Skip to main content
SpringerLink
Log in

A theoretical device for space and time measurements

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

A theoretical device, which incorporates the functions of clock, rod, nonrotating platform, and accelerometer, and whose operation depends on the properties of light rays and free particles, is defined. The device, which we call a metrosphere, is simple enough that it can be introduced at the starting point of relativity theory and versatile enough that it can serve as an aid in the development and conceptualization of the theory. Relative to an inertial frame, a moving metrosphere undergoes a Lorentz-Fitzgerald contraction and the associated clock exhibits a Lorentz-Larmor rate retardation. From this fact and the assumption that there exists one inertial frame, it is possible to generate the kinematical results of special relativity. A metrosphere provides an observer with a local frame of reference, hence it is well adapted to the needs of general relativity, allows the equivalence principle to be introduced in a straightforward manner, and permits a smooth transition from special relativity to general relativity.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. C. Graves,The Conceptual Foundations of Relativity Theory (MIT Press, Cambridge, Massachusetts, 1971), pp. 155–168.

    Google Scholar 

  2. H. Weyl,Space-Time-Matter (Dover, New York, 1950), Appendix I; W. Kundt and B. Hoffman, inRecent Developments in General Relativity (Pergamon, New York, 1962), pp. 303–306; J. C. GravesThe Conceptual Foundations of Relativity Theory (MIT Press, Cambridge, Massachusetts, 1971), pp. 155–168; R. F. Marzke and J. A. Wheeler, inGravitation and Relativity, H. Y. Chiu and W. F. Hoffman, eds. (Benjamin, New York, 1964), pp. 40–64.

    Google Scholar 

  3. R. F. Marzke and J. A. Wheeler, inGravitation and Relativity H. Y. Chiu and W. F. Hoffman, eds. (Benjamin, New York, 1964), pp. 40–64.

    Google Scholar 

  4. J. L. Anderson,Principles of Relativity Physics (Academic Press, New York, 1967), pp. 159–161; H. C. OhanianGravitation and Space-time (W. W. Norton, New York, 1976), pp. 192–196.

    Google Scholar 

  5. H. Minkowski, inProblems in Space and Time, J. J. C. Smart, ed. (Macmillan, New York, 1964), p. 298; also inThe Principle of Relativity (Dover, New York, 1952; originally published by Methuen, 1923), p. 76.

    Google Scholar 

  6. H. Minkowski, inProblems in Space and Time, J. J. C. Smart, ed. (Macmillan, New York, 1964), p. 298; also inThe Principle of Relativity (Dover, New York, 1952; originally published by Methuen, 1923), p. 76.

    Google Scholar 

  7. M. Shallis,On Time (Schocken Books, New York, 1982), Chap. 1.

    Google Scholar 

  8. M. Capek, inDictionary of the History of Ideas, P. P. Wiener, ed. (Charles Scribner's Sons, New York, 1973), Vol. IV, pp. 389–398.

    Google Scholar 

  9. G. J. Whitrow, inDictionary of the History of Ideas P. P. Wiener, ed. (Charles Scribner's Sons, New York, 1973), Vol. IV, pp. 398–405.

    Google Scholar 

  10. H. Bondi,Relativity and Common Sense (Dover, New York, 1980; originally published by Doubleday, New York, 1964), pp. 64–69.

    Google Scholar 

  11. C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (W. H. Freeman, San Francisco, 1973), p. 19.

    Google Scholar 

  12. G. Leibniz, inProblems of Space and Time, J. J. C. Smart, ed. (Macmillan, New York, 1964), pp. 89–98.

    Google Scholar 

  13. H. Minkowski, inProblems of Space and Time, J. J. C. Smart, ed. (Macmillan, New York, 1964), p. 298; also inThe Principle of Relativity (Dover, New York, 1952; originally published by Methuen, 1923), p. 76.

