Nonstandard LorentzEinstein transformations
Abstract
The standard Lorentz transformations establish a relationship between the spacetime coordinates of the same event when detected from two inertial reference frames I and I' in the standard arrangement. This event is characterized by the spacetime coordinates E(x,tE) and E'(x',t'E), tE and t'E representing the readings of the standard synchronized clocks C(x) and C'(x') located in the two frames where the event takes place. We obtain the nonstandard Lorentz transformations establishing a "physically" correct relationship between the readings of the standard synchronized clocks and the readings of other clocks (ta,t'a) of the same inertial reference frames. This relationship of the type tE=f(x,ta), expresses the standard Lorentz transformations as a function of ta and t'a respectively. We present several cases of nonstandard Lorentz transformation (the case of radar detection, the case when one reference frame is filled with an ideal transparent dielectric and the case of relativity of the apparent, actual and synchronized positions of the same moving particle).
 Publication:

arXiv eprints
 Pub Date:
 August 2008
 DOI:
 10.48550/arXiv.0808.0098
 arXiv:
 arXiv:0808.0098
 Bibcode:
 2008arXiv0808.0098R
 Keywords:

 Physics  General Physics