arXiv-phys 15 February 2017
Is the current CCU Draft 2016b of the 9th SI Brochure scientifically and
formally satisfactory? An example of simpler SI definition
Franco Pavese, Torino, Italy
Abstract
This v4 includes a critical review adjourned to the CCU Draft 2016b of November 2016 of the 9th
SI Brochure in the light of four basic principles that a modern system of units should follow, and a
proposal for the text of the CGPM Resolution on the revised SI, intended to resolve the problems
found.
The contents of the previous versions were: v1– discussion of the role of constants (called
fundamental until 2015) in the proposed New SI formulation of the definition of the International
System of Units, namely in the present official documents and in some relevant literature; v2– focus
on how the stipulation of the numerical values of the constants is obtained, according to the specific
features of measurement units, arising some special problems, not all cleared, that the stipulation of
a fundamental constant can place when it becomes part of the definition of the New SI and of a base
unit of it. Some reasons were discussed why it was urgent that these basic issues were clarified; v3–
specific critical review of the text of Sections 1 and 2 of the CCU 2016a Draft of the 9th SI
Brochure on the SI, published on the BIPM website on January 4, 2016; though that draft was
found advanced with respect to the CCU 2013 Draft, it is shown how the description of the complex
structure of the new definition may still be difficult to be clearly caught even by informed readers,
while most users might found themselves lost about their tasks needed to implement the new
definition.
1 Introduction
On November 10, 2016 the BIPM made public the last CCU Draft of the 9th Brochure of the SI
[CCU 2016], containing the last modifications of the proposal to the CIPM for approval in 2018 by
the CGPM.
It contains a change of about 10% of the text, but the most critical contents—Sections 1 and 2—
were only marginally modified.
At this stage of the approval process, and with the intention of keeping firm the future schedule
until fall 2018, it is now worthwhile an analysis of the possible reasons why the Draft 2016 (issued
by BIPM on 15 December 2015) [CCU 2015] was not modified in basic issues, and a comment
about the main remaining criticalities, starting from a number of critics that have already been
raised on that subject matter in published papers in recent years [Pavese 2016a, b, Pavese and
Charki 2016 and references herein; Mari and Pavese 2016; Mari et al. 2017].
A modern system of units such the SI should be constructed according to some basic requirements.
The units should be:
1. constant in time and space;
2. organised in a rational system;
3. easy to realise with high precision;
4. accessible to everybody.
Some of these requirements are explicitly indicated in the Metre Convention [Metre Convention]
and in the present Brochure of the SI [SI 8th]. For a full illustration of them see [Pavese 2016a,c;
Mari et al. 2017].
1
arXiv-phys 15 February 2017
2 General overview
One can summarise the reasoning and the rational underlying the proposed new definition of the SI
as follows:
(0) Starting point: use of substance-free constants of nature for defining the new system of units.
Constraint: ensure the continuity of these units with respect to the ones of the previous system;
(a) By using the present system of units (in the following indicated as ‘present-SI’) and modern
experimental methods, the scientific community was able to improve the precision of the
determination of the numerical values of constants of physics and chemistry.
Let us indicate the numerical results as
{const} = XXX XXXx(y)
(1)
where the symbol X replaces the numerical digits exactly known at present and the symbol y
indicates the uncertainty u associated to the right-most evaluated digit, x.
The uncertainty of several of these constants was lowered in recent years by orders of magnitude, so
that, by means of the analysis performed by the CODATA [CODATA], the degree of consistency
of the set of constants is now considered sufficiently close to the best level of uncertainty carried
out by the modern realisations of metrological standards of the most important quantities subjected
to measurement;
(b) The above levels of the relative uncertainties are such to allow the decision be taken that the
present best numerical values of the constants can act as warrants of the fact that future standards
will respect the fundamental property of invariance in time of the respective units realised by them;
(c) In addition, the choice of using constants of nature acts as a warranty of invariance in space;1
(d) As a consequence of that decision, a set of constants “have been identified as the best choice
taking into account the previous definition of the SI based on seven base units and the progress in
science” [CCU 2016];
(e) Their numerical values are considered to be the best ones presently available, and they were
chosen to be the candidates to become the ‘conventional’ values in the revised SI definition.
