Skip to main content
SpringerLink
Log in

The New Mechanics of Myron Mathisson and Its Subsequent Development

  • Chapter
  • First Online:
Equations of Motion in Relativistic Gravity

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 179))

Abstract

In 1937, Myron Mathisson published a paper which initiated a program of work in general relativity that continues to the present day. The aim of this program was to obtain equations that determine the trajectory of an extended body in an external gravitational field. In Newtonian mechanics this is a straightforward task, but in general relativity even giving a precise meaning to the problem is fraught with difficulties. These difficulties are analysed, Mathisson’s approach is described and it is shown how his approach has been carried to fulfillment by subsequent authors in the years since Mathisson’s untimely death in 1940. This work, however, completes only a part of the overall program. The work is placed in context in this overall program and the issues remaining for that program are identified.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
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

References

  1. M. Mathisson, Neue Mechanik materieller Systeme. Acta Phys. Pol. 6, 163–200 (1937)

    MATH  Google Scholar 

  2. M. Mathisson, Republication of: new mechanics of material systems. Gen. Relativ. Gravit. 42, 1011–1048 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  3. A. Einstein, J. Grommer, Allgemeine Relativitätstheorie und Bewegungsgesetz. Sitzungsber Preuss. Akad. Wiss., Phys.-Math. Kl. 2–13 (1927)

    Google Scholar 

  4. A. Einstein, Allgemeine Relativitätstheorie und Bewegungsgesetz. Sitzungsber. Preuss. Akad. Wiss., Phys.-Math. Kl. 235–245 (1927)

    Google Scholar 

  5. H.P. Robertson, Test corpuscles in general relativity. Proc. Edinb. Math. Soc. 5(2), 63–81 (1937)

    Article  Google Scholar 

  6. T. Sauer, A. Trautman, Myron Mathisson: what little we know of his life. Acta Phys. Pol. B Suppl. 1, 7–26 (2008)

    Google Scholar 

  7. A. Einstein, L. Infeld, B. Hoffman, The gravitational equations and the problem of motion. Ann. Math. 39, 65–100 (1938)

    Article  ADS  MathSciNet  Google Scholar 

  8. A. Bielecki, M. Mathisson, J.W. Weyssenhoff, Sur un théorème concernant une transformation d’intégrales quadruples en intégrales curvilignes dans l’espace de Riemann. Bull. Int. Acad. Polonaise Sci. Lett., Cracovie Cl. Sci. Math. Natur., Sér. A 22–28 (1939)

    Google Scholar 

  9. M. Mathisson, The variational equation of relativistic dynamics. Proc. Camb. Philos. Soc. 36, 331–350 (1940)

    Article  ADS  MathSciNet  Google Scholar 

  10. M. Mathisson, Relativistic dynamics of a spinning magnetic particle. Proc. Camb. Philos. Soc. 38, 40–60 (1942)

    Article  ADS  MathSciNet  Google Scholar 

  11. P. Havas, The early history of the “problem of motion” in general relativity, in Proceedings of the 1986 Osgood Hill Conference, ed. by D. Howard, J. Stachel (Birkhäuser, Boston, 1989), pp. 234–276

    Google Scholar 

  12. M. Mathisson, Das zitternde Elektron und seine Dynamik. Acta Phys. Pol. 6, 218–227 (1937)

    MATH  Google Scholar 

  13. M.H.L. Pryce, The mass-centre in the restricted theory of relativity and its connection with the quantum theory of elementary particles. Proc. R. Soc. (London) A195, 62–81 (1948)

    ADS  MATH  Google Scholar 

  14. C. Møller, On the definition of the centre of gravity of an arbitrary closed system in the theory of relativity. Comm. Dublin Inst. Adv. Studies A5, 1 (1949)

    MATH  Google Scholar 

  15. J. Weyssenhoff, A. Raabe, Relativistic dynamics of spin-fluids and spin-particles. Acta Phys. Pol. 9, 7–18 (1947)

    MathSciNet  Google Scholar 

  16. S. Shanmugadhasan, On Mathisson’s variational equation of relativistic dynamics. Proc. Camb. Philos. Soc. 42, 54–61 (1946)

    Article  ADS  MathSciNet  Google Scholar 

  17. A. Papapetrou, Spinning test-particles in general relativity. I. Proc. R. Soc. (London) A209, 248–258 (1951)

    ADS  MathSciNet  MATH  Google Scholar 

  18. H. Hönl, A. Papapetrou, Über die innere Bewegung des Elektrons III. Z. Phys. 116, 153–183 (1940)

    Article  ADS  Google Scholar 

  19. E. Corinaldesi, A. Papapetrou, Spinning test-particles in general relativity. II. Proc. R. Soc. (London) A209, 259–268 (1951)

