Gravity and the quantum: Are they reconcilable?

General relativity and quantum mechanics are not consistent with each other. This conflict stems from the very fundamental principles on which these theories are grounded. General relativity, on one hand, is based on the equivalence principle, whose strong version establishes the local equivalence between gravitation and inertia. Quantum mechanics, on the other hand, is fundamentally based on the uncertainty principle, which is essentially nonlocal. This difference precludes the existence of a quantum version of the strong equivalence principle, and consequently of a quantum version of general relativity. Furthermore, there are compelling experimental evidences that a quantum object in the presence of a gravitational field violates the weak equivalence principle. Now it so happens that, in addition to general relativity, gravitation has an alternative, though equivalent, description, given by teleparallel gravity, a gauge theory for the translation group. In this theory torsion, instead of curvature, is assumed to represent the gravitational field. These two descriptions lead to the same classical results, but are conceptually different. In general relativity, curvature geometrizes the interaction while torsion, in teleparallel gravity, acts as a force, similar to the Lorentz force of electrodynamics. Because of this peculiar property, teleparallel gravity describes the gravitational interaction without requiring any of the equivalence principle versions. The replacement of general relativity by teleparallel gravity may, in consequence, lead to a conceptual reconciliation of gravitation with quantum mechanics. © 2006 American Institute of Physics.

Invariant conserved currents in gravity theories with local Lorentz and diffeomorphism symmetry

We discuss conservation laws for gravity theories invariant under general coordinate and local Lorentz transformations. We demonstrate the possibility to formulate these conservation laws in many covariant and noncovariant(ly looking) ways. An interesting mathematical fact underlies such a diversity: there is a certain ambiguity in a definition of the (Lorentz-) covariant generalization of the usual Lie derivative. Using this freedom, we develop a general approach to the construction of invariant conserved currents generated by an arbitrary vector field on the spacetime. This is done in any dimension, for any Lagrangian of the gravitational field and of a (minimally or nonminimally) coupled matter field. A development of the regularization via relocalization scheme is used to obtain finite conserved quantities for asymptotically nonflat solutions. We illustrate how our formalism works by some explicit examples. © 2006 The American Physical Society.

Bringing together gravity and the quanta

Due to its underlying gauge structure, teleparallel gravity achieves a separation between inertial and gravitational effects. It can, in consequence, describe the isolated gravitational interaction without resorting to the equivalence principle, and is able to provide a tensorial definition for the energy-momentum density of the gravitational field. Considering the conceptual conflict between the local equivalence principle and the nonlocal uncertainty principle, the replacement of general relativity by its teleparallel equivalent can be considered an important step towards a prospective reconciliation between gravitation and quantum mechanics. © 2006 American Institute of Physics.

Is the equivalence principle doomed forever to Dante's Inferno on account of quantum mechanics?

It is commonly assumed that the equivalence principle can coexist without conflict with quantum mechanics. We shall argue here that, contrary to popular belief, this principle does not hold in quantum mechanics. We illustrate this point by computing the second-order correction for the scattering of a massive scalar boson by a weak gravitational field, treated as an external field. The resulting cross-section turns out to be mass-dependent. A way out of this dilemma would be, perhaps, to consider gravitation without the equivalence principle. At first sight, this seems to be a too much drastic attitude toward general relativity. Fortunately, the teleparallel version of general relativity - a description of the gravitational interaction by a force similar to the Lorentz force of electromagnetism and that, of course, dispenses with the equivalence principle - is equivalent to general relativity, thus providing a consistent theory for gravitation in the absence of the aforementioned principle. © World Scientific Publishing Company.

Finite element analysis of warpage in laminated aluminium alloy plates for machining of primary aeronautic parts

The aim of this paper consists in presenting a method of simulating the warpage in 7xxx series aluminium alloy plates. To perform this simulation finite element software MSC.Patran and MSC.Marc were used. Another result of this analysis will be the influence on material residual stresses induced on the raw material during the rolling process upon the warpage of primary aeronautic parts, fabricated through machining (milling) at Embraer. The method used to determinate the aluminium plate residual stress was Layer Removal Test. The numerical algorithm Modified Flavenot Method was used to convert layer removal and beam deflection in stress level. With such information about the level and profile of residual stresses become possible, during the step that anticipate the manufacturing to incorporate these values in the finite-element approach for modelling warpage parts. Based on that warpage parameter surely the products are manufactured with low relative vulnerability propitiating competitiveness and price. © 2007 American Institute of Physics.

Gravitation: In search of the missing torsion

A linear Lorentz connection has always two fundamental derived characteristics: curvature and torsion. The latter is assumed to vanish in general relativity. Three gravitational models involving non-vanishing torsion are examined: teleparallel gravity, Einstein-Cartan, and new general relativity. Their dependability is critically examined. Although a final answer can only be given by experience, it is argued that teleparallel gravity provides the most consistent approach.

