Are the present measurement standards still valid after SI redefinition?

Abstract

The SI revision potentially places some basic concerns to all users, one being the validity of their present standards under the new definition. The paper compares what is spelled out in the new SI Brochure draft to what should be specified for practical implementation. The result of the analysis is uncertain for some level of implementation and some standards, with, on the other hand, some positive aspects also illustrated in the paper, not always found explicit in the formal texts.

Appendix: base unit definitions in the revised SI

Two examples from CCU draft 2016b [1] Ҥ 2.2.1 Base units:

"Mass: “The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 040 × 10⁻³⁴ when expressed in the unit J s, which is equal to kg m² s⁻¹, where the metre and the second are defined in terms of c and Δν _Cs"

"Amount of substance: The mole, symbol mol, is the SI unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles. It is defined by taking the fixed numerical value of the Avogadro constant N _A to be 6.022 140 857 × 10²³ when expressed in the unit mol⁻¹."

The IUPAC proposal to BIPM for the mole definition [12] is rather:

“The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 8Y × 10²³ elementary entities. This number is called the Avogadro number”.

where “The symbol Y signifies two as yet undecided digits which will be set by the CODATA …”. This author’s preference would have been “… called the Loschmidt constant, symbol L” (a real number), to avoid confusion with the Avogadro number N _A (the integer 602 214 08Y × 10¹⁴) and resolve the conflict “constant” vs. “number”. The conflict was already illustrated in [16, 17].

Actually, the five multi-dimensional base units (length, mass, electrical current, temperature and luminous intensity) should have their definitions partially spelled out in a way different from [1]. For example, for mass, where the kilogram is defined in terms of the base units kilogram, metre and second, one should better write (suggested changes in italics):

“… expressed in the unit of action when equal to kg m² s⁻¹, where the metre and the second are defined above”.

Here, “above” indicates a unit defined before that of the mass—there is a kind of hierarchy among the base units, recognised by the CCU: time, length, mass, electrical current, temperature, amount of substance, luminous intensity.

The suggested notation avoids the circularity occurring in [1] that consists of the following:

(Constant definition ([1] § 2.1) spells base units) ⇔ (Base unit definition ([1] § 2.1) spells constants)

For example, for mass:

• Constant definition in § 2.1: “the Planck constant h is 6.626 070 040×10⁻³⁴ J s”, so using present-SI units, defined only in § 2.2.1;

• Base unit definition in § 2.2.1: “expressed in the unit J s, which is equal to kg m² s⁻¹, where the metre and the second are defined in terms of c and Δν _Cs”, so referring to c and Δν _Cs, already defined in § 2.1.