Instrumentation & Measurement Magazine 26-1 - 11

length 

 and c: m E 2
The eV system mirrors its equations of physics as does the SI.
Someone well-versed in these equations could intuit the above
relations for mass length and time. Otherwise, the same results
can be obtained if the matrix formalism of Figs. 4 and 5
is adapted by replacing the gravitational constant G with E in
Fig. 4 and replacing the exponents below E with (-2, 2, 1). Two of
many consequences of adopting the eV system are: the velocity
of the electron in the Bohr model (6) is equal to α and Einstein's
famous equation is E = m; and there is no need to include c or c2
because the value of c equals 1 in this system. The fine-structure
constant is the same number as in all other unit systems.
The mass of a subatomic particle might then have been
c
measured in GeV (the mass of the Higgs boson was found to
be 125 GeV = 125 × 109
eV) but the result is reported in GeV/c2
[1] to facilitate conversion to mass in other systems of units.
Thus, a mass of 1 GeV in the natural system corresponds to
1.783...× 10−27
and divided by c2 [ =  ].
{ }2 m /s
c 
SI
Can We Conclude That the SI Is Now a
Natural System of Units?
The answer is no. The continuity conditions [5] imposed on the
seven exact numerical constants {Q}SI
of Table 1 have ensured
that any changes to the definitions of the kilogram, ampere, etc.
were imperceptible to most users compared to the units previously
defined in the various ways listed at the start of [1]. This is
a practice that was adopted more than a century ago. For example,
a kilogram as defined by (7) is still approximately equal to
the mass of 0.001 m3
of distilled water at its temperature of maximum
density (4 °C), which was the kg definition adopted in 1799.
Other differences between the SI and systems of natural units are:
◗ The kilogram (SI) is now defined by a particular combination
of three constants h, c, and ΔvCs
, but the combination
is not the mass of any particle found in nature. It is simply
the energy hΔvCs
frequency ΔvCsdivided by c2
/s2
in joules of a massless photon of
in m2
. A measurement in
kg of a physical mass must be traceable to h, c, and ΔvCs
using any suitable method [2], [7].
◗ There is no natural system of units that defines a unit of
time in a way that allows the exquisitely precise measurements
of both time and length that are a hallmark of the
SI [11]. This is not likely to change [8], although moves are
afoot to redefine the second in terms of a different type
of atomic clock so that time intervals can be measured
with even greater accuracy than can be achieved with the
cesium-133 clock.
◗ The SI has seven base units, whereas natural systems aim
to have " as few base units as possible " [1]. The eV system
has only one base unit, thanks to  and c having been
defined to have dimension 1.
February 2023
kg in the SI (GeV is converted to J [ = kg m2
2
s−2
]
eV ,and time (teV) in the eV system are derived from E,
11
eV   E,   , and 11
eV
E c
E
tE E
eV  
.
The SI [2] and the other systems of units discussed [1] have
always had very different ambitions. Nevertheless, the fact
that h and c are both defining constants of the SI brings the SI
close enough to systems of natural units that the remaining differences
are illuminating.
References
[1] N. van Remortel, " The nature of natural units, " Nature Physics,
vol. 12, p. 1082, Nov. 2016. [Online]. Available: https://www.
nature.com/articles/nphys3950.
[2] SI Brochure: The International System of Units (SI) 9th ed. (BIPM
2019). Distributed under the terms of Creative Commons
Attribution 3.0 IGO. [Online]. Available: https://www.bipm.org/
en/publications/si-brochure.
[3] E. F. Redish, " Using math in physics: 1. Dimensional analysis, "
The Physics Teacher, vol. 59, pp. 397-400, Sep. 2021.
[4] R. Davis, " From telegraphy to the revised SI [Basic Metrology], "
IEEE Instrum. Meas. Mag., vol. 20, pp. 39-42, Apr. 2017. [Online].
Available: https://ieeexplore.ieee.org/document/7919133.
[5] R. S. Davis, " How to define the units of the revised SI starting
from seven constants with fixed numerical values, " J. Res. Natl.
Inst. Stan., vol. 123, article 123021, 2018. [Online]. Available:
https://nvlpubs.nist.gov/nistpubs/jres/123/jres.123.021.pdf.
[6] N. Fletcher, G. Rietveld, J. Olthoff, I. Budovsky, and M. Milton,
" Electrical units in the new SI: Saying goodbye to the 1990
values, " NCSLI Measure J. Meas. Sci., vol. 9, pp. 30-35, Sep. 2014.
[Online]. Available: https://www.vsl.nl/sites/default/files/rtf/
ncsli-measure-2014-september-milton.pdf.
[7] E. Tiesinga, P. J. Mohr, D. B. Newell, and B. N. Taylor, " CODATA
recommended values of the fundamental constants: 2018, " Rev.
Mod. Phys., vol. 93, article 025010, Apr.-Jun. 2021. [Online]. Available:
https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=931443.
[8] P. J. Mohr, " Defining units in the quantum based SI, " Metrologia,
vol. 45, pp. 129-133, 2008.
[9] " Matrix multiplication, " Wikipedia (accessed 15 July 2022).
[Online]. Available: https://en.wikipedia.org/wiki/Matrix_
multiplication.
[10] SI Brochure, Appendix 2, " Mise en pratique for the definition of
the kilogram in the SI, " Consultative Committee for Mass and
Related Quantities. [Online]. Available: https://www.bipm.org/
en/publications/mises-en-pratique.
[11] SI Brochure, " Recommended values of standard frequencies, "
[Online]. Available: https://www.bipm.org/en/publications/
mises-en-pratique/standard-frequencies.
Richard Davis (M'73−LM'11) (richard.davis@ieee.org) began
his career in 1972 as a Postdoctoral Associate in the Electricity
Division of NIST, having received the Ph.D. degree in solidstate
physics from the University of Maryland, College Park,
MD, USA. He joined the BIPM in 1990, retired as Head of the
Mass Department in 2010, and was a Consultant to the BIPM
until 2019. He lives in France.
IEEE Instrumentation & Measurement Magazine
11

https://www.nature.com/articles/nphys3950 https://www.nature.com/articles/nphys3950 https://www.bipm.org/en/publications/si-brochure https://www.bipm.org/en/publications/si-brochure https://ieeexplore.ieee.org/document/7919133 https://nvlpubs.nist.gov/nistpubs/jres/123/jres.123.021.pdf https://ncsli.org/mpage/MJ_V9_A18 https://ncsli.org/mpage/MJ_V9_A18 https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=931443 https://en.wikipedia.org/wiki/Matrix_multiplication https://en.wikipedia.org/wiki/Matrix_multiplication https://www.bipm.org/en/publications/mises-en-pratique https://www.bipm.org/en/publications/mises-en-pratique https://www.bipm.org/en/publications/mises-en-pratique/standard-frequencies https://www.bipm.org/en/publications/mises-en-pratique/standard-frequencies

Instrumentation & Measurement Magazine 26-1

Table of Contents for the Digital Edition of Instrumentation & Measurement Magazine 26-1