Table of contents

We address a difficulty in appreciating that the pair-difference chi-squared-like statistic (Steele et al2002 Metrologia39 269–77, Douglas and Steele 2006 Metrologia43 89–97) is truly unmediated (i.e. independent of any reference value), namely the incorrect thought that this aggregating statistic might merely be hiding a reference value that has the same chi-squared. We show that the equation for this reference value commonly has no real solution. Regarding pair-difference statistics as unmediated statistics conveniently avoids any complex reference value, and offers a stark simplicity that exactly captures the simplest way in which measurements are really used in practical chains of metrological inference.

A well-known test of consistency in the results from an interlaboratory evaluation is the Birge test, named after its developer Raymond T Birge, a physicist. We show that the Birge test of consistency may be interpreted as a classical test of the null hypothesis that the variances of the results are less than or equal to their stated values against the alternative hypothesis that the variances of the results are greater than their stated values. A modern protocol for hypothesis testing is to calculate the classical p-value of the test statistic. The p-value is the maximum probability under the null hypothesis of realizing in conceptual replications a value of the test statistic equal to or larger than the realized (observed) value of the test statistic. The null hypothesis is rejected when the p-value is too small. We show that, interestingly, the classical p-value of the Birge test statistic is equal to the Bayesian posterior probability of the null hypothesis based on suitably chosen non-informative improper prior distributions for the unknown statistical parameters. Thus the Birge test may be interpreted also as a Bayesian test of the null hypothesis. The Birge test of consistency was developed for those interlaboratory evaluations where the results are uncorrelated. We present a general test of consistency for both correlated and uncorrelated results. Then we show that the classical p-value of the general test statistic is equal to the Bayesian posterior probability of the null hypothesis based on non-informative prior distributions. The general test makes it possible to check the consistency of correlated results from interlaboratory evaluations. The Birge test is a special case of the general test.

We report on a micro-gravity survey of the laboratories where the LNE's watt balance experiment is being conducted, including the characterization of the Scintrex CG-5 relative gravimeter used for this study. The results of the survey are compared with a model of the gravity field generated by the local mass distribution. The ultimate goal is to transfer an absolute measurement of g from one room to another with minimal uncertainty.

We report on the first-ever use of a quantum ac source to calibrate a thermal transfer standard as part of the NIST calibration service for such devices, with reductions in calibration uncertainty of as much as an order of magnitude over traditional ac–dc transfer methods. We briefly describe the basic quantum ac calibration system, its operation and measurement results. An analysis of the uncertainties for the measurements is presented and plans for further development are described.

Several radiometric and photometric measurements depend on high accuracy area measurement of precision apertures. Some apertures have sharp edges and are generally measured optically. At the Precision Engineering Division of the National Institute of Standards and Technology (NIST), we have developed a contact fibre (fiber) probe for diameter and form measurement of micro-holes (holes of size 100 µm or larger). This probe exerts extremely small forces, under 5 µN, and can therefore be used on knife-edge apertures without causing edge damage. We have measured the diameter and roundness of three knife-edge and one cylindrical apertures with this probe. The uncertainty in diameter ranges from 0.06 µm (k = 1) to 0.17 µm (k = 1). The uncertainty contributions from the probing system and machine positioning are together only 35 nm (k = 1). The largest contributors to the diameter uncertainty are the overall form (sampling uncertainty) and surface finish (mechanical filtering due to finite probe size) of the aperture.

This paper describes three different techniques for fitting straight lines to experimental data and discusses the corresponding evaluation of uncertainty. The techniques are (i) traditional fitting by least-squares, (ii) a Bayesian linear-regression analysis and (iii) an analysis according to the propagation of probability density functions attributed to the points measured. The material is presented to clarify assumptions underlying the techniques, to highlight differences between the techniques and to point to difficulties associated with applying the techniques under current views of 'uncertainty analysis'. Considerable attention is given to the estimation of values of the function and not just to the estimation of parameters of the function. The paper gives a summary of many results of least-squares fitting, including some unfamiliar results for the simultaneous estimation of the unknown function at all points. On many occasions the unknown function will only be approximately linear, in which case we must define a unique unknown gradient to give proper meaning to our 'estimate' of slope. This can be achieved by defining an interval of interest and then applying a least-squares-type result.

This paper proposes to discuss some concepts whose importance is fundamental to any theory of measurement. From the epistemological point of view there is a very significant inconsistency in the concept of measurand contained in the GUM. According to the model adopted by the GUM, a particular measurand remains the same measurand after a change in its definition, notwithstanding the fact that new conditions had been included or other pre-existing conditions had been altered in the definition. And also notwithstanding the very probable fact that, in consequence, the uncertainty component associated with its definition had been changed. The problem that arises from this theoretical model is that a particular measurand is not completely characterized by a precise and unique definition. Instead, it is considered an 'ideal' utopian particular concept to which would converge a specific series of 'measurands' (more properly their definitions), continually redefined in an infinite succession. Such a theoretical basis seems very inappropriate: the model intends to determine the uncertainty of uncertainly defined particular measurands. Of great relevance is the proposal of a new definition for the concept of measurand, a concept that interfaces the realms of Metrology and experimentation. Other concepts have been created or redefined with sufficient precision and selectivity to consider some aspects that remain somewhat confused in the model of measurement currently applied.

Absolute ballistic gravimeters can measure the free-fall acceleration with an uncertainty of few parts in 10⁹. Typically, the vertical trajectory of a test body subjected to the gravity field is tracked using interferometric methods, and a mathematical model of the motion is fitted to the time–position coordinates in a least-squares adjustment. In this paper, we describe a non-linear regression analysis applied to the IMGC-02 transportable gravimeter, developed at the Istituto Nazionale di Ricerca Metrologica (INRIM). We show how the method yields an accurate estimate of the free-fall acceleration avoiding measurement of the vertical gradient.

