Instrumentation & Measurement Magazine 26-4 - 10

fundamentalsmeasurement continued
of
is an actual system and not only a list of quantities: for example,
the SI includes some base units (the metre, the kilogram, the
second, ...), from which all remaining units (the newton, the
joule, the watt, ...) are functionally derived.
Fourth Strategy: Units as Quantities Fulfilling a
Numerical Condition on Constant Quantities in a
System of Quantities
A straightforward next step of the structural and theoretical standpoint
underlying the previous strategy could lead to defining a
system of units by taking some quantities, chosen as constants according
to the best available theories, setting the value of each of
them to 1, and giving a name to them as the so-defined units. For
example, the charge of the electron could be set to 1 el, the speed of
light in vacuum to 1 li, Planck constant to 1 pl, and so on. Appropriate
definitions would be then stated in inverse form: " the el is
the unit of electric charge, defined by setting the numerical value
of the charge of the electron to be 1 in the unit el " , " the li is the unit
of speed, defined by setting the numerical value of the speed of
light in vacuum to be 1 in the unit li " , and so on.
While effective for some physicists, who indeed already
adopt units such as the electronvolt instead of the joule, this
would be hardly acceptable by the society at large-and, of
course, metrology is for the whole society, and not only top science-for
at least two reasons, both related to the quantities to
be chosen as defining constants. First, some of such constants
are instances of general quantities that are unusual in daily life,
like action in the case of Planck constant, and hard to understand
without sufficient background knowledge in physics.
Second, such constants are typically so small, like Planck constant,
or so large, like the speed of light in vacuum, with respect
to the anthropometric scale that values of quantities of daily
life objects would be cumbersome to handle because numerically
very large or very small.
However, these problems are not really critical, as the
previous strategies already taught us how to solve them. In
particular, the second problem can be easily solved by introducing
some appropriate numerical factors, so that for
example the unit of electric charge could be defined as " the
coulomb is the unit of electric charge, defined by setting the
numerical value of the charge of the electron to be 1.602 176
634×10-19
of the metre follows this blueprint, and it is only more complex
due to the fact that among the chosen defining constants
there is a speed and a duration but not a length: " the metre (...)
is defined by taking the fixed numerical value of the speed of
light in vacuum c to be 299 792 458 when expressed in the unit
m s-1
quency ΔνCs
, where the second is defined in terms of the caesium fre " .
Interestingly,
in a so-defined system of units, grounded on
a system of quantities and a set of defining constants, the distinction
between base units and derived units does not have
10
any functional role anymore. Consider, for example, that, were
" X " the name of the unit of speed and " x " its symbol, the definition
of X would be almost identical to, and in fact simpler
than, the one of the metre: " the X is defined by taking the fixed
numerical value of the speed of light in vacuum c to be 299 792
458 when expressed in the unit x " .
This developmental path, where a unit is defined as
1. the quantity of a given object (prototype-based definition,
as in the 1889 definition of the metre), then
2. the quantity considered to be constant for a class of
objects (constant-based definition, as in the 1960 definition
of the metre), then
3. a quantity functionally related to the quantities considered
to be constant for some given classes of objects
(functional constant-based definition, as in the 1983 definition
of the metre), then
4. a quantity functionally related to the quantities considered
to be constant for some given classes of objects
through some numerical factors and stated in inverse
form (inverse functional constant-based definition, as in the
2019 definition of the metre),
may be interpreted as a blueprint of the options towards the
structural guarantee of better and better intersubjective information
that a metrological system can provide to the society.
References
[1] L. Mari and D. Petri, " Measurement: knowledge from
information about empirical properties, " IEEE Instr. Meas.
Magazine, vol. 26, no. 1, Feb. 2023.
[2] ISO 1087:2019, Terminology work and terminology science -
Vocabulary, International Organization for Standardization, 2019.
[3] D. Petri, P. Carbone, and L. Mari, " Quality of measurement
information in decision-making, " IEEE Trans. Instrum. Meas., vol.
70, pp. 1-16, 2021.
[4] A. Frigerio, A. Giordani, and L. Mari, " Outline of a general model
of measurement, " Synthese, vol. 175, no. 2, pp. 123-149, 2010.
[5] L. Mari, M. Wilson, and A. Maul, Measurement Across the Sciences
- Developing a Shared Concept System for Measurement. Cham,
Switzerland: Springer Nature, 2021.
in the unit C " . Indeed, the 2019 CGPM definition
[6] JCGM 200, International Vocabulary of Metrology - Basic and General
Concepts and Associated Terms (VIM) (3rd ed.), Joint Committee
for Guides in Metrology, 2012. [Online]. Available: https://www.
bipm.org/documents/20126/2071204/JCGM_200_2012.pdf.
[7] E. Tal, " Calibration: modelling the measurement process, " Studies
in History and Philosophy of Science (Part A), vol. 65, pp. 33-45, 2017.
[8] Metrology in Short (3rd ed.), Euramet, 2008. [Online]. Available:
https://www.euramet.org/publications-media-centre/
documents/metrology-in-short.
[9] Quality Infrastructure - Building Trust for Trade, United Nations
Industrial Development Organization (UNIDO). [Online].
Available: https://www.unido.org/sites/default/files/2016-05/
UNIDO_Quality_system_0.pdf.
IEEE Instrumentation & Measurement Magazine
June 2023
http://www.bipm.org/documents/20126/2071204/JCGM_200_2012.pdf http://www.bipm.org/documents/20126/2071204/JCGM_200_2012.pdf https://www.euramet.org/publications-media-centre/documents/metrology-in-short https://www.euramet.org/publications-media-centre/documents/metrology-in-short https://www.unido.org/sites/default/files/2016-05/UNIDO_Quality_system_0.pdf https://www.unido.org/sites/default/files/2016-05/UNIDO_Quality_system_0.pdf
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