Relativity in Spacetimes with ShortDistance Structure Governed by an ObserverIndependent (Planckian) Length Scale
Abstract
I show that it is possible to formulate the Relativity postulates in a way that does not lead to inconsistencies in the case of spacetimes whose shortdistance structure is governed by an observerindependent length scale. The consistency of these postulates proves incorrect the expectation that modifications of the rules of kinematics involving the Planck length would necessarily require the introduction of a preferred class of inertial observers. In particular, it is possible for every inertial observer to agree on physical laws supporting deformed dispersion relations of the type E^{2}c^{2} p^{2}c^{4}m^{2} + f(E, p, m; L_{p}) =0, at least for certain types of f.
 Publication:

International Journal of Modern Physics D
 Pub Date:
 2002
 DOI:
 10.1142/S0218271802001330
 arXiv:
 arXiv:grqc/0012051
 Bibcode:
 2002IJMPD..11...35A
 Keywords:

 General Relativity and Quantum Cosmology
 EPrint:
 Same formulas and results as in 1st version, but a change of notation is introduced in order to clarify that the studied illustrative example is consistent with the R.P. for both choices of the overall sign. 1 ref added and 2 refs upgraded. Some rewording of the text in Sec5, and addition of an analogy with background fields in ordinary electromagnetism which I use to illustrate difference between spacetimes with an observerindependent Lp, and spacetimes in which Lp is introduced without modifications of Special Relativity