In this paper we review the theory concerning the radiofrequency (RF) spectrum of a carrier phase modulated by a stochastic process with spectral density of the type |ω|^−α and 0 ⩽ α < 3. This problem is of particular interest in the fields of atomic frequency standards and, in general, in high resolution spectroscopy. We also extend the theory to non-integer slopes (α real) and examine the role of the low-pass filter shape in the RF lineshape, pointing out the peculiar behaviour of the Lorentzian filter. The singular features of the RF spectrum in the case of flicker phase noise are examined as well as the lineshape in the high- and low-noise limits. Analytical expressions for the RF spectrum are also given in terms of special functions for the white phase, flicker phase and white frequency noises.

This paper details the construction of a eutectic platinum–carbon fixed point (melting point approximately 1738 °C) at the Physikalisch-Technische Bundesanstalt (PTB) and its validation by comparison with the one constructed by a PTB guest scientist at the National Metrology Institute of Japan, AIST (NMIJ).

A high-temperature vacuum furnace was used to construct a metal–carbon eutectic fixed point of platinum–carbon alloys suitable for radiation thermometry or radiometry. The furnace and fixed-point filling procedure were first assessed for suitability by constructing a copper fixed point of the same dimensions. With the filling validated a platinum–carbon cell was constructed. This was then compared with the one previously constructed by the PTB in collaboration with NMIJ. The agreement between the two fixed points was (+45 ± 72) mK (k = 2), meeting the reproducibility requirements for platinum–carbon to be used as a reference standard.

The combination of a Watt balance, a calculable capacitor and a single-electron tunnelling device forms a triangle that yields a value for the single-electron charge quantum Q_S in terms of the SI coulomb. Importantly, this result is independent of the Josephson and quantum Hall effects, and thus avoids the possible confounding corrections from these two effects that arise in the traditional quantum metrology triangle. This new triangle can be used to test for corrections to the expected relation Q_S = e, where e is the elementary charge. Combining existing results for Watt balances, calculable capacitors and an electron counting capacitance standard yields (Q_S/e) − 1 = (−0.09 ± 0.92) × 10⁻⁶.

Unambiguous and consistent concepts and associated terms should govern the description of the results of chemical measurements. This is not yet the case as numerous international workshops have shown over the last decade and as the chemical literature amply and continuously demonstrates. A number of concepts and associated terms in measurement are discussed, which are used ambiguously in the daily work of field laboratories, in the chemical literature, in ISO Guides and Standards, in regulatory documents, etc. They illustrate the need for clarification of their definitions. The consistent use of the recently revised edition of the 1993 'International Vocabulary of Basic and General Terms in Metrology', henceforth (2007) called the ISO/IEC Guide 99:2007, 'International Vocabulary of Metrology—Basic and General Concepts and Associated Terms (VIM)', is a step in the direction of achieving this goal.

Based on the standing wave model of the macroscopically resting electron, classical electrodynamics and quantum mechanics, a theoretical relation for the fine structure constant α has been derived. It was found that . The ratio of the rest mass of the electron and its quantum mechanical fraction, m₀/m_m, was calculated to be 1.005 263 277, using a non-relativistic Hamiltonian function. With this new value the reciprocal of the fine structure constant α is obtained to be 137.035 999 252. At Harvard University a new experimental value of α has been derived from the measured anomalous magnetic moment of the electron and the QED calculation of this quantity (relative standard uncertainty 0.37 × 10⁻⁹). The relative deviation between our value and this one is 1.23 × 10⁻⁹, supporting the usefulness and validity of our model. According to our result α seems to be a real constant in time and space. Relativistic QED of a point particle in the four-dimensional (Minkowski) space and non-relativistic wave electrodynamics for a macroscopically resting extended electron with an internal energy flux in the ordinary (3 + 1)-dimensional space time were found to complete each other in the sense of wave–particle dualism.

A new design of the fixed-point cell that contains multiple metal elements in a single crucible has been introduced for fixed-point calibration of secondary thermometers such as thermocouples. A multicell with aluminium, silver and copper was fabricated and used for the calibration of a Pt/Pd thermocouple. The expanded uncertainties (k = 2) of the realization of the multicell were 0.07 °C, 0.12 °C and 0.24 °C, plus an additional term from the inhomogeneity of the thermocouple, for aluminium, silver and copper, respectively. These uncertainties are considerably smaller than those obtained from the method of calibration by comparison in similar temperature ranges. This proves the suitability of the metal multicells for the calibration of secondary thermometers.

An experimental determination of the effect of rotational skew in the alignment of the electrodes of a symmetrical cross capacitor shows that the capacitance as determined by the axial length is reduced by the skew. A theoretical model is introduced to explain the effect.

The pumping speed of a pump in an orifice flow standard was measured to enable calculation of the effective pumping speed in the calibration chamber. The main problems are as follows. (1) The pumping speed of a pump connected to a chamber of finite size is not unambiguously defined; different measuring arrangements lead to different values. It is necessary to measure the pumping speed of the pump in the same arrangement as for the orifice flow standard. (2) If this is to be a primary standard, gauges related to calibration of the gauge to another standard cannot be used for the measurement for the same range of pressures.

The necessary precision of the measurement was determined. The orifice method and the flowmeter method were tested directly in the arrangement for the orifice flow standard. These two methods were used to avoid the necessity of using gauges calibrated to another standard.

The pumping speed of the pump for the CMI orifice flow standard was measured with sufficiently low uncertainty, so that its effect on the uncertainty budget of the entire standard was negligible.