    Google Scholar 

  14. H. A. Buchdahl,Seventeen Simple Lectures on General Relativity Theory (Wiley, New York, 1981), pp. 13–14.

    Google Scholar 

  15. J. L. Synge,Relativity: The Special Theory (North-Holland, Amsterdam, 1972), 2nd edn., p. 11, p. 53; B. F. SchutzA First Course in General Relativity (Cambridge University Press, Cambridge, 1985), pp. 4–5; see also: H. Blatter and T. Greber,Am. J. Phys. 56, 333 (1988).

    Google Scholar 

  16. J. L. Synge,Relativity: The Special Theory (North-Holland, Amsterdam, 1955), p. 11.

    Google Scholar 

  17. Ya. B. Zeldovich and I. D. Novikov,Stars and Relativity (The University of Chicago Press, Chicago, 1971), p. 12, footnote 7; L. D. Landau and E. M. LifshitzThe Classical Theory of Fields, 4th rev. English edn. (Pergamon Press, New York, 1975), pp. 229–230; C. Møller,The Theory of Relativity (Clarendon Press, Oxford, 1952), p. 234.

    Google Scholar 

  18. M. Born,Einstein's Theory of Relativity (Dover, New York, 1962), p. 335.

    Google Scholar 

  19. R. Carnap,Philosophical Foundations of Physics (Basic Books, New York, 1966), Chap. 9.

    Google Scholar 

  20. H. Weyl,Space, Time, and Matter (Dover, New York, 1950), p. 7.

    Google Scholar 

  21. H. Poincaré,The Value of Science (Dover, New York, 1958), Chap. 2, especially the final paragraph; R. CarnapPhilosophical Foundations of Physics (Basic Books, New York, 1966), Chap. 8.

    Google Scholar 

  22. H. Arzelies,Relativistic Kinematics (Pergamon, New York, 1966) p. 21; A. Harvey,Gen. Relativ. Gravit. 7, 891 (1976); S. J. Prokhovnik,The Logic of Special Relativity (Cambridge University Press, Cambridge 1967), p. 58.

    Google Scholar 

  23. J. L. Synge,Relativity: The Special Theory (North-Holland, Amsterdam, 1955), pp. 24–32;Relativity: The General Theory (North-Holland, Amsterdam, 1960), pp. 108, 112–114, 421; G. J. Whitrow, inDictionary of the History of Ideas, P. P. Wiener, ed. (Charles Scribner's Sons, New York, 1973), Vol. IV, p. 405, column 2.

    Google Scholar 

  24. R. F. Marzke and J. A. Wheeler, inGravitation and Relativity, H. Y. Chiu and W. F. Hoffman, eds. (Benjamin, New York, 1964), pp. 40–64.

    Google Scholar 

  25. E. A. Desloge,Classical Mechanics (Wiley, New York, 1982), Chaps. 2, 3, 85.

    Google Scholar 

  26. J. L. Synge,Relativity: The General Theory (North-Holland, Amsterdam, 1960), pp. 114–118; C. W. Misner, K. S. Thorne, and J. A. Wheeler,Gravitation (W. H. Freeman, San Francisco, 1973), pp. 327–332; H. Stephani,General Relativity (Cambridge University Press, Cambridge, 1982), pp. 45–47; J. L. Anderson,Principles of Relativity Physics (Academic Press, New York, 1967), pp. 320–321; C. Møller,The Theory of Relativity (Clarendon Press, Oxford, 1952), pp. 253–258.

    Google Scholar 

  27. W. K. H. Panofsky and M. Phillips,Classical Electricity and Magnetism (Addison Wesley, Reading, Massachusetts, 1955), pp. 245–246; K. R. SymonMechanics, 3rd edn. (Addison Wesley, Reading, Massachusetts, 1971), pp. 510–511.

    Google Scholar 

  28. J. L. Anderson and R. Gautreau,Am. J. Phys. 37, 178 (1969).

    Google Scholar 

  29. W. Rindler,Essential Relativity, 2nd edn. (Springer, New York, 1977), p. 43.

    Google Scholar 

  30. J. Ehlers, F. A. E. Pirani, and A. Schild, inGeneral Relativity, L. O'Raifeartaigh, ed. (Clarendon Press, Oxford, 1972), pp. 62–84.

