The International System of Units—a case for reconsideration

Abstract

The International System of Units (SI) follows a concept that goes back to Maxwell. At that time, a logic sound foundation of mathematics was not yet available. This has lead to concepts and terms that are contradictory and in conflict with today's standard mathematical concepts. The inconsistencies that have evolved in metrology due to the lack of appropriate notions are pointed out. This is most important, as the metrology is a field that is internationally well organized under the umbrella of the Meter Convention, an international treaty for acting on all matters relating to units of measurement. Committees and working groups under the Meter Convention have a leading role in the elaboration of important metrological guides, among others the International Vocabulary of Metrology. Therefore, it is highly desirable that their publications use well-founded concepts and terminology. It is consensus that it is desirable to find a system of units on invariant properties of nature and not on human artifacts, e.g., the prototype of the kilogram. However, the current proposals to improve that are in conflict with standard scientific concepts. It is shown in the paper how these inconsistencies can be avoided. The argumentation is based on the interpretation of numbers developed by mathematicians like Cantor, Dedekind, Peano, and others that have led the logic foundation of mathematics with set and number theory. This foundation excludes dogmas that have been forwarded in the last century under the umbrella of the Meter Convention.

No prospect for change

“…• Complexity, incomprehensibility to users, unteachability and incommunicability [16][17][18][19][20][21][22][23][24]. • Lack of robustness, relevance, practicality and adaptability in a closed and irreversible system [17,[19][20][21][22].…”

“…The resolve of the proponents of the new SI to ignore or misrepresent those concerns is disturbing indeed and is raising serious questions regarding governance of the Treaty of the Metre. The March issue of this journal, ACQUAL [15], in many articles, raised many questions concerning the treatment of chemical measurements and the principles of the new SI [16][17][18][19][20][21][22][23][24]. None have been convincingly addressed by the proponents of the new SI, despite repeated invitations to do so.…”

“…• Lack of robustness, relevance, practicality and adaptability in a closed and irreversible system [17,[19][20][21][22]. • Inability to add new kinds of quantities that may become important in the future (such as biological activity or information) as human understanding grows [17].…”

Criticisms of the proposed “new SI”

“…1. The proposed redefinition of the mole is confusing, unteachable, and/or just wrong [2][3][4][5][6]. 2.…”

“…7. The proposed redefinitions of the SI units are inconsistent and/or circular; for example, the unit amount of substance involves the kilogram, the second is defined in terms of the kelvin and the kelvin in terms of the second, and without the availability of the derived real units joule and watt, the kilogram, kelvin, and candela cannot be realized [2,5,6]. 8.…”