Study of the potential of irregular shaped bodies and orbits around a non-spherical body

In the present work we show the expressions of the gravitational potential of homogeneous bodies with non-spherical three-dimensional shapes in order to study the trajectories around these bodies. The potentials of a prolate and an oblate ellipsoids with different values of semi-major axis are presented. Their results are validated with a test using a spherical body in order to guarantee the approximation of any body as a polyhedral model of the body. With these expressions we study trajectories of a point of mass around the three-dimensional bodies and the results indicated that there is a group of orbits around those bodies and the polyhedral form of the object does work very well. Copyright IAF/IAA. All rights reserved.

Conflict between the classical equivalence principle and quantum mechanics

As far as external gravitational fields described by Newton's theory are concerned, theory shows that there is an unavoidable conflict between the universality of free fall (Galileo's equivalence principle) and quantum mechanics - a result confirmed by experiment. Is this conflict due perhaps to the use of Newton's gravity, instead of general relativity, in the analysis of the external gravitational field? The response is negative. To show this we compute the low corrections to the cross-section for the scattering of different quantum particles by an external gravitational field, treated as an external field, in the framework of Einstein's linearized gravity. To first order the cross-sections are spin-dependent; if the calculations are pushed to the next order they become dependent upon energy as well. Therefore, the Galileo's equivalence and, consequently, the classical equivalence principle, is violated in both cases. We address these issues here.

Ex-post evaluation of the employment effects of a preferential trade agreement: methodological issues, illustrated with a reference to Chile

Includes bibliography

Optimization of satellite constellations in the moon

Nowadays, we return to live a period of lunar exploration. China, Japan and India heavily invest in missions to the moon, and then try to implement manned bases on this satellite. These bases must be installed in polar regions due to the apparent existence of water. Therefore, the study of the feasibility of satellite constellations for navigation, control and communication recovers importance. The Moon's gravitational potential and resonant movements due to the proximity to Earth as the Kozai-Lidov resonance, must be considered in addition to other perturbations of lesser magnitude. The usual satellite constellations provide, as a basic feature, continuous and global coverage of the Earth. With this goal, they are designed for the smallest number of objects possible to perform a specific task and this amount is directly related to the altitude of the orbits and visual abilities of the members of the constellation. However the problem is different when the area to be covered is reduced to a given zone. The required number of space objects can be reduced. Furthermore, depending on the mission requirements it may be not necessary to provide continuous coverage. Taking into account the possibility of setting up a constellation that covers a specific region of the Moon on a non-continuous base, in this study we seek a criterion of optimization related to the time between visits. The propagation of the orbits of objects in the constellation in conjunction with the coverage constraints, provide information on the periods of time in which points of the surface are covered by a satellite, and time intervals in which they are not. So we minimize the time between visits considering several sets of possible constellations and using genetic algorithms.

Flexibility and torsional resistance of three nickel-titanium retreatment instrument systems

Aim To assess the dimensional characteristics, flexibility and torsional behaviour of nickel-titanium retreatment instruments. Methodology Using image analysis software and high-resolution digital images, the instrument length, tip angle, diameter at 3mm from the tip and the distance between the blades (pitch length) of the following eight instruments were measured (n=12 for each measurement parameter): the ProTaper Universal retreatment (PTU-R) D1, D2 and D3 instruments; the R-Endo R1, R2 and R3 retreatment instruments; and the Mtwo retreatment (Mtwo-R) sizes 25 and 15 retreatment instruments. Maximum torque and the angular deflection at fracture as well as the bending moment at 45° were measured (n=12) according to the International Standards Organisation (ISO) specification number 3630-1. Data were analysed using the analysis of variance (α=0.05). Results The length of the active part of the instruments was found to vary according to the depth of the canal into which they were designed to reach. The pitch length also increased along the active length. The PTU-R D1 and the Mtwo-R instruments had active tips. Measurements of the bending moment at 45° revealed that the Mtwo-R 15 instrument was the most flexible, whereas the PTU-R D1 was the least flexible. The maximum torque tended to increase as the instrument diameter at 3mm from the tip increased, whereas the angular deflection at fracture varied in the opposite direction. Conclusions The geometrical characteristics of the retreatment instruments and their flexibility and torsion behaviour were consistent with their intended clinical application. © 2011 International Endodontic Journal.

