Fundamental limitations to high-precision tests of the universality of free fall by dropping atoms

Tests of the universality of free fall and the weak equivalence principle probe the foundations of General Relativity. Evidence of a violation may lead to the discovery of a new force. The best torsion balance experiments have ruled it out to 10^-13. Cold-atom drop tests have reached 10^-7 and promise to do 7 to 10 orders of magnitude better, on the ground or in space. They are limited by the random shot noise, which depends on the number N of atoms in the clouds. As mass-dropping experiments in the non-uniform gravitational field of Earth, they are sensitive to the initial conditions. Random accelerations due to initial condition errors of the clouds are designed to be at the same level as shot noise, so that they can be reduced with the number of drops along with it. This sets the requirements for the initial position and velocity spreads of the clouds with given N. In the STE-QUEST space mission proposal aiming at 2x10^-15 they must be about a factor 8 above Heisenberg's principle limit, and the integration time required to reduce both errors is 3 years, with a mission duration of 5 years. Instead, offset errors at release between different atom clouds are systematic and give rise to a systematic effect which mimics a violation. Such offsets must be demonstrated to be as small as required in all drops, must be small by design and must be measured. For STE-QUEST to meet its goal they must be several orders of magnitude smaller than the size of each individual cloud, which in its turn must be at most 8 times larger than the uncertainty principle limit. Even if all technical problems are solved and the clouds are released with negligible systematic errors, still they must be measured. Then, Heisenberg's principle dictates that the measurement lasts as long as the experiment and the systematic nature of the effect requires many measurements for it to be ruled out as a source of violation

Relevance of the weak equivalence principle and experiments to test it: lessons from the past and improvements expected in space

Tests of the Weak Equivalence Principle (WEP) probe the foundations of physics. Ever since Galileo in the early 1600s, WEP tests have attracted some of the best experimentalists of any time. Progress has come in bursts, each stimulated by the introduction of a new technique: the torsion balance, signal modulation by Earth rotation, the rotating torsion balance. Tests for various materials in the field of the Earth and the Sun have found no violation to the level of about 1 part in 1e13. A different technique, Lunar Laser Ranging (LLR), has reached comparable precision. Today, both laboratory tests and LLR have reached a point when improving by a factor of 10 is extremely hard. The promise of another quantum leap in precision rests on experiments performed in low Earth orbit. The Microscope satellite, launched in April 2016 and currently taking data, aims to test WEP in the field of Earth to 1e-15, a 100-fold improvement possible thanks to a driving signal in orbit almost 500 times stronger than for torsion balances on ground. The `Galileo Galilei' (GG) experiment, by combining the advantages of space with those of the rotating torsion balance, aims at a WEP test 100 times more precise than Microscope, to 1e-17. A quantitative comparison of the key issues in the two experiments is presented, along with recent experimental measurements relevant for GG. Early results from Microscope, reported at a conference in March 2017, show measurement performance close to the expectations and confirm the key role of rotation with the advantage (unique to space) of rotating the whole spacecraft. Any non-null result from Microscope would be a major discovery and call for urgent confirmation; with 100 times better precision GG could settle the matter and provide a deeper probe of the foundations of physics.Comment: To appear: Physics Letters A, special issue in memory of Professor Vladimir Braginsky, 2017. Available online: http://dx.doi.org/10.1016/j.physleta.2017.09.02

testing the weak equivalence principle with macroscopic proof masses on ground and in space a brief review

General relativity is founded on the experimental fact that in a gravitational field all bodies fall with the same acceleration regardless of their mass and composition. This is the weak equivalence principle, or universality of free fall. Experimental evidence of a violation would require either that general relativity is to be amended or that another force of nature is at play. In 1916 Einstein brought as evidence the torsion balance experiments by Eötvös, to 10-8–10-9. In the 1960s and early 70s, by exploiting the "passive" daily rotation of the Earth, torsion balance tests improved to 10-11 and 10-12. More recently, active rotation of the balance at higher frequencies has reached 10-13. No other experimental tests of general relativity are both so crucial for the theory and so precise and accurate. If a similar differential experiment is performed inside a spacecraft passively stabilized by 1 Hz rotation while orbiting the Earth at ≃ 600 km altitude the test would improve by 4 orders of magnitude, to 10-17, thus probing a totally unexplored field of physics. This is unique to weakly coupled concentric macroscopic test cylinders inside a rapidly rotating spacecraft

A Disk--Jet interaction model for the X--Ray Variability in Microquasars

We propose a simple dynamical model that may account for the observed spectral and temporal properties of GRS 1915+105 and XTE J1550-5634. The model is based on the assumption that a fraction of the radiation emitted by a hot spot lying on the accreting disk is dynamically Comptonized by the relativistic jet that typically accompanies the microquasar phenomenon. We show that scattering by the jet produces a detectable modulation of the observed flux. In particular, we found that the phase lag between hard and soft photons depends on the radial position of the hot spot and, if the angle between the jet and the line of sight is sufficiently large, the lags of the fundamental and its harmonics may be either positive or negative.Comment: 14 pages, 4 figures, accepted for publication in ApJ Part