Therefore, after stipulation, they become:
{const*} = XXX XXX
(2)
where * indicates here a constant with stipulated numerical value and the symbols X indicate the
exact numerical digits that are stipulated, identical to those in expression (1). One should notice
that, with the omission of the uncertainty in that description, also the digit x affected by it is
omitted, with respect to description (1).
(f) The fact that these numerical values are valid only as the “values of these defining constants
expressed in the units of the” present-SI, entails the fact that the system of units of the present-SI
1
The CCU Drafts state: “The definition of the [new] SI units is established in terms of a set of seven defining
constants”. Constancy is satisfied according to the declaration: “… the realizations are separated
conceptually from the definitions, so that the units can, as a matter of principle, be realized independently at
any place and at any time”.
2
arXiv-phys 15 February 2017
and their distinction in base- and derived-units requires to be maintained intact in the revised SI,
though they now retain only the function corresponding to their definition in the VIM [VIM]. This
is the only valid reason for that decision. Proposals such the one in [Quincey and Brown 2016]
cannot be taken into consideration. The comment added in [CCU 2016] about the base units and the
ISO standard on the ISQ is totally irrelevant;
(g) The above convention (2) replaces in the revised SI all the conventional numerical values of
constants indicated in the present-SI for “artefacts …, specific physical state …, idealized
experimental prescriptions …, or constants of nature …” [CCU 2016];
(h) Thus, some of the previous units (indicated with 0 in the following) become uncertain:
{IPKo} = 1.000 …x(y); {TPWo} = 273.160 …x(y); {µ0,o} = 2.000 …x(y) × 2π ·10–7
(3)
where the dots indicate other digits today known exactly equal to zero, and x(y) has the same
previous meaning.
(i) Since the numerical values of the constants are those obtained by using the units of the presentSI, those new uncertain values—no more in the definitions—remain consistent with the new
condition set by the use of the constants, at least at the moment when the new definition is issued,
and until evidence will become available that they are not anymore consistent: they still ensure the
consistency (“metrological compatibility” [VIM]) of the old with the new units. This means that the
so-called “principle of continuity” is the respected, within the former uncertainties associated to the
results obtained with the present-SI;
(j) In [CCU 2016] this is formulated as: “preserving continuity, as far as possible, has always been
an essential feature of any changes to the International System of Units” (in upright style the text
added to Draft 2016 [CCU 2015]—see comment herein after in (j1) of the next section).
(k) Clause (f) does not mean that the definition of the base units should remain intact. In the revised
SI, the cause and effect sequence is inverted: since the numerical values of the constants are
originating from the present-SI units, the latter become, in the revised SI, expressed in terms of the
stipulated constants. That places constraints in the choice of the constants indicated in (d) and of
their number;
(l) The set of units expressed by the constants cannot be the same set of the base units, to avoid
incurring in a circular reasoning. That is the reason why in Table 1 of [CCU 2016] the units for the
seven constants are: Hz, m s–1, J s, C, J K–1, mol–1, lm W–1;
(m) The base units are thus redefined.
The second is expressed in the unit Hz, “which is equal to s–1”; 2
The metre is expressed in terms of the constant c, and specifying “where the second is defined in
terms of the caesium frequency ΔνCs”;
The kilogram is expressed in terms of h, and specifying “which is equal to kg m2 s–1, where the
metre and the second are defined in terms of c and ΔνCs”;
The ampere is expressed in terms of e, and specifying “which is equal to A s, where the second is
defined in terms of ΔνCs”;
2
In [CCU 2016] the specification of [CCU 2015] “, for periodic phenomena” was cancelled, as needed
[Pavese 2016a].
3
arXiv-phys 15 February 2017
The kelvin is expressed in terms of k, and specifying “which is equal to kg m2 s-2 K-1, where the
kilogram, metre and second are defined in terms of h, c and ΔνCs”;
The mole is expressed in terms of NA, i.e. in terms of mol–1;
The candela is expressed in terms of Kcd, and specifying “which is equal to cd sr W-1, or cd sr kg-1
m-2 s3, where the kilogram, metre and second are defined in terms of h, c and ΔνCs”;
(n) Then the derived units are defined as in the present-SI (except a distinction between frequencies
and angular frequencies).
