Foundations of Physics Letters

, Volume 13, Issue 5, pp 401–425 | Cite as

MÄRZKE-WHEELER COORDINATES FOR ACCELERATED OBSERVERS IN SPECIAL RELATIVITY

  • M. Pauri
  • M. Vallisneri
Article

Abstract

In special relativity, the definition of coordinate systems adapted to generic accelerated observers is a long-standing problem, which has found unequivocal solutions only for the simplest motions. We show that the Märzke-Wheeler construction, an extension of the Einstein synchronization convention, produces accelerated systems of coordinates with desirable properties: (a) they reduce to Lorentz coordinates in a neighborhood of the observers' world-lines; (b) they index continuously and completely the causal envelope of the world-line (that is, the intersection of its causal past and its causal future: for well-behaved world-lines, the entire space-time). In particular, Märzke-Wheeler coordinates provide a smooth and consistent foliation of the causal envelope of any accelerated observer into space-like surfaces.

We compare the Märzke-Wheeler procedure with other definitions of accelerated coordinates; we examine it in the special case of stationary motions, and we provide explicit coordinate transformations for uniformly accelerated and uniformly rotating observers. Finally, we employ the notion of Märzke-Wheeler simultaneity to clarify the relativistic paradox of the twins, by pinpointing the local origin of differential aging.

special relativity coordinate systems accelerated observers simultaneity synchronization of clocks twin paradox 

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Copyright information

© Plenum Publishing Corporation 2000

Authors and Affiliations

  • M. Pauri
    • 1
    • 2
  • M. Vallisneri
    • 3
    • 1
    • 4
  1. 1.Dipartimento di FisicaUniversità di ParmaParmaItaly
  2. 2.INFN, Sezione di Milano, Gruppo Collegato di ParmaItaly
  3. 3.Theoretical Astrophysics 130-33Caltech PasadenaUSA
  4. 4.INFN, Sezione di Milano, Gruppo Collegato di ParmaItaly

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