Testing the equivalence principle in space after the MICROSCOPE mission

Tests of the weak equivalence principle (WEP) can reveal a new, composition dependent, force of nature, or disprove many models of new physics. For the first time, such a test is being successfully carried out in space by the MICROSCOPE satellite. Early results show no violation of the WEP sourced by the Earth for Pt and Ti test masses with random errors (after 8.26 d of integration time) of about 1 part in 1014 and systematic errors of the same magnitude. This result improves by about 10 times over the best ground tests with rotating torsion balances despite 70 times less sensitivity to differential accelerations, thanks to the much stronger driving signal in orbit. The measurement is limited by thermal noise from internal damping in the gold wires used for electrical grounding, related to their fabrication and clamping. This noise was shown to decrease when the spacecraft was set to rotate faster than planned. The result will improve by the end of the mission, as thermal noise decreases with more data. Not so systematic errors. We investigate major nongravitational effects and find that MICROSCOPE's "zero-check" sensor, with test masses both made of Pt, does not allow their separation from the signal. The early test reports an upper limit of systematic errors in the Pt-Ti sensor, which are not detected in the Pt-Pt one, hence would not be distinguished from a violation. Once all the integration time available is used to reduce random noise, there will be no time left to check systematics. MICROSCOPE demonstrates the huge potential of space for WEP tests of very high precision and indicates how to reach it. To realize the potential, a new experiment needs the spacecraft to be in rapid, stable rotation around the symmetry axis (by conservation of angular momentum), needs high quality state-of-the-art mechanical suspensions as in the most precise gravitational experiments on ground, and must allow multiple checks to discriminate a violation signal from systematic errors. The design of the "Galileo Galilei" (GG) experiment, aiming to test the WEP to 1 part in 1017 unites all the needed features, indicating that a quantum leap in space is possible provided the new experiment heeds the lessons of MICROSCOPE

Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates

The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff-Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix

The GALILEO GALILEI small-satellite mission with FEEP thrusters (GG)

The Equivalence Principle, formulated by Einstein generalizing Galileo’s and Newton’s work, is a fundamental principle of modern physics. As such it should be tested as accurately as possible. Its most direct consequence, namely the Universality of Free Fall, can be tested in space, in a low Earth orbit, the crucial advantage being that the driving signal is about three orders of magnitude stronger than on Earth. GALILEO GALILEI (GG) is a small space mission designed for such a high-accuracy test. At the time of print, GG has been selected by ASI (Agenzia Spaziale Italiana) as a candidate for the next small Italian mission. Ground tests of the proposed apparatus now indicate that an accuracy of 1 part in 1017 is within the reach of this small mission

Indentation of a free beam resting on an elastic substrate with an internal lengthscale

The plane strain problem of a slender and weightless beam-plate loaded by a transversal point force in unilateral contact with a couple stress elastic foundation is investigated. The study aims to explore the consequences of the material internal lengthscale on the contact mechanics. In particular, compatibility between the beam and the foundation surface demands that both displacement and rotation match along the contact line. To this aim, couple tractions are exchanged besides the traditional contact pressure until separation between the beam and the foundation occurs. The problem is formulated making use of the Green's functions for a point force and a point couple acting atop of a couple stress elastic half-plane. A pair of coupled integral equations is thus derived, that governs the distribution of contact pressure and couple tractions, with one of them being immediately solved to provide an explicit relation between the two unknowns. In this sense, we retrieve the concept of a mechanically equivalent action, as it is the case of the Kirchhoff shear for plates. The remaining integral equation sets a cubic eigenvalue problem, whose linear term accounts for the microstructure. Its numerical solution is sought by expanding the equivalent contact pressure in series of Chebyshev polynomials vanishing at the contact region ends points, namely the lift-off points, and then applying a collocation strategy. The contact length, the distributions of contact pressure and couple tractions under the beam and the shearing force and bending moment along the beam are then obtained as a function of the material characteristic length. Results clearly indicate that accounting for the material internal lengthscale is mainly realized through exchange of the couple tractions, in the lack of which results much resemble those of the classical solution. Specifically, greater contact lengths and a stronger focusing effect about the loading point are encountered, which become very significant when the contact length approaches the internal lengthscale

Integrated use of local and technical soil quality indicators and participatory techniques to select them. A review of bib-liography and analysis of research strategies and outcomes

Climate change has strong impacts on soil conservation and agricultural productivity, with severe consequences on smallholders in developing countries, but virtually no research has been carried out so far on this issue. Therefore, it is necessary to foster the implementation of participatory projects to help communities deal with new difficulties. Sustainable soil management can reduce and even reverse land degradation, helping farmers to adapt to climate change effects. Pro-gress toward sustainability cannot be implemented in small rural communities regardless of local knowledge, which can be addressed using participatory techniques. To this purpose the choice and use of indicators is essential to carry out correct assessments of soil vulnerability integrating local and technical knowledge. The purpose of this review was to study how the problem of building a set of integrated indicators to assess soil quality has been addressed so far and which participatory techniques have been more successfully employed, analyzing studies carried out in rural communities of developing countries. We found out that there is a lack of participated studies dealing with environmental issues. Those that do so address them only indirectly, being centered on present agricultural problems. The studies rarely feature a collaboration with social science experts, consequently the use of participatory techniques lacks protocols and a standardized nomenclature to help in the transfer and generalization of experiences. Women are rarely involved and nearly exclusively in African countries: this could be related to social and cultural conditions, but needs more atten-tion. Different aspects need to be improved to help the implementation of a successful approach in future projects. This review provides a tool to facilitate future interdisciplinary research on integration of local and scientific knowledge and will help to devise more successful strategies to tackle the challenges posed by climate change to smallholders in developing countries