Skip to main content
Log in

Cite this article

A new description of gravitational motion will be proposed. It is part of the proper time formulation of physics as presented on the IARD 2000 conference. According to this formulation the proper time of an object is taken as its fourth coordinate. As a consequence, one obtains a circular space–time diagram where distances are measured with the Euclidean metric. The relativistic factor turns out to be of simple goniometric origin. It further follows that the Lagrangian for gravitational dynamics does not require an interpretation in terms of curvature of space–time. The flat space model for gravitational dynamics leads to the correct predictions for the bending of light, the perihelion shift of Mercury and gravitational red-shift. The new theory is free of singularities. More important, the new formulation of gravitational dynamics restores the validity of the principle of addition of potentials. One therefore can find solutions for static gravitational configurations for which it is difficult to find the solution of the corresponding Einstein equations. The method will be illustrated by means of the orbital precession for non-spherical stellar mass distributions. In case of the bipole mass distribution the agreement with the predictions of the general theory of relativity is very striking. Nevertheless, the new model is far more simple.

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


  1. J. M. C. Montanus (2001) Found. Phys. 31 1357 Occurrence Handle10.1023/A:1012274211780 Occurrence Handle1866718

    Article  MathSciNet  Google Scholar 

  2. J. M. C. Montanus (1999) Hadronic J. 22 625 Occurrence Handle0992.83004 Occurrence Handle1741514

    MATH  MathSciNet  Google Scholar 

  3. J. M. C. Montanus (1993) Phys. Essays. 6 540

    Google Scholar 

  4. J. M. C. Montanus (1991) Phys. Essays. 4 350 Occurrence Handle1273097

    MathSciNet  Google Scholar 

  5. P. A. M. Dirac, General Theory of Relativity. Princeton University Press, 1996).

  6. S. Weinberg, Gravitation and Cosmology (Wiley, 1972).

  7. R. D’Inferno, Introducing Einstein’s Relativity (Clarendon Press, 1992), p. 190.

  8. J. M. C. Montanus (1997) Phys. Essays. 10 666 Occurrence Handle1604226

    MathSciNet  Google Scholar 

  9. J. B. Almeida, “4-Dimensional optics, an alternative to relativity”, abs/gr-qc/0107083, (2001).

  10. J. B. Almeida, “Euclidean formulation of general relativity”, 0406026, (2004).

  11. J. B. Almeida, “Maxwell’s equations in 4-dimensional Euclidean space”,, (2004).

  12. J. B. Almeida, “K-calculus in 4-dimensional optics”, 0201002, (2002).

  13. A. Gersten (2003) Found. Phys. 33 1237 Occurrence Handle10.1023/A:1025631125442 Occurrence Handle2021844

    Article  MathSciNet  Google Scholar 

  14. R. F. J. van Linden, “Dimensions in special relativity”, http://www.rfjvanlinden171., (2004).

  15. J. M. C. Montanus (1997) Phys. Essays. 10 116 Occurrence Handle1604226

    MathSciNet  Google Scholar 

  16. L. P. Horwitz C. Piron (1973) Helv. Phys. Acta. 46 316

    Google Scholar 

  17. T.L. Gill J. Lindesay (1993) Int. J. Theor. Phys. 32 2087 Occurrence Handle10.1007/BF00675022 Occurrence Handle1254330

    Article  MathSciNet  Google Scholar 

  18. T. L. Gill W. W. Zachary J. Lindesay (1997) Found. Phys. Lett. 10 547 Occurrence Handle10.1023/A:1022445218792 Occurrence Handle1603646

    Article  MathSciNet  Google Scholar 

  19. J. L. Synge, Relativity: The General Theory (North-Holland, 1971), p. 309.

  20. W. M. Baker B. Rogers (1999) Class .Quantum Grav 16 1273 Occurrence Handle10.1088/0264-9381/16/4/017 Occurrence Handle1999CQGra..16.1273B Occurrence Handle0934.83006

    Article  ADS  MATH  Google Scholar 

  21. J. M. C. Montanus S. L. Kalla (2004) Math. Comput. Model. 40 611 Occurrence Handle10.1016/j.mcm.2003.07.015 Occurrence Handle2102213 Occurrence Handle1098.85001

    Article  MathSciNet  MATH  Google Scholar 

  22. J. M. C. Montanus (1999) Phys Essays. 12 259 Occurrence Handle10.4006/1.3025382 Occurrence Handle1999PhyEs..12..259M

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to J. M. C. Montanus.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Montanus, J.M.C. Flat Space Gravitation. Found Phys 35, 1543–1562 (2005).

Download citation

  • Received:

  • Issue Date:

  • DOI: