We study the limits to the localizability of events and reference frames in the κ-Minkowski quantum spacetime. Our main tool will be a representation of the κ-Minkowski commutation relations between ...coordinates, and the operator and measurement theory borrowed from ordinary quantum mechanics. Spacetime coordinates are described by operators on a Hilbert space, and a complete set of commuting observables cannot contain the radial coordinate and time at the same time. The transformation between the complete sets turns out to be the Mellin transform, which allows us to discuss the localizability properties of states both in space and in time. We then discuss the transformation rules between inertial observers, which are described by the quantum κ-Poincaré group. These too are subject to limitations in the localizability of states, which impose further restrictions on the ability of an observer to localize events defined in a different observer's reference frame.
2 + 1 gravity on the conformal sphere Gryb, Sean; Mercati, Flavio
Physical review. D, Particles, fields, gravitation, and cosmology,
03/2013, Letnik:
87, Številka:
6
Journal Article
Recenzirano
Odprti dostop
We show that there are two equivalent first order descriptions of 2 + 1 gravity with a nonzero cosmological constant. One is the well-known spacetime description, and the other is in terms of ...evolving conformal geometry. The key tool that links these pictures is Cartan geometry, a generalization of Riemannian geometry that allows for geometries locally modeled off arbitrary homogeneous spaces. The two different interpretations suggest two distinct phase space reductions. The spacetime picture leads to the 2 + 1 formulation of general relativity due to Arnowitt, Deser, and Misner, while the conformal picture leads to shape dynamics. Cartan geometry thus provides an alternative to symmetry trading for explaining the equivalence of general relativity and shape dynamics.
The absence of unique time evolution in Einsteinʼs spacetime description of gravity leads to the hitherto unresolved 'problem of time' in quantum gravity. Shape dynamics is an objectively equivalent ...representation of gravity that trades spacetime refoliation invariance for three-dimensional conformal invariance. Its logical completion presented here gives a dimensionless description of gravitational dynamics. We show that in this framework the classical problem of time is completely solved. Since a comparable definitive solution is impossible within the spacetime description, we believe that shape dynamics provides a key ingredient for the creation of quantum gravity.
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 Einstein's 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.
Shape Dynamics and AdS/CFT Mercati, Flavio
Journal of physics. Conference series,
01/2012, Letnik:
360, Številka:
1
Journal Article
Recenzirano
Odprti dostop
I present a semi-classical correspondence between three-dimensional euclidean conformal field theory and the large-volume dynamics of gravity with positive cosmological constant in 3+1 dimensions. ...The correspondence is based on a theory of gravity called Shape Dynamics, whose solutions are a subset of those of General Relativity, namely those that can be foliated with constant mean extrinsic curvature. Shape Dynamics makes it possible to solve exactly for all the local degrees of freedom, while in GR this is possible only approximately, within a derivative expansion, due to the non-linearity of the scalar constraint.
In a recent paper, one of us studied spherically symmetric, asymptotically flat solutions of shape dynamics, finding that the spatial metric has characteristics of a wormhole-two asymptotically flat ...ends and a minimal-area sphere, or “throat,” in between. In this paper, we investigate whether that solution can emerge as a result of gravitational collapse of matter. With this goal, we study the simplest kind of spherically symmetric matter: an infinitely-thin shell of dust. Our system can be understood as a model of a star accreting a thin layer of matter. We solve the dynamics of the shell exactly and find that, indeed, as it collapses, the shell leaves in its wake the wormhole metric. In the maximal-slicing time we use for asymptotically flat solutions, the shell only approaches the throat asymptotically and does not cross it in a finite amount of time (as measured by a clock “at infinity”). This leaves open the possibility that a more realistic cosmological solution of shape dynamics might see this crossing happening in a finite amount of time (as measured by the change of relational or shape degrees of freedom).
Shape dynamics is a 3D conformally invariant theory of gravity that possesses a large set of solutions in common with general relativity. When looked at closely, these solutions are found to behave ...in surprising ways; in order to probe the fitness of shape dynamics as a viable alternative to General Relativity one must find and understand increasingly more-complex, less-symmetrical exact solutions on which to base perturbative studies and numerical analyses to compare them with data. Spherically symmetric exact solutions have been studied, but only in a static vacuum setup. In this work we construct a class of time-dependent exact solutions of Shape Dynamics from first principles, representing a central inhomogeneity in an evolving cosmological environment. By assuming only a perfect fluid source in a spherically symmetric geometry, we show that this fully dynamic nonvacuum solution satisfies in all generality the Hamiltonian structure of shape dynamics. The simplest choice of solutions is shown to be a member of the McVittie family.
We use the results of ultraprecise cold-atom-recoil experiments to constrain the form of the energy-momentum dispersion relation, a structure that is expected to be modified in several ...quantum-gravity approaches. Our strategy of analysis applies to the nonrelativistic (small speeds) limit of the dispersion relation, and is therefore complementary to an analogous ongoing effort of investigation of the dispersion relation in the ultrarelativistic regime using observations in astrophysics. For the leading correction in the nonrelativistic limit the exceptional sensitivity of cold-atom-recoil experiments remarkably allows us to set a limit within a single order of magnitude of the desired Planck-scale level, thereby providing the first example of Planck-scale sensitivity in the study of the dispersion relation in controlled laboratory experiments.
This paper is the second part of a series that develops the mathematical framework necessary for studying field theories on ``T-Minkowski'' noncommutative spacetimes. These spacetimes constitute a ...class of noncommutative geometries, introduced in Part I, that are each invariant under distinct quantum group deformations of the Poincaré group. All these noncommutative geometries possess certain physically desirable characteristics, which allow me to develop all the tools of differential geometry and functional analysis, that are necessary in order to build consistent and T-Poincaré invariant noncommutative classical field theories.
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