Skip to main content
SpringerLink
Log in

Three Constants of Nature

  • Chapter
  • First Online:
Rational Reconstructions of Modern Physics

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 174))

  • 1522 Accesses

Abstract

In accordance with the results of the preceding Chaps. 2 and 3, we assume that the two fundamental theories of modern physics, the Theory of Relativity (SR) and Quantum Mechanics (QM), can be obtained from the classical space-time theory and classical mechanics (CM) by abandoning or relaxing hypothetical assumptions contained in these classical structures. In addition, it became also obvious in the preceding chapters that classical mechanics and Newton’s space-time theory describe a fictitious world that does not exist in reality. Hence, we do not expect to find in modern physics any indications that refer to classical mechanics and to Newton’s space-time. Possible traces of absolute time and absolute space are equally eliminated in Special and General Relativity as the classical limit in Quantum Mechanics. In modern physics we can completely dispense with the pretended classical roots. In Quantum Mechanics as well as in Relativity there is no need and no room for anything like a correspondence principle or a non-relativistic limit, respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

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

  2. 2.

    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.).

  3. 3.

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

  4. 4.

    Cf. for instance Gamov (1946).

  5. 5.

    Penrose (1959).

  6. 6.

    Terrell (1959).

  7. 7.

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

  8. 8.

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

  9. 9.

    The original Latin formulation reads: “Tempus absolutum, verum et mathematicum, in se per natura sua absque relatione ad externum quodvis, aequabiliter fluit”. Newton (1934), p. 6.

  10. 10.

    Ignatowski (1910) and Franck and Rothe (1911).

  11. 11.

    Levy-Leblond (1976) and Mittelstaedt (1976).

  12. 12.

    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 Hegerfeldt (1972).

  13. 13.

    Mittelstaedt (1995), pp. 22–23.

  14. 14.

    For more details cf. Mittelstaedt (1995), pp. 83–116.

  15. 15.

    Mittelstaedt (2006).

  16. 16.

    Hawking and Ellis (1973), p. 38.

  17. 17.

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

  18. 18.

    Vilenkin (1982) and Linde (1990).

  19. 19.

    Ellis et al. (2003) and Carr (2007).

  20. 20.

    Dalla Chiara and Giuntini (2001).

  21. 21.

    Mittelstaedt (2005).

  22. 22.

    Cf. Section 1.3.

  23. 23.

    Dalla Chiara and Giuntini (2001).

  24. 24.

    Mac Laren (1965), Mittelstaedt (2005) and Piron (1976).

  25. 25.

    Solèr (1995).

  26. 26.

    Dalla Chiara (1995) and Foulis and Bennett (1994).

  27. 27.

    Mittelstaedt (2005).

  28. 28.

    Mittelstaedt (1995) and Piron (1976).

  29. 29.

    Foulis and Bennett (1994) and Busch et al. (1995), p. 25.

  30. 30.

    Busch et al. (1995), p. 52 and Mittelstaedt (1995).

  31. 31.

    Jauch (1968).

  32. 32.

    Jauch (1968).

  33. 33.

    Busch (1985) and Busch et al. (1995, 2007).

  34. 34.

    Busch et al. (2007).

  35. 35.

    Cf. Mittelstaedt (2008)

  36. 36.

    Misner et al. (1973), pp. 417–428, in particular p. 426.

  37. 37.

    Sakharov (1967).

References

  • Borchers, H. J., & Hegerfeldt, G. C. (1972). Über ein Problem der Relativitätstheorie: Wann sind Punktabbildungen des Rn linear? (Nachrichten der Akademie der Wissenschaften in Göttingen, II, Vol. Mathematisch-Physikalische Klasse, 10, pp. 205–229). Göttingen: Vandenhoeck & Ruprecht.

    Google Scholar 

  • Busch, P. (1985). Indeterminacy relations and simultaneous measurements in quantum theory. International Journal of Theoretical Physics, 24, 63–92.

    Article  MathSciNet  ADS  Google Scholar 

  • Busch, P., Grabowski, M., & Lahti, P. (1995). Operational quantum physics. Heidelberg: Springer.

    MATH  Google Scholar 

  • Busch, P., Heinonen, T., & Lahti, P. (2007). Heisenberg´s uncertainty principle. Physics Reports, 452, 155–176.

    Article  ADS  Google Scholar 

  • Carr, B. (2007). Universe or multiverse ? Cambridge: Cambridge University Press.

