Skip to main content
Log in

Abstract

Empirical and theoretical evidence show that the astrophysical problem of dark matter might be solved by a theory of Einstein-Mayer type. In this theory, up to global Lorentz rotations, the reference system is determined by the motion of cosmic matter. Thus, one is led to a “Riemannian space with teleparallelism” realizing a geometric version of the Mach-Einstein doctrine. The field equations of this gravitational theory contain hidden matter terms, where the existence of hidden matter is inferred solely from its gravitational effects. It is argued that, in the nonrelativistic mechanical approximation, they provide an inertia-free mechanics, where the inertial mass of a body is induced by the gravitational action of the comic masses. Interpreted from the Newtonian point of view, this mechanics shows that the effective gravitational mass of astrophysical objects depends on r such that one expects the existence of dark matter.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  1. J. Binney and S. Tremaine, Galactic Dynamics (Princeton University Press, Princeton, 1987).

    Google Scholar 

  2. R. Berna⇋ei, L. Catena, and A. Incichitti (eds.), The Dark Side of the Universe. Experimental Efforts and Theoretical Framework (World Scientific, Singapore, 1996).

    Google Scholar 

  3. F. Zwicky, Morphological Astronomy (Springer, Berlin, 1957).

    Google Scholar 

  4. H. Hertz, Die Prinzipien der Mechanik (Barth, Leipzig, 1894). The English edition was pu⇋lished ⇋y Macmillan in 1900.

    Google Scholar 

  5. E. Mach, Die Mechanik in ihrer Entwicklung Historisch–krizisch dargestellt, 6th edn. (Brockhaus, Leipzig, 1908).

    Google Scholar 

  6. H.–H. v. Borzeszkowski, H.–J. Treder, and W. Yourgrau, Ann. Phys. ( Leipzig ) 35, 471 (1978).

    Google Scholar 

  7. R. H. Sanders, Astron. Astrophys. 136, L21, (1984).

    Google Scholar 

  8. M. Milgrom, Astrophys. J. 270, 365 (1983); Astrophys. J. 478, 7 (1997).

    Google Scholar 

  9. J. Bekenstein and M. Milgrom, Astrophys. J. 286, 7 (1984).

    Google Scholar 

  10. R. Reissner, Phys. Z. 15, 371 (1914); 16, 179 (1915).

    Google Scholar 

  11. E. Schrödinger, Ann. Phys. (Leipzig ) 77, 181 (1925).

    Google Scholar 

  12. H.–J. Treder, Die Relativität der Trägheit (Akademie, Berlin, 1972).

    Google Scholar 

  13. H.–J. Treder, Ü⇋er Prinzipien der Dynamik ⇋ei Einstein, Hertz, Mach und Poincaré (Akademie, Berlin, 1974).

    Google Scholar 

  14. H.–J. Treder, H.–H. von Borzeszkowski, A. van der Merwe, and W. Yourgrau, Fundamental Principles of General Relativity Theories ( Plenum, New York, 1980).

    Google Scholar 

  15. A. Einstein, Vierteljahresschrift für gerichtliche Medizin und öffentliches Sanitätswesen 44, 37 (1912); cf. also the reprint in The Collected Papers of Al⇋ert Einstein, Vol. 4, The Swiss Years: Writings 19121914, M. J. Klein, A. J. Kox, J. Renn, and R. Schulmann, eds. (Princeton University Press, Princeton, 1995), Doc. 7.

    Google Scholar 

  16. H.–J. Treder, Astron. Nachr. 298, 237 (1977).

    Google Scholar 

  17. B. and J. Friedländer, A⇋solute oder relative Bewegung? (Leonhard Simon, Berlin, 1896).

    Google Scholar 

  18. A. Föppl, “Ü⇋er a⇋solute und relative Bewegung,” Sitzungs⇋er. Bayer. Akad. Wiss. 383 (1904).

  19. H. Thirring, Phys. Z. 19, 33 (1918); errata in Phys. Z. 22, 29 (1921).

    Google Scholar 

  20. A. Einstein, The Meaning of Relativity (Princeton University Press, 1922).

  21. H.–J. Treder, Astron. Nachr. 296, 9 (1975).

    Google Scholar 

  22. H.–H. v. Borzeszkowski and H.–J. Treder, Found. Phys. 27, 661 (1997).

    Google Scholar 

  23. R. Weitzen⇋oeck, “Differentialinvarianten in der Einsteinschen Theorie des Fernparallelismus,” Berliner Ber. 1928, p. 466.

  24. A. Einstein, “Riemann–Geometrie und Aufrechterhaltung des Begriffs des Fernparallelismus,” Berliner Ber. 1928, p. 219.

  25. A. Einstein, “Einheitliche Feldtheorie und Hamiltonsches Prinzip,” Berliner Ber. 1929, p. 124.

  26. A. Einstein and W. Mayer, “Systematische Untersuchung ü ⇋er kompati⇋le Feldgleichungen, welche von einem Riemannschen Raum mit Fernparallelismus gesetzt werden können,” Berliner Ber. 1931, p. 3.

  27. C. H. Brans, Phys. Rev. 125, 388 (1962).

    Google Scholar 

  28. E. H. Milne and W. H. McCrea, Quart. J. Math. (Oxford ) 5, 73 (1934).

    Google Scholar 

  29. E. H. Milne, Relativity, Gravitation, and World Structure (University Press, Oxford, 1935).

    Google Scholar 

  30. H. Weyl, “Masse, Trägheit und Kosmos—ein Dialog,” Naturwissenschaften 12, 197 (1924); cf. also Hermann Weyl, Gesammelte A⇋handlungen (Springer, Berlin, 1968), Vol. II, No. 65.

    Google Scholar 

  31. A. Einstein, “Bemerkungen” zu: A. Einstein and M. Grossmann, “Entwurf einer verall-gemeinertenRelativita Étstheorie und einer Theorie der Gravitation,” Z. Math. Phys. 62,260 ( 1914); cf. also the reprint in The Collected Papers of Albert Einstein, Vol. 4, op. cit.Doc. 26.

  32. A. Einstein, “ Die formale Grundlage der allgemeinen Relativitätstheorie, ” Berliner Ber. 1914, p. 1030; cf. also the reprint in The Collected Papers of Al⇋ert Einstein, Vol. 6, The Berlin Years: Writings1914–1917, A. J. Kox, M. J. Klein, and R. Schullmann, eds. (Princeton University Press, Princeton, 1996), Doc. 9.

  33. H. Weyl, Z. Phys. 56, 330 (1929); cf. also Hermann Weyl, Gesammelte A⇋handlungen (Springer, Berlin, 1968), Vol. III, No. 85.

    Google Scholar 

  34. H. Weyl, Naturwissenschaften 19, 4 (1931); cf. also Hermann Weyl, Gesammelte A⇋handlungen (Springer, Berlin, 1968), Vol. III, No. 93.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Borzeszkowski, HH.v., Treder, HJ. Dark Matter versus Mach's Principle. Foundations of Physics 28, 273–290 (1998). https://doi.org/10.1023/A:1018756904277

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018756904277

Keywords

Navigation