Foundations of Physics Letters

, Volume 13, Issue 5, pp 401–425

MÄRZKE-WHEELER COORDINATES FOR ACCELERATED OBSERVERS IN SPECIAL RELATIVITY

  • M. Pauri
  • M. Vallisneri
Article

DOI: 10.1023/A:1007861914639

Cite this article as:
Pauri, M. & Vallisneri, M. Found Phys Lett (2000) 13: 401. doi:10.1023/A:1007861914639

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 

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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