Instrumentation & Measurement Magazine 23-6 - 4

Fig. 2. A logo of the newly-revised SI showing the seven base units on the
outside ring and the seven reference constants on the inner ring. (Used with
permission from BIPM.)

Fig. 1. A Canadian national prototype kilogram, K50, in its storage jars. This
prototype is visually identical to the IPK.

From the outset, the SI has been based on the properties
of physical artifacts as the apex of traceability, whether it be a
cylinder of PtIR for mass, a bar of PtIr for length, the earth's rotation for time, or the thermodynamic properties of water for
temperature. Base units that have been introduced more recently may be less obviously dependent on physical artifacts,
but they generally are not independent of the units for mass,
length and time. Indeed, our system of units is hierarchical in
nature, and thus, the units are ultimately traceable to the properties of physical artifacts or materials.

The 2019 Revisions to the SI
The comprehensive revision to the SI that came into effect on
May 20, 2019 completes the progressive elimination of the
properties of these physical artifacts from the apex of traceability and replaces them with a set of fundamental reference
constants. These reference constants are believed by science to
be invariant in time and space and they are universally accessible (Fig. 2). There is not a simple one-to-one mapping of the
properties of the physical artifacts and the fundamental reference constants, but combinations of these reference constants
map onto all of the units defined by the older artifacts.
This removal process has been going on for some time. The
unit of time interval was changed from astronomical measurements of the earth to the hyperfine splitting of 133Cs in 1967,
heralding the age of "atomic time." The meter was defined
with respect to the second and a fixed value of the speed of
light in vacuum in 1983, enshrining the principles of special
relativity into the heart of our measurement system. But the
4

kilogram and the kelvin, and indirectly the ampere and the
mole, were still based on the properties of physical artifacts until this latest revision.
The revised SI exactly fixes the values of the following
seven defining constants [2], [5], [6]:
the hyperfine transition freΔνCs = 9 192 631 770 Hz
quency of 133Cs
c = 299 792 458 m/s
speed of light in vacuum
Planck constant
h = 6.626 070 15 × 10−34 J/ Hz
elementary charge
e = 1.602 176 634 × 10−19 C
Boltzmann constant
k = 1.380 649 × 10−23 J/K
NA = 6.022 140 76 × 1023 mol−1 Avogadro constant
luminous efficacy of 540 × 1012
Kcd = 683 lm/W
Hz radiation
The values and use of c, ΔνCs, and Kcd had already been established within the SI before 2019 and this has made the recent
change more manageable. Note again that the units of the fixed
constants do not all match up with individual SI base units:
there is not a simple one-to-one correspondence, since the
equations of physics are also now embedded in our system.
The mole is defined uniquely by the Avogadro constant, but
obviously other units are also dependent on the second, like
the meter (c / ΔνCs) and the ampere (e × ΔνCs). To understand
how these fundamental constants are inter-related with our
measurement units, it is necessary to be aware of some aspects
of fundamental constants [5]-[8].
Consider the ordering of the fundamental physical constants of nature by their relative uncertainties with the smallest
first. The Rydberg constant, R∞ , is first at 5.9 × 10−12, followed by
the fine structure constant, α, at 2.3 × 10−10 [7]. It is expected that
this ordering will persist for some decades into the future and
that consequentially, their very small uncertainties can be used
to relate various other constants with minimal uncertainty. For

IEEE Instrumentation & Measurement Magazine

September 2020

Instrumentation & Measurement Magazine 23-6

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