Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale

Giovanni Amelino-Camelia

doi:10.1142/S0218271802001330

paper

Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale

arXiv:gr-qc/0012051 · doi:10.1142/S0218271802001330

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 $E^{2} - c^{2} p^{2} - c^{4} m^{2} + f (E, p, m; L_{p}) = 0$ , at least for certain types of $f$ .

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

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Quantum theory's last challenge

Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale

Abstract

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