POS  Vol.4 No.1 , February 2013
Relativistic versus Newtonian Frames
ABSTRACT

Only a causal class among the 199 Lorentzian ones, which do not exists in the Newtonian space-time, is privileged to construct a generic, gravity free and immediate (non retarded) relativistic positioning system. This is the causal class of the null emission coordinates. Emission coordinates are defined and generated by four emitters broadcasting their proper times. The emission coordinates are covariant (frame independent) and hence valid for any user. Any observer can obtain the values of his (her) null emission coordinates from the emitters which provide him his (her) position and trajectory.


Cite this paper
Pascual-Sánchez, J. , Miguel, A. and Vicente, F. (2013) Relativistic versus Newtonian Frames. Positioning, 4, 109-114. doi: 10.4236/pos.2013.41011.
References
[1]   N. Ashby, “Relativity in the Global Positioning System,” Living Reviews in Relativity, Vol. 6, 2003, p. 1.

[2]   J.-F. Pascual-Sánchez, “Introducing Relativity in Global Navigation Satellite Systems,” Annalen der Physik, Vol. 16, No. 4, 2007, pp. 258-273. doi:10.1002/andp.200610229

[3]   J.-F. Pascual-Sánchez, “The Relativistic Framework of Positioning Systems,” First Colloquium on Scientific and Fundamental Aspects of the Galileo Program, 2007, arXiv:0710.1282.

[4]   B. Coll, “Reference Frames and Gravitomagnetism,” World Scientific, Singapore, 2001, p. 53.

[5]   B. Coll and J. A. Morales, “199 Causal Classes of Space-Time Frames,” International Journal of Theoretical Physics, Vol. 31, 1992, p. 1045.

[6]   B. Coll, “Physical Relativistic Frames,” Proc. Jour. Sys. Ref. Spat. Temp., Brussels, ed N. Capitaine, Observatoire de Paris, 2001, p. 169.

[7]   B. Coll, J. J. Ferrando and J. A. Morales, “Four Causal Classes of Newtonian Frames,” Foundations of Physics, Vol. 39, 2009, p. 1280.

[8]   A. Trautman, “Sur la Théorie Newtonienne de la Gravitation,”Comptes Rendus de l'Académie des Sciences, Vol. 257, 1963, p. 617.

[9]   C. Rovelli, “GPS Observables in General Relativity,” Physical Review D, Vol. 65, No. 4, 2002, Article ID: 044 017. doi:10.1103/PhysRevD.65.044017

[10]   M. Blagojevic, J. Garecki, F. W. Hehl and Yu. N. Obukhov, “Real Null Coframes in General Relativity and GPS Type Coordinates,” Physical Review D, Vol. 65, No. 4, 2002, Article ID: 044018. doi:10.1103/PhysRevD.65.044018

[11]   B. Coll, J. J. Ferrando and J. A. Morales, “Two-Dimensional Approach to Relativistic Positioning Systems,” Physical Review D, Vol. 73, No. 8, 2006, Article ID: 084 017. doi:10.1103/PhysRevD.73.084017

[12]   A. Tarantola and B. Coll, “Using Pulsars to Define Space-Time Coordinates,” 2009, arXiv:0905.4121.

[13]   M. L. Ruggiero, E. Capolongo and A. Tartaglia, “Pulsars as Celestial Beacons to Detect the Motion of the Earth,” International Journal of Modern Physics, Vol. 20, No. 6, 2011, pp. 1025-1038.

[14]   P. Graven, et al., “XNAV for Deep Space Navigation,” Proceedings of 31st Annual AAS Guidance and Control Conference, AAS 08-054, 2008.

[15]   B. Coll, J. M. Pozo, “Relativistic Positioning Systems: The Emission Coordinates,” Classical and Quantum Gravity, Vol. 23, No. 24, 2006, p. 7395. doi:10.1088/0264-9381/23/24/012

[16]   A. Tarantola, L. Klimes, J. M. Pozo and B. Coll, “Gravimetry, Relativity, and the Global Navigation Satellite Systems,” 2009, arXiv:0905.3798.

[17]   B. Coll, J. J. Ferrando and J. A. Morales, “Positioning with Stationary Emitters in a Two-Dimensional Space-Time,” Physical Review D, Vol. 74, No. 10, 2006, Article ID: 104003. doi:10.1103/PhysRevD.74.104003

[18]   M. Lachièze-Rey, “The Covariance of GPS Coordinates and Frames,” Classical and Quantum Gravity, Vol. 23, No. 10, 2006, p. 3531. doi:10.1088/0264-9381/23/10/019

[19]   B. Coll, J. J. Ferrando and J. A. Morales-Lladosa, “Positioning Systems in Minkowski Spacetime: From Emission to Inertial Coordinates,” Classical and Quantum Gravity, Vol. 27, No. 6, 2010, Article ID: 065013. doi:10.1088/0264-9381/27/6/065013

[20]   D. Bini, A. Geralico, M. L. Ruggiero and A. Tartaglia, “Emission versus Fermi Coordinates: Applications to Relativistic Positioning Systems,” Classical and Quantum Gravity, Vol. 25, No. 20, 2008, Article ID: 205011. doi:10.1088/0264-9381/25/20/205011

 
 
Top