Maintaining consensus for the redefined kilogram

Abstract

According to the 2013 recommendation of the Consultative Committee for Mass and Related Quantities (CCM), the upcoming redefinition of the kilogram based on the value of the Planck constant specifies that ‘ at least three independent experiments, including work from Watt balance and XRCD experiments, yield consistent values of the Planck constant with relative standard uncertainties not larger than ’, and that ‘ at least one of these results should have a relative standard uncertainty not larger than ’. The consistency condition is questioned by the most recent measurement results for the Planck constant. To nonetheless proceed with the redefinition of the kilogram, the CCM proposes in its 2017 recommendation that the results of an ongoing key comparison are used for a correction of future measurement results, to ensure the consistent dissemination of the redefined kilogram.Two corresponding correction procedures are presented and discussed. The procedures make different assumptions about the temporal behavior of potential inconsistencies and they are based on established models from statistics for meta-analysis. Simple formulas are derived which provide a reasonable approximation, and which illustrate the basic principles of the correction procedures. Potentials and risks in the application of these procedures are explored, and the procedures are applied to the most recent measurement results for the Planck constant. Only one of the two procedures produces sufficiently small uncertainties for corrected measurement results in the sense of the CCM 2013 recommendation. The procedures and their assumptions are discussed, and we critically assess the attempt to reestablish consistency in a redefinition of the kilogram through a statistical correction procedure. Finally, we draw some conclusions.