Invariant EKF Design for Scan Matching-aided Localization

Localization in indoor environments is a technique which estimates the robot's pose by fusing data from onboard motion sensors with readings of the environment, in our case obtained by scan matching point clouds captured by a low-cost Kinect depth camera. We develop both an Invariant Extended Kalman Filter (IEKF)-based and a Multiplicative Extended Kalman Filter (MEKF)-based solution to this problem. The two designs are successfully validated in experiments and demonstrate the advantage of the IEKF design

How far does the analogy between causal horizon-induced thermalization with the standard heat bath situation go?

After a short presentation of KMS states and modular theory as the unifying description of thermalizing systems we propose the absence of transverse vacuum fluctuations in the holographic projections as the mechanism for an area behavior (the transverse area) of localization entropy as opposed to the volume dependence of ordinary heat bath entropy. Thermalization through causal localization is not a property of QM, but results from the omnipresent vacuum polarization in QFT and does not require a Gibbs type ensemble avaraging (coupling to a heat bath).Comment: 10 pages, based on talk given at the 2002 Londrina Winter Schoo

Black holes, quantum information, and unitary evolution

The unitary crisis for black holes indicates an apparent need to modify local quantum field theory. This paper explores the idea that quantum mechanics and in particular unitarity are fundamental principles, but at the price of familiar locality. Thus, one should seek to parameterize unitary evolution, extending the field theory description of black holes, such that their quantum information is transferred to the external state. This discussion is set in a broader framework of unitary evolution acting on Hilbert spaces comprising subsystems. Here, various constraints can be placed on the dynamics, based on quantum information-theoretic and other general physical considerations, and one can seek to describe dynamics with "minimal" departure from field theory. While usual spacetime locality may not be a precise concept in quantum gravity, approximate locality seems an important ingredient in physics. In such a Hilbert space approach an apparently "coarser" form of localization can be described in terms of tensor decompositions of the Hilbert space of the complete system. This suggests a general framework in which to seek a consistent description of quantum gravity, and approximate emergence of spacetime. Other possible aspects of such a framework -- in particular symmetries -- are briefly discussed.Comment: 39 pages, 5 figures. v2: refs added, very minor clarifications v3: few small changes to agree with published version v4: corrected sign in eq. 3.3

Snyder's Model -- de Sitter Special Relativity Duality and de Sitter Gravity

Between Snyder's quantized space-time model in de Sitter space of momenta and the \dS special relativity on \dS-spacetime of radius $R$ with Beltrami coordinates, there is a one-to-one dual correspondence supported by a minimum uncertainty-like argument. Together with Planck length $\ell_P$, $R\simeq (3/\Lambda)^{1/2}$ should be a fundamental constant. They lead to a dimensionless constant $g{\sim\ell_PR^{-1}}=(G\hbar c^{-3}\Lambda/3)^{1/2}\sim 10^{-61}$. These indicate that physics at these two scales should be dual to each other and there is in-between gravity of local \dS-invariance characterized by $g$. A simple model of \dS-gravity with a gauge-like action on umbilical manifolds may show these characters. It can pass the observation tests and support the duality.Comment: 32 page

A Converse Hawking-Unruh Effect and dS^2/CFT Correspondance

Given a local quantum field theory net A on the de Sitter spacetime dS^d, where geodesic observers are thermalized at Gibbons-Hawking temperature, we look for observers that feel to be in a ground state, i.e. particle evolutions with positive generator, providing a sort of converse to the Hawking-Unruh effect. Such positive energy evolutions always exist as noncommutative flows, but have only a partial geometric meaning, yet they map localized observables into localized observables. We characterize the local conformal nets on dS^d. Only in this case our positive energy evolutions have a complete geometrical meaning. We show that each net has a unique maximal expected conformal subnet, where our evolutions are thus geometrical. In the two-dimensional case, we construct a holographic one-to-one correspondence between local nets A on dS^2 and local conformal non-isotonic families (pseudonets) B on S^1. The pseudonet B gives rise to two local conformal nets B(+/-) on S^1, that correspond to the H(+/-)-horizon components of A, and to the chiral components of the maximal conformal subnet of A. In particular, A is holographically reconstructed by a single horizon component, namely the pseudonet is a net, iff the translations on H(+/-) have positive energy and the translations on H(-/+) are trivial. This is the case iff the one-parameter unitary group implementing rotations on dS^2 has positive/negative generator.Comment: The title has changed. 38 pages, figures. To appear on Annales H. Poincare

OPERA neutrinos and relativity

In a recent study, Cohen and Glashow argue that superluminal neutrinos of the type recently reported by OPERA should be affected by anomalous Cherenkov-like processes. This causes them to loose much of their energy before reaching the OPERA detectors. Related concerns were reported also by Gonzalez-Mestres and Bi et. al., who argued that pions cannot decay to superluminal neutrinos over part of the energy range studied by OPERA. We observe here that these arguments are set within a framework in which Lorentz symmetry is broken, by the presence of a preferred frame. We further show that these anomalous processes are forbidden if Lorentz symmetry is instead "deformed", preserving the relativity of inertial frames. These deformations add non-linear terms to energy momentum relations, conservation laws and Lorentz transformations in a way that is consistent with the relativity of inertial observers.Comment: 5 pages, some citations added; in v3 a footnote added and minor changes in the text made, the final version to appear in MPL

The principle of relative locality

We propose a deepening of the relativity principle according to which the invariant arena for non-quantum physics is a phase space rather than spacetime. Descriptions of particles propagating and interacting in spacetimes are constructed by observers, but different observers, separated from each other by translations, construct different spacetime projections from the invariant phase space. Nonetheless, all observers agree that interactions are local in the spacetime coordinates constructed by observers local to them. This framework, in which absolute locality is replaced by relative locality, results from deforming momentum space, just as the passage from absolute to relative simultaneity results from deforming the linear addition of velocities. Different aspects of momentum space geometry, such as its curvature, torsion and non-metricity, are reflected in different kinds of deformations of the energy-momentum conservation laws. These are in principle all measurable by appropriate experiments. We also discuss a natural set of physical hypotheses which singles out the cases of momentum space with a metric compatible connection and constant curvature.Comment: 12 pages, 3 figures; in version 2 one reference added and some minor modifications in sects. II and III mad