Giacomo Rosati

OPERA-reassessing data on the energy dependence of the speed of neutrinos

We offer a preliminary exploration of the two sides of the challenge provided by the recent OPERA data on superluminal neutrinos. On one side we stress that some aspects of this result are puzzling even from the perspective of the wild quantum-gravity literature, where arguments in favor of the possibility of superluminal propagation have been presented, but not considering the possibility of such a sizeable effect for neutrinos of such low energies. We feel this must encourage particularly severe scrutiny of the OPERA result. On the other side, we notice that the OPERA result is reasonably consistent with μ-neutrino-speed data previously obtained at FERMILAB, reported in papers of 2007 and 1979. And it is intriguing that these FERMILAB79 and FERMILAB07 results, when combined with the new OPERA result, in principle provide a window on μ-neutrino speeds at different energies broad enough to compare alternative phenomenological models. We test the discriminating power of such an approach by using as illustrative examples the case of special-relativistic tachyons, the case of momentum-independent violations of the special-relativistic speed law, and the cases of linear and quadratic energy dependence of the speed of ultrarelativistic muon neutrinos. Even just using μ-neutrino data in the range from ~3 GeVs to ~200 GeVs the special-relativistic tachyon and the quadratic-dependence case are clearly disfavoured. The linear-dependence case gives a marginally consistent picture and the momentum-independent scenario fits robustly the data. We also comment on Supernova 1987a and its relevance for consideration of other neutrino species, also in relation with some scenarios that appeared in the large-extra-dimension literature.

Taming nonlocality in theories with Planck-scale deformed Lorentz symmetry.

We report a general analysis of worldlines for theories with deformed relativistic symmetries and momentum dependence of the speed of photons. Our formalization is faithful to Einsteins program, with spacetime points viewed as an abstraction of physical events. The emerging picture imposes the renunciation of the idealization of absolutely coincident events, but is free from some pathologies which had been previously conjectured.

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

We study the translational invariance of the relative-locality framework proposed in Amelino-Camelia et al (2011 Phys. Rev. D 84 084010), 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 ?-Poincar?-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 Freidel and Smolin (2011 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 Amelino-Camelia et al (2011 Phys. Lett. B 700 150) are reproduced. We establish that the torsion of the ?-Poincar? 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.

Speed of particles and a relativity of locality in κ-Minkowski quantum spacetime

The last decade of research on κ-Minkowski noncommutative spacetime has been strongly characterized by a controversy concerning the speed of propagation of massless particles. Most arguments suggested that this speed should depend on the momentum of the particle strongly enough to be of interest for some ongoing experimental studies. But the only explicit derivations of worldlines in κ-Minkowski predicted no momentum dependence for the speed of massless particles. We return to this controversy equipped with the recent understanding that in some quantum spacetimes coincidences of events assessed by an observer who is distant from the events can be artifactual. We therefore set up our investigation in such a way that we never rely on the assessment of coincidences of events by distant observers. This allows us to verify explicitly that in κ-Minkowski simultaneously-emitted massless particles of different momentum are detected at different times, and establish a linear dependence of the detection times on momentum.

Relative locality in a quantum spacetime and the pregeometry of κ-Minkowski

We develop a description of the much-studied κ-Minkowski noncommutative spacetime, centered on representing on a single Hilbert space not only the κ-Minkowski coordinates, but also the κ-Poincaré symmetry generators and some suitable relativistic-transformation parameters. In this representation the relevant operators act on the kinematical Hilbert space of the covariant formulation of quantum mechanics, which we argue is the natural framework for studying the implications of the step from commuting spacetime coordinates to the κ-Minkowski case, where the spatial coordinates do not commute with the time coordinate. Within this kinematical-Hilbert-space representation we can give a crisp characterization of the “fuzziness” of points in κ-Minkowski spacetime, also allowing us to describe how the same fuzzy point is seen by different relativistic observers. The most striking finding of our analysis is a relativity of spacetime locality in κ-Minkowski. While previous descriptions of relative locality had been formulated exclusively in classical-spacetime setups, our analysis shows how relative locality in a quantum spacetime takes the shape of a dependence of the fuzziness of a spacetime point on the distance at which an observer infers properties of the event that marks the point.