    Google Scholar 

  • Dalla Chiara, M. L. (1995). Unsharp quantum logics. International Journal of Theoretical Physics, 34, 1331–1336.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Ellis, G. F. R. et al. (2003). Multiverse and physical cosmology. http://arxiv.org/pdf/astro-ph/0305292.pdf.

  • Foulis, D. J., & Bennett, M. K. (1994). Effect algebras and unsharp quantum logics. Foundation of Physics, 24, 1331–1352.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Franck, P., & Rothe, H. (1911). Über die Transformation der Raum-Zeitkoordinaten von ruhenden auf bewegte Systeme. Annalen der Physik, 34, 825–855.

    Article  ADS  Google Scholar 

  • Gamov, G. (1946). Mr. Tompkins in wonderland. New York: The Macmillan Company.

    Google Scholar 

  • Hawking, S. W., & Ellis, G. F. R. (1973). The large scale structure of space-time. Cambridge: Cambridge University Press.

    Book  MATH  Google Scholar 

  • Ignatowski, W. (1910). Einige allgemeine Bemerkungen zum Relativitätsprinzip. Physikalische Zeitschrift, 11, 972–976.

    Google Scholar 

  • Jauch, J. M. (1968). Foundations of Quantum Mechanics. Reading: Addison –Wesley.

    MATH  Google Scholar 

  • Lévy-Leblond, J. M. (1976). One more derivation of the Lorentz transformation. American Journal of Physics, 44, 271–277.

    Article  ADS  Google Scholar 

  • Linde, A. D. (1990). Inflation and quantum cosmology. San Diego/London: Academic Press, Inc.

    MATH  Google Scholar 

  • MacLaren, M. D. (1965). Nearly modular orthocomplemented lattices. Transactions of the American Mathematical Society, 114, 401–416.

    Article  MathSciNet  MATH  Google Scholar 

  • Martzke, R., & Wheeler, J. A. (1964). Gravitation as geometry I: The geometry of space-time and the geometrodynamical standard meter. In H. Y. Chiu & W. F. Hoffman (Eds.), Gravitation and relativity (pp. 40–64). New York: A. Benjamin.

    Google Scholar 

  • Misner, C. W., Thorne, K. S., & Wheeler, J. A. (1973). Gravitation. San Francisco: W. H. Freeman.

    Google Scholar 

  • Mittelstaedt, P. (1976a). Philosophical problems of modern physics. Dordrecht: D. Reidel Publishing Company.

    Book  Google Scholar 

  • Mittelstaedt, P. (1995). Klassische Mechanik (2nd ed.). Mannheim: Bilbliographisches Institut.

    Google Scholar 

  • Mittelstaedt, P. (2005). Quantum physics and classical physics − in the light of quantum logic. International Journal of Theoretical Physics, 44, 771–781.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Mittelstaedt, P. (2006). Intuitiveness and truth in modern physics. In E. Carson & R. Huber (Eds.), Intuition and the axiomatic method (pp. 251–266). Dordrecht: Springer.

    Chapter  Google Scholar 

  • Penrose, R. (1959). The apparent shape of a relativistically moving sphere. Mathematical Proceedings of the Cambridge Philosophical Society, 55, 137–139.

    Article  MathSciNet  Google Scholar 

  • Piron, C. (1976). Foundations of quantum physics. Reading: W. A. Benjamin.

    MATH  Google Scholar 

  • Sakharov, A. D. (1967). Vacuum quantum fluctuations in curved space and the theory of gravitation. Doklady Akad. Nauk S.S.S.R., 177, 70–71. English translation Soviet Physics Doklady 12, 1040–1041.

    Google Scholar 

  • Sexl, R. U., & Urbantke, H. K. (1992). Relativität, Gruppen, Teilchen (3rd ed.). New York: Springer.

    MATH  Google Scholar 

  • Solèr, M.-P. (1995). Characterisation of Hilbert spaces by orthomodular lattices. Communications in Algebra, 23(1), 219–243.

    Article  MathSciNet  MATH  Google Scholar 

  • Terrell, J. (1959). Invisibility of the Lorentz contraction. Physical Review, 116, 1041–1045.

    Article  MathSciNet  ADS  Google Scholar 

  • Vilenkin, A. (1982). Creation of universes from nothing. Physics Letters, 117 B, 25–28.

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, Köln, Germany

    Peter Mittelstaedt

Authors
  1. Peter Mittelstaedt
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Mittelstaedt, P. (2013). Three Constants of Nature. In: Rational Reconstructions of Modern Physics. Fundamental Theories of Physics, vol 174. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5593-2_4

Download citation

Publish with us

Policies and ethics

Search

Navigation