G. Amelino-Camelia, M. Arzano, J. Kowalski-Glikman, G. Rosati, G. Trevisan, G. Amelino-Camelia, A. Marcianó, M.Matassa and G. Rosati, G. Amelino-Camelia, N. Loret and G. Rosati, G. Amelino-Camelia, M. Matassa, F. Mercati, G. Rosati, V. G. Kadyshevsky, M. D. Mateev, R. M. Mir-Kasimov and I. P. Volobuev, G. Amelino-Camelia, L. Freidel, J. Kowalski-Glikman and L. Smolin, National Science Center under the agreement DEC. M a t o m / κ a t o m, which, in the best case κ a t o m ∼ M P l is of order of 10 − 19, but might be few orders ofįor JKG this work was supported in parts by the grantĢ011/01/B/ST2/03354 and for JKG and GR by funds provided by the Non-relativistic E ∼ N a t o m s m a t o m. Then, since weĬan safely assume in the present context that the moving body is Therefore κ in ( 20) is theĮffective value of the deformation parameter, which equals, forĮxample κ = N a t o m s κ a t o m, with κ a t o mīeing the deformation parameter at the atomic scale. Which is N times bigger than the deformation scale for theĬonstituents κ c o n s t, with N being the number ofĬonstituents. The star is) are governed by the deformation scale κ e f f Interactions of a composite body (which, no doubts, the planet or Right size of the correction term we must invoke the way thisĪpparent paradox is solved. This is nothing but the ‘soccer ball problem’ (seeĪmelinoCamelia:2011uk and references therein), and to get the ![]() If we take κ ∼ M P l the correction E / κ will beĮnormously large. The planetary system or a star in the binary system or the galaxy, Clearly, if the body in question is a planet in Let us estimate the magnitude of the κ correction term in This amounts to look for spacetime coordinates which have canonical Poisson brackets with momenta. bob that, if one considers the whole set of relativistic transformations (so to include also boosted observers), one cannot remove the effects of relative locality by a coordinate transformation (relative locality is not a coordinate artifact), it is still interesting to ask ourselves if it is possible to choose spacetime coordinates such that purely translated observers agree on the locality of distant events. Įven though it has been shown in previous studies such as Ref. ![]() Then the equations of motion are not sufficient for establishing the physical motion of particles, but one has to consider also the non trivial properties of translations k-bob DSR-DeSitter. If one restricts to purely translated observers, one can ascribe the presence of these misleading inferences to the fact that the Poisson brackets between spacetime coordinates and momenta depend on momenta. The relative locality perspective is then that the physical observations corresponds to the ones made by observers local to the event of measurement bob. See Kowalski-Glikman:2013rxa for the up to date review.Īs it is well known from previous studies on relative locality bob k-bob DSR-DeSitter, the nontriviality (momentum dependence) in the (deformed-)relativistic transformations of spacetime coordinates imply that events distant from the origin of a given observer’s frame are characterized by “misleading inferences” regarding their position in spacetime. ![]() Kadyshevsky:1977mu and references therein)., i.e., starts having a non-trivial geometry, with the characteristic scale κ Majid:1999tc Magueijo:2001cr KowalskiGlikman:2002ft KowalskiGlikman:2003we Oriti:2009wn Arzano:2010jw Chang:2010ir AmelinoCamelia:2011bm. born and Snyder:1946qz, and was later developed by the Russian group (see Ref. Particles and fields depends on a mass scale κ, which in theĬase of elementary systems could be identified with the Planck mass.įurther it is argued that the presence of the mass scale has anĮffect similar to the one well known in 2+1 gravity deSousaGerbert:1990yp Matschull:1997du Meusburger:2005mg Schroers:2007ey, namely that the momentum space becomes ‘curved’ 1 1 1The idea of a curved momentum space appeared already in Refs. ![]() Quantum gravity, in which both G and ℏ are very small, while Might be offered by a possible semiclassical, weak gravity regime of As advocated in AmelinoCamelia:2011bm such an opportunity
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