Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2007-07-02
Foundations of Physics 39, 1280-1295 (2009); Physical Review D 80, 064038 (2009)
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
26 pages, 4 figures
Scientific paper
In Newtonian space-time there exist four, and only four, causal classes of frames. Natural frames allow to extend this result to coordinate systems, so that coordinate systems may be also locally classified in four causal classes. These causal classes admit simple geometric descriptions and physical interpretations. For example, one can generate representatives of the four causal classes by means of the {\em linear synchronization group}. Of particular interest is the {\em local Solar time synchronization}, which reveals the limits of the frequent use of the concept of `causally oriented oordinate', such as that of `time-like coordinate'. Classical {\em positioning systems}, based in sound or light signals, are, by themselves, interesting examples of location systems, i.e. of physically constructible coordinate systems. They show that one can locate events in Newtonian space-time {\em without} any use of the concept of synchronization. In fact, the coordinate systems associated to positioning systems, belong to all the classes but the standard one, i.e. the one based in the simultaneity synchronization. The relativistic analogs of these examples, emphasize the contrast between the four Newtonian and the one hundred and ninety nine Lorentzian causal classes of frames of classical and relativistic space-times, respectively.
Coll Bartolomé
Ferrando Joan Josep
Morales Juan Antonio
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