Relative-locality distant observers and the phenomenology of momentum-space geometry

We study the translational invariance of the relative-locality framework proposed in arXiv:1101.0931, which had been previously established only for the case of a single interaction. We provide an explicit example of boundary conditions at endpoints of worldlines, which indeed ensures the desired translational invariance for processes involving several interactions, even when some of the interactions are causally connected (particle exchange). We illustrate the properties of the associated relativistic description of distant observers within the example of a $\kappa$-Poincar\'e-inspired momentum-space geometry, with de Sitter metric and parallel transport governed by a non-metric and torsionful connection. We find that in such a theory simultaneously-emitted massless particles do not reach simultaneously a distant detector, as expected in light of the findings of arXiv:1103.5626 on the implications of non-metric connections. We also show that the theory admits a free-particle limit, where the relative-locality results of arXiv:1102.4637 are reproduced. We establish that the torsion of the $\kappa$-Poincar\'e connection introduces a small (but observably-large) dependence of the time of detection, for simultaneously-emitted particles, on some properties of the interactions producing the particles at the source.Comment: 45 pages, 10 figure

Tests of Lorentz invariance: a 2013 update

We present an updated review of Lorentz invariance tests in effective field theories (EFTs) in the matter as well as in the gravity sector. After a general discussion of the role of Lorentz invariance and a derivation of its transformations along the so-called von Ignatovski theorem, we present the dynamical frameworks developed within local EFT and the available constraints on the parameters governing the Lorentz breaking effects. In the end, we discuss two specific examples: the OPERA 'affaire' and the case of Ho\u159ava- Lifshitz gravity. The first case will serve as an example, and a caveat, of the practical application of the general techniques developed for constraining Lorentz invariance violation to a direct observation potentially showing these effects. The second case will show how the application of the same techniques to a specific quantum gravity scenario has far-reaching implications not foreseeable in a purely phenomenological EFT approach