    Google Scholar 

  31. E. Whittaker,A History of the Theories of Aether and Electricity (American Institute of Physics, New York, 1987; originally published by Nelson, London, 1951); P. M. Harman,Energy, Force, and Matter: The Conceptual Development of Nineteenth Century Physics (Cambridge University Press, Cambridge, 1982); L. P. Williams,Relativity Theory: Its Origins and Impact on Modern Thought (Wiley, New York, 1968), pp. 1–5; J. C. MaxwellA Treatise on Electricity and Magnetism (Dover, New York, 1925; originally published by Clarendon Press, Oxford, 1891), Articles 59, 60, 110, 645, 781, 865, 866; S. L. Jaki,The Relevance of Physics (University of Chicago Press, Chicago, 1966), pp. 79–84.

    Google Scholar 

  32. W. K. H. Panofsky and M. Phillips,Classical Electricity and Magnetism (Addison Wesley, Reading, Massachusetts, 1955), pp. 250–252; H. Erlichson,Am. J. Phys. 41, 1068 (1973).

    Google Scholar 

  33. E. Whittaker,A History of the Theories of Aether and Electricity (American Institute of Physics, New York, 1987; originally published by Nelson, London, 1951); P. M. Harman,Energy, Force, and Matter: The Conceptual Development of Nineteenth Century Physics (Cambridge University Press, Cambridge, 1982); L. P. Williams,Relativity Theory: Its Origins and Impact on Modern Thought (Wiley, New York, 1968), pp. 1–5; J. C. Maxwell,A Treatise on Electricity and Magnetism (Dover, New York, 1925; originally published by Clarendon Press, Oxford, 1891), Articles 59, 60, 110, 645, 781, 865, 866; S. L. Jaki,The Relevance of Physics (University of Chicago Press, Chicago, 1966), pp. 79–84.

    Google Scholar 

  34. H. A. Lorentz,The Theory of Electrons, 2nd edn. (Dover, New York, 1952; first edition originally published in 1909; 2nd edn. originally published in 1915), Secs. 188, 189, 194, and Note 72; W. Rindler,Am. J. Phys. 38, 111 (1970); H. Erlickson,Am. J. Phys. 41, 1068 (1973); L. Silberstein,The Theory of Relativity (Macmillan, London, 1924), Chaps. 1–3.

    Google Scholar 

  35. W. F. Magie, inRelativity Theory: Its Origins and Impact on Modern Thought, L. P. Williams, ed. (Wiley, New York, 1968), pp. 117–124.

    Google Scholar 

  36. H. A. Lorentz,The Theory of Electrons, 2nd edn., (Dover, New York, 1952), Sec. 194; A. d'Abro,The Evolution of Scientific Thought, 2nd rev. edn. (Dover, New York, 1950), pp. 136–139; L. Silberstein,The Theory of Relativity (Macmillan, London, 1924), Chaps. 1–3; R. C. Tolman,Relativity, Thermodynamics, and Cosmology (Oxford University Press, Oxford, 1934; Dover, New York, 1987), pp. 14–15.

    Google Scholar 

  37. O. J. Lodge,Ether and Reality (George H. Doran Co., New York, 1925); O. J. Lodge,Relativity (George H. Doran Co., New York, 1926), pp. 24–33; E. Whittaker,A History of the Theories of Aether and Electricity (American Institute of Physics, New York, 1987; originally published by Nelson, London, 1951), Preface; S. J. Prokhovnik,The Logic of Special Relativity (Cambridge University Press, Cambridge, 1967), Chap. 5; L. Janossy,Theory of Relativity Based on Physical Reality (Akademiai Kiado, Budapest, 1971), Chap. 2; S. Goldberg,Understanding Relativity (Birkhauser, Boston, 1984), Chap. 8; G. Builder,Aust. J. Phys. 11, 279 (1958).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Physics Department, Florida State University, 32306, Tallahassee, Florida

    Edward A. Desloge

Authors
  1. Edward A. Desloge
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Desloge, E.A. A theoretical device for space and time measurements. Found Phys 19, 1191–1213 (1989). https://doi.org/10.1007/BF00731879

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00731879

Keywords

Search

Navigation