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

Free Quantum Fields on the Poincare' Group

A class of free quantum fields defined on the Poincare' group, is described by means of their two-point vacuum expectation values. They are not equivalent to fields defined on the Minkowski spacetime and they are "elementary" in the sense that they describe particles that transform according to irreducible unitary representations of the symmetry group, given by the product of the Poincare' group and of the group SL(2, C) considered as an internal symmetry group. Some of these fields describe particles with positive mass and arbitrary spin and particles with zero mass and arbitrary helicity or with an infinite helicity spectrum. In each case the allowed SL(2, C) internal quantum numbers are specified. The properties of local commutativity and the limit in which one recovers the usual field theories in Minkowski spacetime are discussed. By means of a superposition of elementary fields, one obtains an example of a field that present a broken symmetry with respect to the group Sp(4, R), that survives in the short-distance limit. Finally, the interaction with an accelerated external source is studied and and it is shown that, in some theories, the average number of particles emitted per unit of proper time diverges when the acceleration exceeds a finite critical value.Comment: 49 pages, plain tex with vanilla.st

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

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

Time-of-arrival formalism for the relativistic particle

A suitable operator for the time-of-arrival at a detector is defined for the free relativistic particle in 3+1 dimensions. For each detector position, there exists a subspace of detected states in the Hilbert space of solutions to the Klein Gordon equation. Orthogonality and completeness of the eigenfunctions of the time-of-arrival operator apply inside this subspace, opening up a standard probabilistic interpretation.Comment: 16 pages, no figures, uses LaTeX. The section "Interpretation" has been completely rewritten and some errors correcte

Urban mining of municipal solid waste incineration (MSWI) residues with emphasis on bioleaching technologies: a critical review

Metals are essential in our daily lives and have a finite supply, being simultaneously contaminants of concern. The current carbon emissions and environmental impact of mining are untenable. We need to reclaim metals sustainably from secondary resources, like waste. Biotechnology can be applied in metal recovery from waste streams like fly ashes and bottom ashes of municipal solid waste incineration (MSWI). They represent substantial substance flows, with roughly 46 million tons of MSWI ashes produced annually globally, equivalent in elemental richness to low-grade ores for metal recovery. Next-generation methods for resource recovery, as in particular bioleaching, give the opportunity to recover critical materials and metals, appropriately purified for noble applications, in waste treatment chains inspired by circular economy thinking. In this critical review, we can identify three main lines of discussion: (1) MSWI material characterization and related environmental issues; (2) currently available processes for recycling and metal recovery; and (3) microbially assisted processes for potential recycling and metal recovery. Research trends are chiefly oriented to the potential exploitation of bioprocesses in the industry. Biotechnology for resource recovery shows increasing effectiveness especially downstream the production chains, i.e., in the waste management sector. Therefore, this critical discussion will help assessing the industrial potential of biotechnology for urban mining of municipal, post-combustion waste

Assessment of seasonal changes in water chemistry of the ridracoli water reservoir (Italy): Implications for water management

The Ridracoli artificial basin is the main water reservoir of the Emilia-Romagna region (Northeast Italy). The reservoir was made by construction of a dam on the Bidente River in 1982. It is used as the main drinking water supply of the region and for hydropower production. The physical and chemical parameterseters (temperature, pH, electrical conductivity, and dissolved oxygen) of shallow water are continuously monitored whereas vertical depth profiles of water chemical data (major anions and cations, as well as heavy metals) are available on a bimonthly base. The dataset used in this research is related to the years 2015 and 2016. Data show that the reservoir is affected by an alternation of water stratification and mixing processes due to seasonal change in water temperature, density, and the reservoir water level. In late summer and winter months, the water column is stratified with anoxic conditions at the bottom. During the spring, on the other hand, when storage is at its maximum, water recirculation and mixing occur. The reservoir is characterized by a dynamic system in which precipitation, dissolution, and adsorption processes at the bottom affect water quality along the reservoir depth column. The temperature stratification and anoxic conditions at the reservoir bottom influence the concentration and mobility of some heavy metals (i.e., Fe and Mn) and, consequently, the quality of water that reaches the treatment and purification plant. This study is relevant for water resource management of the reservoir. Assessing the seasonal changes in water quality along the reservoir water column depth is fundamental to plan water treatment operations and optimize their costs. The reservoir assessment allows one to identify countermeasures to avoid or overcome the high concentrations of heavy metals and the stratification problem (i.e., artificial mixing of the water column, new water intakes at different depths operating at different times of the year, blowers, etc.)

Lower Neutrino Mass Bound from SN1987A Data and Quantum Geometry

A lower bound on the light neutrino mass $m_\nu$ is derived in the framework of a geometrical interpretation of quantum mechanics. Using this model and the time of flight delay data for neutrinos coming from SN1987A, we find that the neutrino masses are bounded from below by $m_\nu\gtrsim 10^{-4}-10^{-3}$eV, in agreement with the upper bound $m_\nu\lesssim$ $({\cal O}(0.1) - {\cal O} (1))$ eV currently available. When the model is applied to photons with effective mass, we obtain a lower limit on the electron density in intergalactic space that is compatible with recent baryon density measurements.Comment: 22 pages, 3 figure