3 Critical analysis of CCU Draft 2016b
Concerning the above clauses, one should notice a number of issues:
(f1) The full sentence in [CCU 2016] is “the exact values of these defining constants expressed in
the units of the SI”, modified from “the units of these defining constants” in [CCU 2015]. However,
the values of a constant can only be qualified as “invariant”, not as “exact”. In addition, to which SI
the sentence is referring to? Necessarily to the present-SI, not to the revised one, whose units are
said to be expressed by the constants in [CCU 2015, CCU 2016].
(f2) Actually, basing the rational for using the base units in the revised SI based on an ISO standard
means inverting the common hierarchy status of the ISO standards with respect to the definition of
the SI as an outcome of the Metre Convention.
(h1) In future, the {IPKo} could be found lower than 1, and in {µ0,o} the first factor could be lower
than 2;
(h2) for the unit of length, the same constant c is used in the revised SI that was already stipulated in
1983;
(h3) for the unit of time the same “specific physical state” ΔνCs is used in the revised SI that was
already stipulated in 1967;
(h4) for the unit of amount of substance the same numerical value is attributed to the Avogadro
constant in the revised SI that was already stipulated in 1971;
(h5) for the unit of luminous intensity the same physiological constant Kcd is used in the revised SI
that was already stipulated in 1979;
(j1) Should consistency be ensured in the revised SI to an uncertainty level higher than the one
obtained with the present-SI—as at present happens for the electrical unit [Bronnikov et al. 2015]—
this fact should be explicitly indicated and quantified in the new Brochure;
(l2) Having cancelled in [CCU 2016] the specification in terms of base units existing in [CCU 2015]
is not sufficient. For full clarity, the units in which the constants are expressed should be indicated
with their specific name, as done in [Newell 2014]. That should involve also their formal definition
reported just above Table 1 in [CCU 2016], where the definitions should instead use “units of
frequency”, “units of speed”, “units of action”, “units of electrical charge”, “units of heat capacity”,
“units of reciprocal mole”, 3 “units of luminous intensity”, because at this stage of the text the base
3
For the reciprocal mole that solution remains doubtful: IUPAC should be entitled to indicate an expression.
4
arXiv-phys 15 February 2017
and derived units are not yet re-defined in the revised SI [Pavese and Charki 2016]. The numerical
value associated to each of these units is 1;
(m1) For some base units, the definition is not consistent with the previous principles and with the
concept flow.4
For the metre, “when expressed in the unit m s–1, where the second is defined in terms of the
caesium frequency ΔνCs” should be spelled instead “when expressed in the unit of speed, m s–1,
where the second is defined above”;
For the kilogram, “when expressed in the unit J s, which is equal to kg m2 s–1,which is equal to kg
m2 s–1, where the metre and the second are defined in terms of c and ΔνCs” should be spelled instead
“when expressed in the unit action, J s, which is equal to kg m2 s–1,wich is equal to kg m2 s–1, where
the metre and the second are defined above”;
For the ampere, “when expressed in the unit C, which is equal to A s, where the second is defined in
terms of ΔνCs” should be spelled instead “when expressed in the unit electrical charge, C, which is
equal to A s, where the second is defined above”;
For the kelvin, “when expressed in the unit J K–1, which is equal to kg m2 s-2 K-1, where the
kilogram, metre and second are defined in terms of h, c and ΔνCs” should be spelled instead “when
expressed in the unit of heat capacity, J K–1, which is equal to kg m2 s-2 K-1, where the kilogram,
metre and second are defined above”;
For the candela “when expressed in the unit lm W–1, which is equal to cd sr W-1, or cd sr kg-1 m-2 s3,
where the kilogram, metre and second are defined in terms of h, c and ΔνCs” should be spelled
instead “when expressed in the unit luminous intensity, lm W–1, which is equal to cd sr kg-1 m-2 s3,
where the kilogram, metre and second are defined above and the sr is defined in Section 2.2.4”;
(m2) From [Pavese 2016a]: “As to the degree Celsius, having the New SI eliminated to constraint
for the numerical value of the triple point of water to be 273.16 K exactly, the equation ‘t/°C = T/K
