Instrumentation & Measurement Magazine 26-4 - 8

fundamentalsmeasurement continued
of
temperature of body A here and now = temperature of
body B there and then
(3)
(not dealing with measurement uncertainty for the sake of
simplicity).
Were values of quantities, like 23.4 °C, purely mathematical
entities, this inference would be a trivial consequence of the
transitivity of the equality relation. But, as argued in [1], values
of quantities are classifiers for quantities of objects, which
are empirical entities, as highlighted by the reference to a unit,
the degree Celsius in the example, in them. Hence, inference
(3) is valid until the quantity stated to be the unit is actually
the same everywhere and everytime, a condition that the VIM
calls metrological traceability, the " property of a measurement
result whereby the result can be related to a reference through
a documented unbroken chain of calibrations, each contributing
to the measurement uncertainty " [6]. In fact, as measuring
instruments need to be calibrated by means of measurement
standards, each standard is expected to realize a (quantity,
value of a quantity) pair, for example (a given temperature, 20
°C). This is obtained by comparing the quantity realized by the
standard with the quantity realized by another, already available,
standard, so that, for example, from
temperature of standard A = 20 °C
and
temperature of standard A = temperature of standard B
one can reliably infer that
temperature of standard B = 20 °C
a process that is also called calibration, now performed on a
measurement standard instead of on a measuring instrument.
The unbroken chain of calibrations mentioned in the definition
above relies therefore on a principle of delegation: any
measuring instrument is calibrated against one or more measurement
standards, and a measurement standard is usually
calibrated against another measurement standard, which is in
a " higher " position in such a traceability chain, where the concept
'metrological traceability chain' is in fact defined by the
VIM as a " sequence of measurement standards and calibrations
that is used to relate a measurement result to a reference "
[6]. The more a traceability chain for a given quantity is reliably
widespread in the society, the more the measurement results
produced by the instruments connected to that chain are traceable,
and therefore able to convey intersubjective information:
this justifies the importance of a both technically and organizationally
effective worldwide metrological system [8], as today
grounded on the National Metrology Institutes (like NIST in
8
the USA, PTB in Germany, NPL in UK, etc.) under the coordination
of the International Bureau of Weights and Measures
(BIPM) in the context of the Metre Convention. This is a critical
component of the so-called quality infrastructure, of which
metrology, together with standardization and accreditation, is
a pillar [9].
At the root of the entire system there must be a public scale
of the relevant quantity, where such a scale can be derived by
somehow defining a unit for ratio quantities, or a unit and a
zero for interval quantities, as it is the case of thermodynamic
temperature (whose SI unit is the kelvin) and thermometric
temperature (for example the Celsius scale, which is now defined
in reference to the kelvin, and in the past had its zero
defined in reference to the freezing point of water and its unit
as one hundredth of the difference between the boiling and the
freezing point of water) respectively [1]. Let us focus here on
the simpler and more usual case of ratio quantities, for which
a public scale is obtained by a unit with its multiples and submultiples.
For a measured value, like 296.5 K, to be able to
convey intersubjective information, the quantity that is the
unit - the kelvin in the example - must then be known to be the
same quantity everywhere and everytime.
If the concerned quantity is functionally dependent on
other quantities whose unit has been already defined, such a
functional dependence can be exploited to define the sought
unit. An obvious case is about frequency, defined as duration
to the minus one: once a unit of duration (the second, in the
SI) has been defined, the unit of frequency is immediately defined
as the unit of duration to the minus one (the hertz, in the
SI) (and note that there is nothing intrinsic in the direction of
this functional dependence, so that the argument could be reversed,
by defining the second as hertz to the minus one). But
of course this delegation process-defining a unit in reference
to somehow previously defined units-requires a starting
point. To this purpose, four strategies have been pursued in
the course of history [5]: the case of length is particularly clear
on this matter (Fig. 1).
First Strategy: Units as Quantities of Artifacts
The definition of a unit as the quantity of a given, suitably
manufactured, object, sometimes called a " prototype " or an
" artifact " , is the first historically adopted strategy. In 1889 the
first General Conference of Weights and Measures (CGPM)
so defined the metre, stating that " the Prototype of the metre
chosen by the CIPM (...) at the temperature of melting ice shall
henceforth represent the metric unit of length " (this and the
other definitions of the metre that follow are taken from the SI
Brochure [10]), where the mentioned prototype was in fact a
specially manufactured rod.
While conceptually simple, this strategy has at least two
drawbacks that have become more and more apparent with
the progressive globalization of measurement science and its
IEEE Instrumentation & Measurement Magazine
June 2023
Instrumentation & Measurement Magazine 26-4

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