    ADS  MathSciNet  MATH  Google Scholar 

  20. W. Tulczyjew, Motion of multipole particles in general relativity theory. Acta Phys. Pol. 18, 393–409 (1959)

    MathSciNet  MATH  Google Scholar 

  21. B. Tulczyjew, W. Tulczyjew, On multipole formalism in general relativity, Recent Developments in General Relativity (Pergamon Press, London, 1962), pp. 465–472

    Google Scholar 

  22. W.G. Dixon, A covariant multipole formalism for extended test bodies in general relativity. Nuovo Cimento 34, 317–339 (1964)

    Article  MathSciNet  Google Scholar 

  23. A.H. Taub, The motion of multipoles in general relativity, in Proceedings Galileo IV Centenary Conference, (Florence, 1965), pp. 77–89

    Google Scholar 

  24. J. Madore, The equations of motion of an extended body in general relativity. Ann. Inst. Henri Poincaré 11, 221–237 (1969)

    MathSciNet  Google Scholar 

  25. W.G. Dixon, Dynamics of extended bodies in general relativity III. Equations of motion. Philos. Trans. R. Soc. (London) A277, 59–119 (1974)

    ADS  MathSciNet  Google Scholar 

  26. W.G. Dixon, Description of extended bodies by multipole moments in special relativity. J. Math. Phys. 8, 1591–1605 (1967)

    Article  ADS  Google Scholar 

  27. W.G. Dixon, Dynamics of extended bodies in general relativity I. Momentum and angular momentum. Proc. R. Soc. (London) A.314, 499–527 (1970)

    ADS  MathSciNet  Google Scholar 

  28. W.G. Dixon, Dynamics of extended bodies in general relativity II. Moments of the charge-current vector. Proc. R. Soc. (London) A.319, 509–547 (1970)

    ADS  MathSciNet  Google Scholar 

  29. R.L. Bishop, R.J. Crittenden, Geometry of Manifolds (Academic Press, New York, 1964)

    MATH  Google Scholar 

  30. I.M. Gel’fand, G.E. Shilov, Generalized Functions Volume 1: Properties and Operations (Academic Press, New York, 1964)

    MATH  Google Scholar 

  31. J.L. Synge, Relativity: The General Theory (North-Holland Publ. Co., Amsterdam, 1960)

    MATH  Google Scholar 

  32. B.S. DeWitt, R.W. Brehme, Radiation damping in a gravitational field. Ann. Phys. (N. Y.) 9, 220–259 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  33. O. Veblen, T.Y. Thomas, The geometry of paths. Trans. Am. Math. Soc. 25, 551–608 (1923)

    Article  MathSciNet  Google Scholar 

  34. T.Y. Thomas, The Differential Invariants of Generalized Spaces (Cambridge University Press, Cambridge, 1934)

    MATH  Google Scholar 

  35. J.A. Schouten, Ricci-Calculus, chapter III, section 7, 2nd edn. (Springer, Berlin, 1954)

    Google Scholar 

  36. R. Schattner, The center of mass in general relativity. Gen. Relativ. Gravit. 10, 377–393 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  37. R. Schattner, The uniqueness of the center of mass in general relativity. Gen. Relativ. Gravit. 10, 395–399 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  38. J. Ehlers, E. Rudolph, Dynamics of extended bodies in general relativity: centre-of-mass description and quasirigidity. Gen. Relativ. Gravit. 8, 197–217 (1977)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

The author would like to thank the organisers of the 524th WE-Heraeus-Seminar “Equations of Motion in Relativistic Gravity”, and Dirk Puetzfeld in particular, for inviting him to attend and speak at this seminar and the management of the Physikzentrum, Bad Honnef, for its hospitality.

Author information

Authors and Affiliations

  1. Churchill College, University of Cambridge, Cambridge, CB3 0DS, England

    W. G. Dixon

Authors
  1. W. G. Dixon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to W. G. Dixon .

Editor information

Editors and Affiliations

  1. ZARM University of Bremen, Bremen, Germany

    Dirk Puetzfeld

  2. ZARM University of Bremen, Bremen, Germany

    Claus Lämmerzahl

  3. Max-Planck-Institut fĂĽr Gravitationsphysik, Golm, Brandenburg, Germany

    Bernard Schutz

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Dixon, W.G. (2015). The New Mechanics of Myron Mathisson and Its Subsequent Development. In: Puetzfeld, D., Lämmerzahl, C., Schutz, B. (eds) Equations of Motion in Relativistic Gravity. Fundamental Theories of Physics, vol 179. Springer, Cham. https://doi.org/10.1007/978-3-319-18335-0_1

Download citation

Publish with us

Policies and ethics

Search

Navigation