In vacuo dispersion features for gamma-ray-burst neutrinos and photons

Ultrarelativistic photons and neutrinos from gamma-ray bursts offer a testbed for quantum gravity effects that would lead to an energy dependence of the travel times. A statistical analysis of astrophysical data shows that this behaviour may have been observed.

Generally covariant formulation of Relative Locality in curved spacetime

Institute for Theoretical Physics, University of Wroc law,Pl. Maksa Borna 9, Pl{50-204 Wroc law, Poland(Dated: January 15, 2014)We construct a theory of particles moving in curved both momentum space and spacetime,being a generalization of Relative Locality. We nd that in order to construct such theory,with desired symmetries, including the general coordinate invariance, we have to use nonlocal position variables. It turns out that free particles move on geodesics and momentumdependent translations of Relative Locality are replaced with momentum dependent geodesicdeviations.I. INTRODUCTIONIn the recent years the largely forgotten idea that momentum space may have a nontrivial geometricstructure, known under the name of Born reciprocity [1], has been revived in many di erent guises in thecontext of quantum gravity. It was noticed in [2] that there is a one-to-one correspondence between space-time noncommutativity, expected to be one of the features of quantum gravity, and nontrivial geometricstructures in momentum space. This general observation is supported by explicit calculations done in thecontext of gravity in 2+1 dimensions [3], [4]. Few years later it was realized that many nontrivial features ofDoubly Special Relativity class of theories [5], [6], [7] can be conveniently described in terms of the geometryof de Sitter momentum space [8].Relative Locality [9], [10], [11] is a theoretical framework that has its roots in Born reciprocity. In thisframework the momentum space is brought to foreground. It is rst observed that most, if not all, physicalmeasurements correspond, in fact, to momentum space data. Second it is noticed that the emergence ofa nontrivial geometry in momentum space requires, as a prerequisite, the presence of a mass scale. Suchscale must be provided by a fundamental theory, and it was assumed that there exists a regime of quantumgravity, in which the length scale, the Planck length, is negligibly small, while the mass scale, the Planckmass, remains nite.In the couple of years that passed since Relative Locality was rst proposed the bulk of research investi-gated systems de ned on at Minkowski spacetime. The question arises however if curved momentum spacecould coexists with a nontrivial geometry of spacetime. This possibility is particularly intriguing from the

Weakness of accelerator bounds on departures from Lorentz symmetry for the electron

Dipartimento di Fisica, Università di Roma “La Sapienza”, P.le A. Moro 2, 00185 Roma, EU INFN, Sez. Roma1, P.le A. Moro 2, 00185 Roma, EU Department of Physics, University of California, Berkeley , CA 94720, USA PCCP and APC, Universit/’e Denis Diderot Paris 7, Batiment C ondorcet, 10 rue Alice Domon et Léonie Duquet, 75205 Paris, France Departamento de Fı́sica Téorica, Universidad de Zaragoza , Zaragoza 50009, Spain

RELATIVE LOCALITY IN CURVED SPACETIME

In this paper we construct the action describing dynamics of the particle moving in curved spacetime, with a nontrivial momentum space geometry. Curved momentum space is the core feature of theories where relative locality effects are present. So far aspects of nonlinearities in momentum space have been studied only for flat or constantly expanding (de Sitter) spacetimes, relying on their maximally symmetric nature. The extension of curved momentum space frameworks to arbitrary spacetime geometries could be relevant for the opportunities to test Planck-scale curvature/deformation of particles momentum space. As a first example of this construction we describe the particle with κ-Poincare momentum space on a circular orbit in Schwarzschild spacetime, where the contributes of momentum space curvature turn out to be negligible. The analysis of this problem relies crucially on the solution of the soccer ball problem.

GRAVITY'S WEIGHT ON WORLDLINE FUZZINESS

We investigate a connection between recent results in three-dimensional (3D) quantum gravity, providing an effective noncommutative-spacetime description, and some earlier heuristic descriptions of a quantum-gravity contribution to the fuzziness of the worldlines of particles. We show that 3D-gravity-inspired spacetime noncommutativity reflects some of the features suggested by previous heuristic arguments. Most notably, gravity-induced worldline fuzziness, while irrelevantly small on terrestrial scales, could be observably large for propagation of particles over cosmological distances.