Precise comparison of theory and new experiment for the Casimir force leads to stronger constraints on thermal quantum effects and long-range interactions

We report an improved dynamic determination of the Casimir pressure between two plane plates obtained using a micromachined torsional oscillator. The main improvements in the current experiment are a significant suppression of the surface roughness of the Au layers deposited on the interacting surfaces, and a decrease in the experimental error in the measurement of the absolute separation. A metrological analysis of all data permitted us to determine both the random and systematic errors, and to find the total experimental error as a function of separation at the 95% confidence level. In contrast to all previous experiments on the Casimir effect, our smallest experimental error ($\sim 0.5$%) is achieved over a wide separation range. The theoretical Casimir pressures in the experimental configuration were calculated by the use of four theoretical approaches suggested in the literature. All corrections to the Casimir force were calculated or estimated. All theoretical errors were analyzed and combined to obtain the total theoretical error at the 95% confidence level. Finally, the confidence interval for the differences between theoretical and experimental pressures was obtained as a function of separation. Our measurements are found to be consistent with two theoretical approaches utilizing the plasma model and the surface impedance over the entire measurement region. Two other approaches to the thermal Casimir force, utilizing the Drude model or a special prescription for the determination of the zero-frequency contribution to the Lifshitz formula, are excluded on the basis of our measurements at the 99% and 95% confidence levels, respectively. Finally, constraints on Yukawa-type hypothetical interactions are strengthened by up to a factor of 20 in a wide interaction range.Comment: 43 pages, 15 figures, elsart.cls is used. Accepted for publication in Annals of Physics. (Several misprints in the text are corrected.

Comment on "Anomalies in electrostatic calibration for the measurement of the Casimir force in a sphere-plane geometry"

Recently W. J. Kim, M. Brown-Hayes, D. A. R. Dalvit, J. H. Brownell, and R. Onofrio [Phys. Rev. A, v.78, 036102(R) (2008)] performed electrostatic calibrations for a plane plate above a centimeter-size spherical lens at separations down to 20-30 nm and observed "anomalous behavior". It was found that the gradient of the electrostatic force does not depend on separation as predicted on the basis of a pure Coulombian contribution. Some hypotheses which could potentially explain the deviation from the expected behavior were considered, and qualitative arguments in favor of the influence of patch surface potentials were presented. We demonstrate that for the large lenses at separations of a few tens nanometers from the plate, the electrostatic force law used by the authors is not applicable due to possible deviations of the mechanically polished and ground lens surface from a perfect spherical shape. A model is proposed which explains the observed "anomalous behavior" using the standard Coulombian force.Comment: 9 pages, 3 figure

Tests of new physics from precise measurements of the Casimir pressure between two gold-coated plates

A micromechanical torsion oscillator has been used to strengthen the limits on new Yukawa forces by determining the Casimir pressure between two gold-coated plates. By significantly reducing the random errors and obtaining the electronic parameters of the gold coatings, we were able to conclusively exclude the predictions of large thermal effects below 1 $\mu$m and strengthen the constraints on Yukawa corrections to Newtonian gravity in the interaction range from 29.5 nm to 86 nm.Comment: 8 pages, 3 figures, to appear in Phys. Rev.

Geometric Random Inner Products: A New Family of Tests for Random Number Generators

We present a new computational scheme, GRIP (Geometric Random Inner Products), for testing the quality of random number generators. The GRIP formalism utilizes geometric probability techniques to calculate the average scalar products of random vectors generated in geometric objects, such as circles and spheres. We show that these average scalar products define a family of geometric constants which can be used to evaluate the quality of random number generators. We explicitly apply the GRIP tests to several random number generators frequently used in Monte Carlo simulations, and demonstrate a new statistical property for good random number generators

Fichte and Hegel on Recognition

In this paper I provide an interpretation of Hegel’s account of ‘recognition’ (Anerkennung) in the 1802-3 System of Ethical Life as a critique of Fichte’s account of recognition in the 1796-7 Foundations of Natural Right. In the first three sections of the paper I argue that Fichte’s account of recognition in the domain of right is not concerned with recognition as a moral attitude. I then turn, in section four, to a discussion of Hegel’s critique and transformation of Fichte’s conception of recognition. Hegel’s transformation consists, I argue, in the claim that a comprehensive account of recognition in the domain of right must be concerned with recognition as a moral attitude

Stronger constraints on non-Newtonian gravity from the Casimir effect

We review new constraints on the Yukawa-type corrections to Newtonian gravity obtained recently from gravitational experiments and from the measurements of the Casimir force. Special attention is paid to the constraints following from the most precise dynamic determination of the Casimir pressure between the two parallel plates by means of a micromechanical torsional oscillator. The possibility of setting limits on the predictions of chameleon field theories using the results of gravitational experiments and Casimir force measurements is discussed.Comment: 9 pages, 2 figures, Proceedings of QFEXT07, to appear in J. Phys.

Gravitational solution to the Pioneer 10/11 anomaly

A fully relativistic modified gravitational theory including a fifth force skew symmetric field is fitted to the Pioneer 10/11 anomalous acceleration. The theory allows for a variation with distance scales of the gravitational constant G, the fifth force skew symmetric field coupling strength omega and the mass of the skew symmetric field mu=1/lambda. A fit to the available anomalous acceleration data for the Pioneer 10/11 spacecraft is obtained for a phenomenological representation of the "running" constants and values of the associated parameters are shown to exist that are consistent with fifth force experimental bounds. The fit to the acceleration data is consistent with all current satellite, laser ranging and observations for the inner planets.Comment: 14 pages, 3 figures, 3 tables. typo's were corrected at Equations (4) and (12) and a third table including our predictions for the anomalous perihelion advance of the planets was adde

Experimental procedures for precision measurements of the Casimir force with an Atomic Force Microscope

Experimental methods and procedures required for precision measurements of the Casimir force are presented. In particular, the best practices for obtaining stable cantilevers, calibration of the cantilever, correction of thermal and mechanical drift, measuring the contact separation, sphere radius and the roughness are discussed.Comment: 14 pages, 7 figure

Probing long-range leptonic forces with solar and reactor neutrinos

In this work we study the phenomenological consequences of the existence of long-range forces coupled to lepton flavour numbers in solar neutrino oscillations. We study electronic forces mediated by scalar, vector or tensor neutral bosons and analyze their effect on the propagation of solar neutrinos as a function of the force strength and range. Under the assumption of one mass scale dominance, we perform a global analysis of solar and KamLAND neutrino data which depends on the two standard oscillation parameters, \Delta m^2_{21} and \tan^2\theta_{12}, the force coupling constant, its range and, for the case of scalar-mediated interactions, on the neutrino mass scale as well. We find that, generically, the inclusion of the new interaction does not lead to a very statistically significant improvement on the description of the data in the most favored MSW LMA (or LMA-I) region. It does, however, substantially improve the fit in the high-\Delta m^2 LMA (or LMA-II) region which can be allowed for vector and scalar lepto-forces (in this last case if neutrinos are very hierarchical) at 2.5\sigma. Conversely, the analysis allows us to place stringent constraints on the strength versus range of the leptonic interaction.Comment: 20 pages, 8 figure