On the Observables Describing a Quantum Reference Frame

A reference frame F is described by the element g of the Poincare' group P which connects F with a given fixed frame F_0. If F is a quantum frame, defined by a physical object following the laws of quantum physics, the parameters of g have to be considered as quantum observables. However, these observables are not compatible and some of them, namely the coordinates of the origin of F, cannot be represented by self-adjoint operators. Both these difficulties can be overcome by considering a positive-operator-valued measure (POVM) on P, covariant with respect to the left translations of the group, namely a covariance system. We develop a construction procedure for this kind of mathematical structure. The formalism is also used to discuss the quantum observables measured with respect to a quantum reference frame.Comment: 23 pages, no figure

The norm-1-property of a quantum observable

A normalized positive operator measure $X\mapsto E(X)$ has the norm-1-property if \no{E(X)}=1 whenever $E(X)\ne O$. This property reflects the fact that the measurement outcome probabilities for the values of such observables can be made arbitrary close to one with suitable state preparations. Some general implications of the norm-1-property are investigated. As case studies, localization observables, phase observables, and phase space observables are considered.Comment: 14 page

Events in a Non-Commutative Space-Time

We treat the events determined by a quantum physical state in a noncommutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued measures (POVMs). We consider in detail the model proposed by Snyder in 1947 and calculate the POVMs defined on the real line that describe the measurement of a single coordinate. The approximate joint measurement of all the four space-time coordinates is described in terms of a generalized Wigner function (GWF). We derive lower bounds for the dispersion of the coordinate observables and discuss the covariance of the model under the Poincare' group. The unusual transformation law of the coordinates under space-time translations is interpreted as a failure of the absolute character of the concept of space-time coincidence. The model shows that a minimal length is compatible with Lorents covariance.Comment: 13 pages, revtex. Introductory part shortened and some arguments made more clea

Non-Linear Relativity in Position Space

We propose two methods for obtaining the dual of non-linear relativity as previously formulated in momentum space. In the first we allow for the (dual) position space to acquire a non-linear representation of the Lorentz group independently of the chosen representation in momentum space. This requires a non-linear definition for the invariant contraction between momentum and position spaces. The second approach, instead, respects the linearity of the invariant contraction. This fully fixes the dual of momentum space and dictates a set of energy-dependent space-time Lorentz transformations. We discuss a variety of physical implications that would distinguish these two strategies. We also show how they point to two rather distinct formulations of theories of gravity with an invariant energy and/or length scale.Comment: 7 pages, revised versio

Ameloblastic fibroma in a 6-year old child:case report.

Ameloblastic fibroma (AF) is defined in WHO classification as a ''neoplasm composed of proliferating odontogenic epithelium embedded in a cellular ectomesenchymal tissue that resembles dental papilla, and with varying degrees of inductive change and dental hard tissue formation''. AF is a rather uncommon tumor, accounting for only 2.5% of all odontogenic tumors. AF is a true mixed tumor, in which the epithelial and ectomesenchymal elements are neoplastic. AF raises at any age, ranging from 6 months to 42 years (mean 14.6 to 15.5 years); it does not show sex predilection. The lesion occurs in nearly 70% of cases in posterior areas of the mandible. Patients exhibit swelling of the jaw; pain is not usually described. Authors present a clinical and surgical management of an early onset of a large mandibular ameloblastic fibroma in a 6-year-old girsl

Observers and Measurements in Noncommutative Spacetimes

We propose a "Copenhagen interpretation" for spacetime noncommutativity. The goal is to be able to predict results of simple experiments involving signal propagation directly from commutation relations. A model predicting an energy dependence of the speed of photons of the order E/E_Planck is discussed in detail. Such effects can be detectable by the GLAST telescope, to be launched in 2006.Comment: 10 pp; v2: equivalence of observers explicitely stated; v3: minor changes, references and remarks added, burst spreading with energy emphasized as a signature rather than nois

Classical limit of quantum gravity in an accelerating universe

A one-parameter deformation of Einstein?Hilbert gravity with an inverse Riemann curvature term is derived as the classical limit of quantum gravity compatible with an accelerating universe. This result is based on the investigation of semi-classical theories with sectional curvature bounds which are shown not to admit static spherically symmetric black holes if otherwise of phenomenological interest. We discuss the impact on the canonical quantization of gravity, and observe that worldsheet string theory is not affected.Comment: 11 pages, no figure

The Time-Energy Uncertainty Relation

The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.Comment: 33 pages, Latex. This expanded version (prepared for the 2nd edition of "Time in quantum mechanics") contains minor corrections, new examples and pointers to some additional relevant literatur

State and trait characteristics of anterior insula time-varying functional connectivity.

The human anterior insula (aINS) is a topographically organized brain region, in which ventral portions contribute to socio-emotional function through limbic and autonomic connections, whereas the dorsal aINS contributes to cognitive processes through frontal and parietal connections. Open questions remain, however, regarding how aINS connectivity varies over time. We implemented a novel approach combining seed-to-whole-brain sliding-window functional connectivity MRI and k-means clustering to assess time-varying functional connectivity of aINS subregions. We studied three independent large samples of healthy participants and longitudinal datasets to assess inter- and intra-subject stability, and related aINS time-varying functional connectivity profiles to dispositional empathy. We identified four robust aINS time-varying functional connectivity modes that displayed both "state" and "trait" characteristics: while modes featuring connectivity to sensory regions were modulated by eye closure, modes featuring connectivity to higher cognitive and emotional processing regions were stable over time and related to empathy measures