Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
2000/12/26 by Giovanni Amelino-Camelia, GIOVANNI AMELINO-CAMELIA · 161 citations
Physics and Astronomy · #Noncommutative and Quantum Gravity Theories #Quantum Electrodynamics and Casimir Effect #Relativity and Gravitational Theory #gr-qc
paper · pdf · doi:10.1142/s0218271802001330
published as Int.J.Mod.Phys. D11 (2002) 35-60 · 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 space-times with an observer-independent Lp, and space-times in which Lp is introduced without modifications of Special Relativity
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 space-times whose short-distance structure is governed by an observer-independent 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 E2- c2 p2- c4 m2 + f(E,p,m;Lp)=0, at least for certain types of f.
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