There is a need to develop an unambiguous digital version of the International System of Units (SI), as required for information systems and distributed sensor networks. This leads to a reconsideration of the status of the non-SI units accepted for use with the SI. Here, the case of the non-SI units dalton (Da), neper (Np), bel (B) and decibel (dB) is considered.

Building confidence in the accuracy and global comparability of measurements requires the creation of a machine-actionable, unambiguous full digital representation of the SI. The SI has been used around the world as the preferred system of units since it was established in 1960 by a resolution of the General Conference on Weights and Measures (CGPM). The CGPM is an intergovernmental organization created by a diplomatic treaty called the Metre Convention, signed in Paris in 1875 by representatives of 17 nations. There are currently 64 member states and 36 associate states and economies. In almost all countries, the legislation on measurement units is nowadays based on the SI. Standardization bodies may specify further details for quantities, units, symbols and the rules for their application, e.g. in the ISO/IEC 80000 series of international standards. A key reference providing a list of factors to allow conversion between SI units and numerous non-SI units is the NIST

Beyond the proposal arising from the aforementioned SmartCom project, a significant highlight is the creation within the International Committee for Weights and Measures (CIPM) of a Task Group on the SI Digital Framework. The aim is to develop and establish a world-wide, uniform, unambiguous and secure data exchange format for use in IoT (Internet of Things) networks based on the SI described in the SI Brochure. In March 2023, the CIPM decided to establish a cross-sectional Forum on Metrology and Digitalization. Its agenda now includes establishing a unique SI Reference Point (SIRP), also available through machine-actionable interfaces, thus transporting the SI Brochure into the digital world. The unique SIRP would facilitate interoperability between systems like QUDT and UCUM. Irrespective of the unit representation system, all should lead back to a fully digital representation within the unique SIRP. The concept of what a kilogram is (or what a metre is) has been changing. The symbol m (for metre) should be accompanied by a timeline in order to be machine-interpretable, because there are different definitions of the metre: metre 1889, metre 1927, metre 1983, metre 1960 and metre 2018.

Since 20 May 2019, all SI units are now defined in terms of seven defining constants. The redefinition of the SI ended the decades-long coexistence of two systems of electrical units by fixing the values of the Planck constant,

The redefinition of the SI opened up improvements and new possibilities across the whole mass scale, especially in the range of atomic masses. With the kilogram defined in terms of the Planck constant, the realization of mass can be achieved at any desired scale level without the need to trace the measurements to a 1 kg mass. Employing atom interferometry, the measurement of the recoil velocity of an atom of mass

Table 1 shows the evolution of

Evolution of the relative standard uncertainties of

The SI Brochure refers to quantities defined as the ratio of two quantities of the same kind, e.g. refractive index. Such quantities are considered simply numbers, and the associated unit is the unit one, symbol 1. Of this large number of ratio quantities with the same unit (the number one), some additionally receive special names. Among them, let us now consider the logarithmic ratio quantities with units neper (Np), bel (B) and decibel (dB). The neper is based on the use of the neperian logarithm, while bel and decibel are based on the use of the decadic logarithm. They are currently considered in the SI Brochure as non-SI units accepted for use with the SI. In 1999, during the 21st General Conference on Weights and Measures (CGPM), a resolution was considered, proposing that the neper rather than the bel should be adopted as the coherent derived SI unit, mainly for mathematical reasons. In view of the doubts expressed, the matter remained open and was later approved in the 2001 CIPM meeting, with one abstention and one vote against (the latter by the author of this paper). After publishing further arguments (Valdés, 2002), the discussion was reopened. The CIPM then decided that both the neper and the bel remained as they were, maintaining until now the status quo of non-SI units accepted for use with the SI. The CIPM Consultative Committee for Acoustics, Ultrasound and Vibration took note that the industrial acoustical community was very happy to know that the neper would not be preferred over the bel. And 20 years after those discussions, the issue may now reappear, motivated by the digital transformation. In order to eliminate ambiguities as required by a Digital SI, the previously mentioned guide, D-SI, proposes to consider both the neper and the bel as silver class units, and with it also the decibel. This supposes to be allowed for the exchange of metrological data only for a limited transition period. The name silver “2024” suggests that this should happen rather soon.

With respect to the units neper, bel and decibel, the SI Brochure additionally includes the following explanatory note: “In using these units it is important that the nature of the quantity be specified and that any reference value used be specified”. In the field of acoustics, the decibel may be used with different power and field quantities that must be also specified. For instance, when we measure pressure levels in decibel (dB) relative to the SI unit pascal (Pa) and we measure pressure levels in decibel (dB) relative to 20

Logarithmic ratio quantities are framed within a more general logic, let's call it logic A, which considers the ratio of two quantities as a new quantity. Another logic could also be conceived, let's call it logic B, according to which dividing one quantity by another of the same kind merely expresses the number of times that one quantity fits into the other, resulting in just a number. This number may simply be called a coefficient, a factor or a ratio. Logic A or logic B? It's a matter of choice (Valdés, 2005). Other authors also addressed the question of choosing between what we call logic A or logic B. One of the critics of logic A (Emerson, 2004) wrote: “All dimensionless quantities now find themselves saddled with meaningless and unnecessary `units'. Their units are all of the same name 1,

Here we refer to a guide for the digital transfer of metrological data. It includes a medal system that categorizes metrological data into different quality classes of machine-readability. The ambiguity of accepting non-SI units for use with the SI is one of the problems to be resolved in order to avoid confusion in a highly machine-readable data representation. The referred guide proposes a change from units that are familiarly used by humans towards a communication using only SI-base units, supported by a transition period. Although the non-SI units dalton, neper, bel and decibel are all categorized as silver “2024” in that guide, we conclude that the transition period should not be the same for the dalton as for the other three. The removal of the non-SI unit dalton, opening the way to the kilogram also on the atomic mass scale, would not have a negative impact as before the redefinition of the SI, since the experimental uncertainties achieved in the most precise cases are now very close. Changing the current status of the logarithmic ratio quantities in the SI Brochure would also require considerably more time, until a digital version of the SI Brochure as a Unique SI Reference Point would be approved. Furthermore, in the transition under discussion from the current version VIM3 of the

The data that support the findings of this study are available upon request to the author if required.

The author has declared that there are no competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors.

This article is part of the special issue “Sensors and Measurement Science International SMSI 2023”. It is a result of the 2023 Sensor and Measurement Science International (SMSI) Conference, Nuremberg, Germany, 8–11 May 2023.

The author thanks Héctor Laiz for very useful and fruitful discussions.

This paper was edited by Sebastian Wood and reviewed by two anonymous referees.