Foundations of Physics Letters

, Volume 19, Issue 4, pp 353–365 | Cite as

Relativity Principles in 1+1 Dimensions and Differential Aging Reversal

  • E. Minguzzi


We study the behavior of clocks in 1+1 spacetime assuming the relativity principle, the principle of constancy of the speed of light, and the clock hypothesis. These requirements are satisfied by a class of Finslerian theories parametrized by a real coefficient β, special relativity being recovered for β = 0. The effect of differential aging is studied for the different value of β. Below the critical values |β| = 1/c the differential aging has the usual direction—after a round trip the accelerated observer returns younger than the twin at rest in the inertial frame - while above the critical value the differential aging changes sign. The non-relativistic case is treated by introducing a formal analogy with thermodynamics.

Key words:

clock problem Finsler spacetimes anisotropic spacetimes 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    1. G. S. Asanov, Finsler Geometry, Relativity and Gauge Theories (Reidel, Dordrecht, 1985).MATHGoogle Scholar
  2. 2.
    2. V. Berzi and V. Gorini, “Reciprocity principle and Lorentz transformations,” J. Math. Phys. 10, 1518–1524, (1969).MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    3. G. Yu. Bogoslovsky. “Lorentz symmetry violation without violation of relativistic symmetry,” Phys. Lett. A 350, 5–10 (2006).CrossRefADSGoogle Scholar
  4. 4.
    4. G. Yu. Bogoslovsky and H. F. Goenner, “On a possibility of phase transitions in the geometric structure of space-time,” Phys. Lett. A 244, 222–228 (1998).CrossRefADSGoogle Scholar
  5. 5.
    5. G. Yu. Bogoslovsky and H. F. Goenner, “Finslerian spaces possessing local relativistic symmetry,” Gen. Relativ. Gravit. 31, 1565–1603 (1999).MATHMathSciNetCrossRefADSGoogle Scholar
  6. 6.
    6. T. Budden, “A star in the Minkowskian sky: Anisotropic special relativity,” Stud. Hist. Phil. Mod. Phys. 28, 325–361 (1997).MathSciNetCrossRefGoogle Scholar
  7. 7.
    7. C. Duval, G. Burdet, H. P. Künzle, and M. Perrin, “Bargmann structures and Newton-Cartan theory,” Phys. Rev. D 31, 1841–1853 (1985).MathSciNetCrossRefADSGoogle Scholar
  8. 8.
    8. C. Duval, G. Gibbons, and P. Horváthy, “Celestial mechanics, conformal structures, and gravitational waves,” Phys. Rev. D 31, 1841–1853 (1985).MathSciNetCrossRefADSGoogle Scholar
  9. 9.
    9. J. H. Field, “A new kinematical derivation of the Lorentz transformation and the particle description of light,” Helv. Phys. Acta 70, 542–564 (1997).MATHMathSciNetGoogle Scholar
  10. 10.
    10. A. R. Lee and T. M. Kalotas, “Lorentz transformations from the first postulate,” Am. J. Phys. 43, 434–437 (1975).CrossRefADSGoogle Scholar
  11. 11.
    11. A. R. Lee and T. M. Kalotas, “Response to ‘Comments on Lorentz transformations from the first postulate’,” Am. J. Phys. 44, 1000–1002 (1976).CrossRefADSGoogle Scholar
  12. 12.
    12. H. Leutwyler and F. Stern, “Relativistic dynamics on a null plane,” Ann. Phys. 112, 94–164 (1978).MathSciNetCrossRefGoogle Scholar
  13. 13.
    13. J. M. Lévy-Leblond, “One more derivation of the Lorentz transformation,” Am. J. Phys. 44, 271–277 (1976).CrossRefADSGoogle Scholar
  14. 14.
    14. A. L. Macdonald, “World's fastest derivation of the Lorentz transformation,” Am. J. Phys. 49, 483–483 (1981).CrossRefGoogle Scholar
  15. 15.
    15. S. Mahajan, “Comments on Lorentz transformation from the first postulate',” Am. J. Phys. 44, 998–999 (1976).CrossRefADSGoogle Scholar
  16. 16.
    16. B. Mashhoon, “The hypothesis of locality in physics,” Phys. Lett. A 145, 147–153 (1990).CrossRefADSGoogle Scholar
  17. 17.
    17. B. Mashhoon, “Limitations of spacetimes measurements,” Phys. Lett. A 143, 176–182 (1990).CrossRefADSGoogle Scholar
  18. 18.
    18. E. Minguzzi, “Differential aging from acceleration: An explicit formula,” Am. J. Phys. 73, 876–880 (2005).MathSciNetCrossRefGoogle Scholar
  19. 19.
    19. W. Rindler, Essential Relativity (Springer, New York, 1977).MATHGoogle Scholar
  20. 20.
    20. H. Round, The Differential Geometry of Finsler Spaces (Springer, Berlin, 1959).Google Scholar
  21. 21.
    21. D. A. Sardelis, “Unified derivation of the Galileo and the Lorentz transformations,” Eur. J. Phys. 3, 96–99 (1982).CrossRefGoogle Scholar
  22. 22.
    22. R. Weinstock, “Derivation of the Lorentz-transformation equations without a linearity assumption,” Am. J. Phys. 32, 260–264 (1964).MATHMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Applied MathematicsFlorence UniversityFlorenceItaly
  2. 2.INFNRomaItaly

Personalised recommendations