, Nature 388, 827–829 (1997).
N. C. A. da Costa and D. Krause, Stud. Logica 53, 533 (1994).
M. L. Dalla Chiara and G. Toraldo di Francia, in Bridging the Gap: Philosophy, Mathematics, Physics, G. Corsi et al., eds. (Kluwer Academic, Dordrecht, 1993), p. 261; Reprint from Versus 40, 29 (1985).
W. Heisenberg, Physics and Philosophy (Allen 6 Unwin, London, 1958).
N. Huggett, J. Philos. 96, 5–24 (1999).
D. Krause, Notre Dame J. Formal Logic 33, 402–411 (1992).
D. Krause and S. French, Synthese 102, 195–214 (1995).
D. Krause, Logique Anal. 153-154, 69–93 (1996).
D. Krause, A. S. Sant'Anna, and A. G. Volkov, Found. Phys. Lett. 12, 51–66 (1999).
Yu. I. Manin, in Proceedings of Symposia in Pure Mathematics 28, F. E. Browder, ed. (American Mathematical Society, Providence, RI, 1976), p. 36.
W. M. de Muynck, Int. J. Theor. Phys. 14, 327–346 (1975).
E. Mendelson, Introduction to Mathematical Logic (Chapman 6 Hall, London, 1997).
H. Primas, in Sixty-Two Years of Uncertainty, A. I. Miller, ed. (Plenum, New York, 1990), p. 233.
M. Redhead and P. Teller, Found. Phys. 21, 43 (1991).
M. Redhead and P. Teller, Br. J. Philos. Sci. 43, 201 (1992).
J. J. Sakurai, Modern Quantum Mechanics (Addison_Wesley, Reading, MA, 1994).
E. Schroödinger, Sci. Am. 52 (Sept. 1953).
A. S. Sant'Anna, Logique Anal. 157, 45–66 (1997).
A. S. Sant'Anna and D. Krause, Found. Phys. Lett. 10, 409–426 (1997).
P. Teller, An Interpretive Introduction to Quantum Field Theory (Princeton University Press, Princeton, NJ, 1995).
G. Toraldo di Francia, Scientia 113, 57 (1978).
B. van Fraassen, Quantum Mechanics: An Empiricist View (Clarendon Press, Oxford, 1991).
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Sant'Anna, A.S., Santos, A.M.S. Quasi-Set-Theoretical Foundations of Statistical Mechanics: A Research Program. Foundations of Physics 30, 101–120 (2000). https://doi.org/10.1023/A:1003643109795
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DOI: https://doi.org/10.1023/A:1003643109795