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On the Meaning of the Constant “c” in Modern Physics

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Abstract

In modern physics, the constant “c” plays a twofold role. On the one hand, “c” is the well known velocity of light in an empty Minkowskian space–time, on the other hand “c” is a characteristic number of Special Relativity that governs the Lorentz transformation and its consequences for the measurements of space–time intervals. We ask for the interrelations between these two, at first sight different meanings of “c”. The conjecture that the value of “c” has any influence on the structure of space–time is based on the operational interpretation of Special Relativity, which uses light rays for measurements of space–time intervals. We do not follow this way of reasoning but replace it by a more realistic approach that allows to show that the structure of the Minkowskian space–time can be reconstructed already on the basis of a restricted classical ontology (Mittelstaedt, Philosophie der Physik und der Raum-Zeit, Mannheim: BI-Wissenschaftsverlag, 1988 and Mittelstaedt, Kaltblütig: Philosophie von einem rationalen Standpunkt, Stuttgart: S. Hirzel Verlag, pp. 221–240, 2003), and that without any reference to the propagation of light. However, the space–time obtained in this way contains still an unknown constant. We show that this constant agrees numerically with “c” but that it must conceptually clearly be distinguished from the velocity of light. Hence, we argue for a clear distinction between the two faces of “c” and for a dualism of space–time and matter.

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Notes

  1. Mittelstaedt (2006).

  2. Mittelstaedt (2008).

  3. Except, of course of domains that are not considered in the present paper.

  4. The first measurement of the velocity of light by O. Rømer was performed in 1670, several years before Newton’s “Principia” appeared in 1686 (1st ed.) and 1723 (2nd ed.).

  5. Marzke and Wheeler (1964), Misner et al. (1973, p. 397).

  6. Cf. for instance Gamov (1946).

  7. Penrose (1959).

  8. Terrell (1959).

  9. For more details cf. Mittelstaedt (2006, p. 260).

  10. “Hypotheses non fingo”, (Principia, 3. ed, p. 943).

  11. For the role and importance of metaphysics in physical sciences cf. Vollmer (2007).

  12. The original Latin formulation reads: “Tempus absolutum, verum et mathematicum, in se per natura sua absque relatione ad externum quodvis, aequabiliter fluit”.

  13. v. Ignatowski (1910), Frank et al. (1911).

  14. We will not discuss here the reasons for the inadequacy of this axiomatic approach.

  15. Levy-Leblond (1976), Mittelstaedt (1976).

  16. Mittelstaedt (1995), Mittelstaedt (2006).

  17. Levy-Leblond (1976), Mittelstaedt (1976), Mittelstaedt (1995).

  18. It is an important and difficult problem, how many test bodies must at least be used in the ensemble Γ in order to allow for deriving the linearity of the transformations between inertial systems. We will not discuss this question here and refer to the literature. Cf. Borchers and Hegerfeld (1972).

  19. Mittelstaedt (1995, pp. 22–23).

  20. For more details cf. Mittelstaedt (1995, pp. 92–95).

  21. Mittelstaedt (1995), l.c.

  22. Mittelstaedt (2006).

  23. Hawking and Ellis (1973, p. 38).

  24. Cf. Mittelstaedt (1995, p. 114), Sexl and Urbantke (1992, p. 68).

  25. Vilenkin (1982), Linde (1990).

  26. Ellis et al. (2003), Carr (2007).

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Acknowledgments

It is a pleasure to thank Friedrich Hehl for useful criticisms and suggestions.

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  1. Institut für Theoretische Physik, Universität zu Köln, Zülpicherstraße 77, 50937, Cologne, Germany

    Peter Mittelstaedt

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Mittelstaedt, P. On the Meaning of the Constant “c” in Modern Physics. J Gen Philos Sci 41, 45–53 (2010). https://doi.org/10.1007/s10838-010-9114-0

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