Instrumentation & Measurement Magazine 26-4 - 9

650 763.73 wavelengths in
vacuum of the radiation
corresponding to the transition
between the levels
2p10
and 5d5 of the krypFig.
1. The four strategies pursued for defining units: the case of length.
applications. First, objects at the anthropometric scale are usually
not completely stable, with the consequence that, once a
definition like
metre := length of a given prototype
is agreed, any change of the length of the prototype will result
in the change of the numerical values of all the lengths
measured in reference to that unit, even if the lengths as such
did not change (this could have been the case of the kilogram,
defined until recently as the mass of a given object, the
International Prototype of the Kilogram: in 1994, a verification
revealed that most copies of the Prototype appeared as if
they had gained some mass, despite their independent handling
and storage; plausibly, it was instead the Prototype that
had lost mass [11]). Second, defining a unit as the quantity of a
given object implies that all traceability chains must start from
that object, and therefore that all measuring instruments for
that quantity must be directly or indirectly calibrated against
it: this is operationally inconvenient and could generate political
struggles, given the power that the situation confers to the
owner of the object.
Second Strategy: Units as Constant Quantities
of Classes of Objects
With the aim of avoiding these problems, another strategy
has been developed, based on the consideration that some domain-related
theories may assert the existence of classes of
objects that in given conditions have constant, and therefore
stable, quantities. A unit can be then defined as one of such
constants, or, were the constant too far from the anthropometric
scale to be suitable for its expected use, as an appropriate
multiple or submultiple of the constant. In 1960 the CGPM
redefined the metre accordingly, as " the length equal to 1
June 2023
ton 86 atom " . The critical
point of this definition is
the assumption that the
wavelength of the chosen
radiation is constant,
whereas the numerical
value, 1 650 763.73, was
only chosen to guarantee
that the metre remained
the same length despite the
change of its definition.
With respect to the previous
one, this strategy has
an essential theoretical grounding, as its definition of the metre
assumes the constancy of a quantity, as indeed implied by
a theory.
Third Strategy: Units as Constant Quantities in a
System of Quantities
The previous two strategies assume that for each relevant general
quantity, like length, mass, duration, and so on, a unit is
independently defined. This is obviously possible, but also
very ineffective, once it is acknowledged that physics provides
us with a knowledge of the physical world in terms of a set of
general quantities mutually connected in a network through
relations that are either definitional or empirical, the latter
being physical laws (thus justifying the term " nomological
network " , where the adjective comes from the Greek " nomos "
meaning " law " ). Such a network is what the VIM calls a system
of quantities, the most important case being the International
System of Quantities, as documented in the ISO and IEC 80000
series of technical standards.
By exploiting the relations in a system of quantities, a more
sophisticated version of the previous strategy allows for the
definition of a unit as a function of constant quantities of different
kinds, and possibly of previously defined units. This
is how in 1983 the CGPM redefined the metre, " the length of
the path travelled by light in vacuum during a time interval
of 1/299 792 458 of a second " , where, once again, the numerical
value was chosen to guarantee that the metre remained the
same length.
This strategy adds a structural context to the theoretical
grounding of the second strategy, given that its definition of
the metre assumes both the relation, length = speed times duration,
and the constancy of the speed of all light beams in
vacuum and of the quantity according to which the second is
defined. It is then basing on this strategy that a system of units
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