– 273.15’ cannot hold anymore if the numerical value 273.15 is kept exact, because of the statement
‘The unit of Celsius temperature is the degree Celsius, symbol °C, which is by definition equal in
magnitude to the unit kelvin’ [CCU 2016]. If the kelvin temperature value of the triple point of
water is no more 273.16 exactly, also the numerical value 273.15 cannot be exact. In turn, should
instead the latter be taken exact, the unit degree Celsius cannot be anymore by definition equal in
magnitude to the unit kelvin”
(m3) The relationship between some of the base units and the constants is multidimensional. In
principle, when multi-dimensionality occurs, i.e. when measurements of the value of a constant
involve quantities with different dimensions, one can satisfy the condition of consistency of the
results with the stipulated values of the constants with several different sets of numerical values,
whose combination results in the same numerical result. This would entail a non-uniqueness of the
units. However, a simple check of the role that each quantity plays on the numerical value of each
constant (expression (1)), shows that only one constant dominates the uncertainty of that value (y in
expression (1)): for the kelvin, the contributions to the uncertainty of ΔνCs and h are not significant
(utot = 4.16·10–7 taking them into account, compared with 4.15·10–7 for k only); similarly for the
kilogram (utot = 3.01·10–48 instead of 2.97·10–48 for h only); and, for the ampere (utot = 3.23·10–12
instead of 3.22·10–12 for e only), for the candela (utot = 1.68·10–18 instead of 1.58·10–18 for Kcd only);
and for the metre (utot = 9.64·10–11 instead of 9.53·10–11for c only).5
4
See the Appendix for an alternative way to solve the problem.
There is a position pretending that, since the values of the constants are stipulated, one could not anymore
take anymore in any kind of consideration the uncertainties associated to the original uncertain values. This
position does not account for the fact that the stipulation is a convention that cannot cancel the uncertainties
associated to the values originating by their experimental origin and that can still be necessary for other uses
of the constants.
5
5
arXiv-phys 15 February 2017
Thus, in the implementation of primary methods, i.e. those having at least one of those constants in
their experimental equation (the model), it is unlikely that the ‘secondary’ constants will contribute
in a critical manner to the results.
4 Summary of omissions found in the present drafts and some possible remedies
Partly due to the ambiguity or lack of consistency of the present text [CCU 2016], the proposed
revision of the SI shows some critical lacks of clarity, especially in respect to its implementation.
4.1 Units of the revised SI
As indicated in Section 3 (f1) and (l2), the explicit distinction between the constants’ units and the
base/derived units is omitted, leaving an apparent conceptual conflict in the definition about this
basic issue. An example of this fact is the title of Section 2.2 “Definitions of the SI units”
describing the base units. In fact, there is an irresolvable conflict between indicating in the
definition of the SI (i.e. of the constants) numerical values that can only be associated to the base
units set, and the need to use the constants units that are a different set. The issue is fully discussed
in [Mari et al. 2017] and the possible solution is summarised here.
The conceptual roadmap should follow a set of steps, based on the concept that the revised SI,
contrarily to the present-SI is based on the two distinct frames, (i) of the constants and (ii) of the
base units (shown, as an example, for only three quantities):
“D5¨. The SI is the system of units in which:
(i) the unit of duration6 is the second, symbol s, the unit of length is the metre, symbol m,
and the unit of mass is the kilogram, symbol kg;
(ii) the frequency ΔνCs is kΔνCs s–1, the speed c is kc m s–1, the action h is kh kg m2 s–1;
(iii) then the second is kΔνCs ΔνCs–1, the metre is kc–1 c s, and the kilogram is kh–1 h s m–2;
(iv) the numerical value kΔνCs is 9 192 631 770, the numerical value kc is 299 792 458, and the
numerical value kh is 6.626 069 3 × 10−34 “[Mari et al. 2017].
where it is clear that only under frame (ii) one can introduce the (stipulated) numerical values,
which act as the conversion factors between the two frames.