Mapeamento geoambiental como subsídio na determinação de áreas de instabilidades da faixa de dutos Osvat/Osplan - São Sebastião, SP

Works of linear engineering such as roads, pipelines and transmission lines have specific mapping due to their large scale impact on the environment, thus requiring mapping methods that are both efficient and of low cost. This paper presents a proposal of Geoenvironmental mapping for works linear. The work chosen for the implementation of the method was the Osvat/Osplan pipeline located in the cities of São Sebastião and Caraguatatuba. The geoenvironment mapping was elaborate trough photo-interpretation of images of the ETM+/Landsat-7 sensor and analysis of the drainage network, thus resulting in the partitioning of the geoenvironmental units and the fracture area (structural lineaments and lines of strikes), these maps were subsequently integrated into a product called Map of environmental susceptibility to gravitational and erosive processes, which helped define the areas with potential geotechnical problems that could damage both the pipeline and the environment.

Chaotic diffusion caused by close encounters with several massive asteroids: II. the regions of (10) Hygiea, (2) Pallas, and (31) Euphrosyne

Context. Close encounters with (1) Ceres and (4) Vesta, the two most massive bodies in the main belt, are known to be a mechanism of dynamical mobility able to significantly alter proper elements of minor bodies, and they are the main source of dynamical mobility for medium-sized and large asteroids (D > 20 km, approximately). Recently, it has been shown that drift rates caused by close encounters with massive asteroids may change significantly on timescales of 30 Myr when different models (i.e., different numbers of massive asteroids) are considered. Aims. So far, not much attention has been given to the case of diffusion caused by the other most massive bodies in the main belt: (2) Pallas, (10) Hygiea, and (31) Euphrosyne, the third, fourth, and one of the most massive highly inclined asteroids in the main belt, respectively. Since (2) Pallas is a highly inclined object, relative velocities at encounter with other asteroids tend to be high and changes in proper elements are therefore relatively small. It was thus believed that the scattering effect caused by highly inclined objects in general should be small. Can diffusion by close encounters with these asteroids be a significant mechanism of long-term dynamical mobility? Methods. By performing simulations with symplectic integrators, we studied the problem of scattering caused by close encounters with (2) Pallas, (10) Hygiea, and (31) Euphrosyne when only the massive asteroids (and the eight planets) are considered, and the other massive main belt asteroids and non-gravitational forces are also accounted for. Results. By finding relatively small values of drift rates for (2) Pallas, we confirm that orbital scattering by this highly inclined object is indeed a minor effect. Unexpectedly, however, we obtained values of drift rates for changes in proper semi-major axis a caused by (10) Hygiea and (31) Euphrosyne larger than what was previously found for scattering by (4) Vesta. These high rates may have repercussions on the orbital evolution and age estimate of their respective families. © 2013 ESO.

Small particles in Pluto's environment: Effects of the solar radiation pressure

Impacts of micrometeoroids on the surfaces of the plutonian small satellites Nix and Hydra can generate dust particles. Even in this region so far from the Sun these tiny ejected particles are under the effects of the solar radiation pressure. In this work, we investigate the orbital evolution of the escaping ejecta from both the small satellites under the effects of the radiation pressure combined with the gravitational effects of Pluto, Charon, Nix and Hydra. The mass production rate of micron-sized dust particles generated by micrometeoroids hitting the satellites is obtained, and numerical simulations are performed to derive the lifetime of the ejecta. These pieces of information allow us to estimate the optical depth of a putative ring, which extends from the orbits of Nix to Hydra. The ejected particles, between the orbits of Nix and Hydra, form a wide ring of about 16 000 km. Collisions with the massive bodies and escape from the system are mainly determined by the effects of the solar radiation pressure. This is an important loss mechanism, removing 30 per cent of the initial set of 1 μm-sized particles in 1 yr. The surviving particles form a ring too faint to be detectable with the derived maximum optical depth of 4 × 10-11. © 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society.

Determination of the force systems produced by different configurations of tear drop orthodontic loops

Objective: To determine the mechanical characteristics of teardrop loop with and without helix fabricated using different metal alloy compositions (stainless steel and beta-titanium), submitted to different intensities of bends preactivation (0° and 40°), and with different cross-sectional dimension of the wire used to build these loops (0.017 x 0.025-in and 0.019 x 0.025-in). Methods: Eighty loops used to close spaces were submitted to mechanical tests. The magnitudes of horizontal force, the moment/force ratio, and the load/deflection ratio produced by the specimens were quantified. Loops were submitted to a total activation of 5.0 mm and the values were registered for each 1.0 mm of activation. For statistic data analysis, a analysis of variance was performed and a Tukey's Multiple Comparison test was used as supplement, considering a 5% level of significance. Results: In general, teardrop loops with helix produced lower magnitudes of horizontal force and load/deflection ratio, and higher moment/force ratio than teardrop loops without helix. Among all analyzed variables, metal alloy composition presented greater influence in the horizontal force and in the load/deflection ratio. The moment/force ratio showed to be more influenced by the preactivation of loops for space closure. © 2013 Dental Press Journal of Orthodontics.