Mutual consistency of independent kilogram realizations and the end of consensus-value dissemination (CCM Phase 3 transition)

Since the 2019 SI redefinition, the kilogram is realized from the fixed Planck constant by Kibble balances, joule balances, and the X-ray crystal density (XRCD) method, yet the experiments' results are not mutually consistent at the level of their claimed uncertainties. As an interim remedy, world mass dissemination runs through a periodically recalculated 'consensus value' (currently 1 kg − 12 µg relative to the pre-2019 IPK-based unit, with a fixed 20 µg standard uncertainty, in force since 1 March 2026). The problem is: will the primary realization experiments achieve — and be demonstrably shown to achieve — mutual consistency at the level of their individual uncertainties, so that internationally coordinated dissemination through the consensus value can end and each national metrology institute can disseminate the unit from its own validated realization (the CCM 'Phase 3' transition)? Resolving it requires simultaneously driving at least five experiments to relative standard uncertainties of order 10⁻⁸ with reproducible, mutually compatible results, keeping travelling-standard sorption and vacuum-to-air transfer effects subdominant, and correctly accounting for correlated uncertainty components within and between comparisons.

Background

Until 20 May 2019 the kilogram was defined as the mass of the International Prototype of the Kilogram (IPK), a platinum–iridium cylinder held at the International Bureau of Weights and Measures (BIPM) in Sèvres, France. The redefinition instead fixes the Planck constant $h = 6.626\,070\,15\times 10^{-34}$ J s exactly, so the unit can in principle be realized by any experiment linking mass to $h$. Two primary methods reach relative uncertainties of a few parts in $10^8$: the Kibble balance (also called watt balance; a two-step variant developed at the National Institute of Metrology, China, is the joule balance), which compares the weight of a 1 kg artefact with an electromagnetic force determined via quantum electrical standards, and the XRCD (X-ray crystal density) method, which determines the number of atoms in an isotopically enriched $^{28}$Si sphere from its lattice spacing and volume and converts it to mass using the atomic mass of silicon derived from $h$.

Before redefinition, the Consultative Committee for Mass and Related Quantities (CCM) organized a Pilot Study (2016, published 2018) comparing the then-existing realizations. It found agreement within uncertainties for four of five participants, with the vacuum-to-air transfer and buoyancy corrections not yet limiting, and it explicitly flagged the follow-up problems: a formal protocol for future key comparisons, the prospect that travelling-standard behavior (surface sorption, cleaning, air–vacuum cycling, transport) becomes limiting as uncertainties fall, the need to keep vacuum-to-air transfer subdominant, correlated uncertainty components between XRCD determinations (shared lattice-parameter, point-defect and isotopic inputs; a correlation coefficient of about 13% was estimated between the PTB (Physikalisch-Technische Bundesanstalt, Germany) and NMIJ (National Metrology Institute of Japan) results), and the continuity question raised by the eventual CODATA value of $h$ differing from the 2014 value used in the study. In 2017, however, the special adjustment by CODATA (the Committee on Data for Science and Technology, which publishes the internationally recommended values of the fundamental physical constants) found the eight available $h$ determinations mutually inconsistent (differences up to four standard uncertainties), so the CCM decided that dissemination would proceed through a consensus value until the dispersion of realization results becomes compatible with their individual uncertainties.

The resulting framework (CCM detailed note on the dissemination process, 2019) defines phases: traceability via the IPK (until 2019), then dissemination from a consensus value (CV) computed as the arithmetic mean of the key comparison reference values (KCRVs) of the three most recent key comparisons of realization experiments (CCM.M-K8 series, piloted by the BIPM, in which participants calibrate 1 kg travelling standards with their realization experiment and send them to the BIPM for mutual comparison against BIPM platinum–iridium working standards). A KCRV is the weighted mean of participant results; degrees of equivalence quantify pairwise agreement. The CV has been implemented three times (1 kg − 2 µg in 2021, 1 kg − 7 µg in 2023, 1 kg − 12 µg in 2026, always with 20 µg standard uncertainty). Transition to the final phase — dissemination from individual, sovereign realizations — is governed by explicit CCM criteria: (a) at least five consistent realization experiments achieving key-comparison results with relative standard uncertainty of 40 parts in $10^9$ or better, consistent with the KCRV, and stable across two consecutive key comparisons; (b) at least three of these with uncertainties of 20 parts in $10^9$ or less; (c) the consistent set must include two independent methods (e.g. Kibble balance and XRCD); and (d) the difference between the consensus value and the KCRV of the final key comparison must be less than 5 parts in $10^9$. Sorption here means adsorption/desorption of residual gas and water on artefact surfaces, which changes their mass between air and vacuum weighing and is measured with sorption artefacts (standards of different surface area).

Problem Statement

Determine whether — and establish the conditions under which — the primary realization experiments of the redefined kilogram (Kibble balances, the NIM joule balance, and XRCD silicon-sphere experiments) achieve mutual consistency at the level of their individual claimed uncertainties, such that the CCM criteria for ending consensus-value dissemination are demonstrably met and each participating national metrology institute may disseminate the SI mass unit from its own validated realization. Concretely, an answer must address: (i) whether at least five experiments can produce key-comparison results with relative standard uncertainties of 40 parts in $10^9$ or better, consistent with the key comparison reference value, and stable (equivalent) across two consecutive key comparisons, including at least three experiments at or below 20 parts in $10^9$ and at least two independent realization methods; (ii) whether the consensus value and the reference value of the decisive key comparison agree to better than 5 parts in $10^9$; and (iii) which residual systematic effects — experiment-specific offsets between Kibble/joule-balance and XRCD results (historically up to about 50 µg at 1 kg between the NRC (National Research Council Canada) and PTB Kibble-balance and XRCD results), travelling-standard surface sorption and air–vacuum cycling (observed at the 3–18 parts in $10^9$ level per realization cycle), and correlated uncertainty components within and between determinations — currently limit the agreement, with quantified corrections or uncertainty contributions demonstrating they are subdominant to the realization uncertainties.

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