18 research outputs found
Rainbow metric formalism and Relative Locality
This proceeding is based on a talk prepared for the XIII Marcell Grossmann
meeting. We summarise some results of work in progress in collaboration with
Giovanni Amelino-Camelia about momentum dependent (Rainbow) metrics in a
Relative Locality framework and we show that this formalism is equivalent to
the Hamiltonian formalization of Relative Locality obtained in arXiv:1102.4637.Comment: appears in Proceedings of the 13th Marcell Grossmann meeting on
General Relativity, World Scientific, Singapore, (2014
Quantum Gravity phenomenology and metric formalism
In this proceedings for the MG14 conference, we discuss the construction of a
phenomenology of Planck-scale effects in curved spacetimes, underline a few
open issues and describe some perspectives for the future of this research
line
Dual redshift on Planck-scale-curved momentum spaces
Several approaches to the investigation of the quantum-gravity problem have
provided "theoretical evidence" of a role for the Planck scale in
characterizing the geometry of momentum space. One of the main obstructions for
a full exploitation of this scenario is the understanding of the role of the
Planck-scale-curved geometry of momentum space in the correlations between
emission and detection times, the "travel times" for a particle to go from a
given emitter to a given detector. These travel times appear to receive
Planck-scale corrections for which no standard interpretation is applicable,
and the associated implications for spacetime locality gave rise to the notion
of "relative locality" which is still in the early stages of investigation. We
here show that these Planck-scale corrections to travel times can be described
as "dual redshift" (or "lateshift"): they are manifestations of momentum-space
curvature of the same type already known for ordinary redshift produced by
spacetime curvature. In turn we can identify the novel notion of "relative
momentum-space locality" as a known but under-appreciated feature associated to
ordinary redshift produced by spacetime curvature, and this can be described in
complete analogy with the relative spacetime locality that became of interest
in the recent quantum-gravity literature. We also briefly comment on how these
findings may be relevant for an approach to the quantum-gravity problem
proposed by Max Born in 1938 and centered on Born duality.Comment: 13 pages, LaTe
Planck-scale dual-curvature lensing and spacetime noncommutativity
It was recently realized that Planck-scale momentum-space curvature, which is
expected in some approaches to the quantum-gravity problem, can produce
dual-curvature lensing, a feature which mainly affects the direction of
observation of particles emitted by very distant sources. Several gray areas
remain in our understanding of dual-curvature lensing, including the
possibility that it might be just a coordinate artifact and the possibility
that it might be in some sense a by product of the better studied
dual-curvature redshift. We stress that data reported by the IceCube neutrino
telescope should motivate a more vigorous effort of investigation of
dual-curvature lensing, and we observe that studies of the recently proposed
"-Minkowski noncommutative spacetime" could be valuable from this
perspective. Through a dedicated -Minkowski analysis, we show that
dual-curvature lensing is not merely a coordinate artifact and that it can be
present even in theories without dual-curvature redshift
Hamilton geometry: Phase space geometry from modified dispersion relations
We describe the Hamilton geometry of the phase space of particles whose
motion is characterised by general dispersion relations. In this framework
spacetime and momentum space are naturally curved and intertwined, allowing for
a simultaneous description of both spacetime curvature and non-trivial momentum
space geometry. We consider as explicit examples two models for Planck-scale
modified dispersion relations, inspired from the -de Sitter and
-Poincar\'e quantum groups. In the first case we find the expressions
for the momentum and position dependent curvature of spacetime and momentum
space, while for the second case the manifold is flat and only the momentum
space possesses a nonzero, momentum dependent curvature. In contrast, for a
dispersion relation that is induced by a spacetime metric, as in General
Relativity, the Hamilton geometry yields a flat momentum space and the usual
curved spacetime geometry with only position dependent geometric objects.Comment: 32 pages, section on quantisation of the theory added, comments on
additin of momenta on curved momentum spaces extende
Quantum-gravity-induced dual lensing and IceCube neutrinos
Momentum-space curvature, which is expected in some approaches to the
quantum-gravity problem, can produce dual redshift, a feature which introduces
energy dependence of the travel times of ultrarelativistic particles, and dual
lensing, a feature which mainly affects the direction of observation of
particles. In our recent arXiv:1605.00496 we explored the possibility that dual
redshift might be relevant in the analysis of IceCube neutrinos, obtaining
results which are preliminarily encouraging. Here we explore the possibility
that also dual lensing might play a role in the analysis of IceCube neutrinos.
In doing so we also investigate issues which are of broader interest, such as
the possibility of estimating the contribution by background neutrinos and some
noteworthy differences between candidate "early neutrinos" and candidate "late
neutrinos".Comment: In this version V2 we give a definition of variation probability
which could be considered in alternative to the notion of variation
probability already introduced in version V1; both notions of variation
probability are contemplated in the data analysis. arXiv admin note: text
overlap with arXiv:1605.0049
Hamilton Geometry - Phase Space Geometry from Modified Dispersion Relations
Quantum gravity phenomenology suggests an effective modification of the
general relativistic dispersion relation of freely falling point particles
caused by an underlying theory of quantum gravity. Here we analyse the
consequences of modifications of the general relativistic dispersion on the
geometry of spacetime in the language of Hamilton geometry. The dispersion
relation is interpreted as the Hamiltonian which determines the motion of point
particles. It is a function on the cotangent bundle of spacetime, i.e. on phase
space, and determines the geometry of phase space completely, in a similar way
as the metric determines the geometry of spacetime in general relativity. After
a review of the general Hamilton geometry of phase space we discuss two
examples. The phase space geometry of the metric Hamiltonian
and the phase space geometry of the first order q-de
Sitter dispersion relation of the form which is suggested from quantum gravity phenomenology. We
will see that for the metric Hamiltonian the geometry of phase space is
equivalent to the standard metric spacetime geometry from general relativity.
For the q-de Sitter Hamiltonian the Hamilton equations of motion for
point particles do not become autoparallels but contain a force term, the
momentum space part of phase space is curved and the curvature of spacetime
becomes momentum dependent.Comment: 6 page
Planck-scale-modified dispersion relations in homogeneous and isotropic spacetimes
The covariant understanding of dispersion relations as level sets of Hamilton functions on phase space enables us to derive the most general dispersion relation compatible with homogeneous and isotropic spacetimes. We use this concept to present a Planck-scale deformation of the Hamiltonian of a particle in Friedman-Lemaître-Robertson-Walker (FLRW) geometry that is locally identical to the κ-Poincaré dispersion relation, in the same way as the dispersion relation of point particles in general relativity is locally identical to the one valid in special relativity. Studying the motion of particles subject to such a Hamiltonian, we derive the redshift and lateshift as observable consequences of the Planck-scale deformed FLRW universe. © 2017 American Physical Society
Modeling transverse relative locality
We investigate some aspects of relativistic classical theories with "relative
locality", in which pairs of events established to be coincident by nearby
observers may be described as non-coincident by distant observers. While
previous studies focused mainly on the case of longitudinal relative locality,
where the effect occurs along the direction connecting the distant observer to
the events, we here focus on transverse relative locality, in which instead the
effect is found in a direction orthogonal to the one connecting the distant
observer to the events. Our findings suggest that, at least for theories of
free particles such as the one in arXiv:1006.2126, transverse relative locality
is as significant as longitudinal relative locality both conceptually and
quantitatively. And we observe that "dual gravity lensing", first discussed in
arXiv:1103.5626, can be viewed as one of two components of transverse relative
locality. We also speculate about a type of spacetime noncommutativity for
which transverse relative locality could be particularly significant.Comment: LaTex, 13 page