Model uncertainty and reference value of the Planck constant

partially_open1noopenMana, G.Mana, Giovann

Diffraction effects in length measurements by laser interferometry

High-accuracy dimensional measurements by laser interferometers require corrections because of diffraction, which makes the effective fringe-period different from the wavelength of a plane (or spherical) wave $\lambda_0$. By using a combined X-ray and optical interferometer as a tool to investigate diffraction across a laser beam, we observed wavelength variations as large as $10^{-8}\lambda_0$. We show that they originate from the wavefront evolution under paraxial propagation in the presence of wavefront- and intensity-profile perturbations.Comment: preprint, 10 pages, 6 figures, submitted to Optics Expres

Bayesian estimate of the degree of a polynomial given a noisy data sample

A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a crucial role and the model choice can have a significant impact on the result. In this paper, the problem of identifying the most appropriate model is formulated and solved in terms of Bayesian selection. Besides, probability calculus is the best way to choose among different alternatives. The results obtained are applied to the case of both univariate and bivariate polynomials used as trial solutions of systems of thermodynamic partial differential equations.Comment: 10 pages, 5 figures, submitted to Metrologi

The fundamental constants of physics and the International System of Units

Air Canada managed to have a passenger aircraft run out of fuel in mid-air due to confusion about metric units (Stephenson in Mars climate orbiter mishap investigation board phase I report, NASA, 1999), and NASA lost an entire spacecraft due to a misunderstanding amongst engineers about the units used in the propulsion system design (Witkin in Jet's fuel ran out after metric conversion errors, The New York Times, 1983). Measurements only make sense if the units are correct and well-defined. A unit of measurement is a definite magnitude of a quantity, defined by convention or law. Any other quantity of that kind can then be expressed as a multiple or submultiple of the unit of measurement. The Egyptians used the Farao as definite magnitude, while many years later, the french revolutionists introduced the earth as a reference and laid the foundations for the modern decimal system. Since recently, we have a truly universal and stable system that uses physics's natural constants and laws to define the base units of measurement. This paper explains how this new concept works and how it is implemented in practice