4.2 Structure of the revised metrological hierarchies
In the present-SI, according to the Metre Convention, there is no hierarchy between any two NMIs
who have realised the definitional methods of the base units (see (g) in Section 2). In fact, in the
case of the kilogram, depending on a unique material standard, the IPK, the hierarchy is avoided by
assigning the role of maintaining the IPK to an international body, the BIPM.
In [CCU 2016] there is not a clear statement about whether in the revised SI that would translate
into the requirement to realise the constants or not.
On one hand, such a translation would demand to most of the present NMIs now standing at the top
of the international hierarchical pyramid an effort that is incommensurably stronger than the present
one, and unreachable or not convenient for many of them.
On the other hand, not requiring that effort, and allowing for only realisations within the “mises en
pratique” would void the new definition, as it is spelled out at present, at least unless the task of
maintaining the reference realisation of all the relevant constant would be assigned by CGPM to the
BIPM.
6
“The reference should be to duration, indeed, not time, which is not a quantity. Exactly in the same sense
the metre is, correctly, the unit of length, not space.” [Mari et al. 2017]
6
arXiv-phys 15 February 2017
As illustrated since 2014 in [Pavese, 2014], unless a solution is explicitly indicated in the revised SI
definition many NMIs will lose their international top position in the hierarchical ladder
4.3 Primary realisations and “mises en pratique”
In [CCU 2016] the “mise en pratique” is referred to as it had the same status that it has in the
present-SI. That is not correct, as illustrated in [Pavese 2016, Pavese and Charki 2016].
In the present-SI, realisations of the “mise en pratique” allow only a lower hierarchical step with
respect to the realisation of the definitional method, and the so-called “primary methods” are simply
such as to their top-level accuracy.
The revised SI does not define any definitional method. As it is spelled out at present, the
equivalent of the previous requirement are realisations of measurement of the constants values.
Obviously, being the value of each stipulated, a realisation does not provide a value, but only the
stipulated one must be assigned by default. The fact that the realised value might be correct or not,
can only be possibly detected by means of inter-comparison (key comparisons of the MRA [MRA]
in this case), as it happens today, e.g., with the triple point of water (see, e.g., [Pavese 2016a]).
However, that is possible only for those methods which have at least a constant in their
experimental model: they, and only them, should be called “primary methods”, irrespective to the
uncertainty of the realisation.
Other methods do not contain such a quantity in their model (e.g., the ITS-90 for temperature),
though they can be traced to compatible constants values. For them, and only for them, the (lower)
status of realisations of the “mise en pratique” still stands, irrespective to the uncertainty of the
realisation.
This distinction is omitted in [CCU 2016], where all the implementations of the revised SI are
illustrated in Section 2.2.2 entitled “Practical realisations of the SI”, an incorrect term: “practical”
always indicates only a lower-rank realisation.
APPENDIX – A possible resolving solution for the revised SI definition
The proposed solution is based on the normal type of spelling a Resolution used by the CGPM, so
possibly be used by the CGPM also in its 2018 Resolution.
Considering that
a) The 2018 CGPM Resolution should define a revised SI;
b) The present SI was defined in CGPM Resolution 6 (1956), defining 6 base (then a 7th one and
several derived units some years later);
c) The 2018 Resolution will, almost certainly, refer first to the previous definition because the new
one is using elements of the previous one –it is not brand new,
the starting point for correctly resolving the sequence of the conceptual structure of the new
Resolution, while remaining on the same bases of the present Drafts, could possibly be spelled like
in the following simple way (in French because it is the official language):
“Le système pratique d’unités de mesure, le Système International d’Unités, SI, tell qu’il est défini
par la Resolution 6 de la 10me Réunion du CGPM (1954) et modifications successives, est
ultérieurement modifié de la manière suivante.
7
arXiv-phys 15 February 2017
Aux fins du SI, la valeur numérique des grandeurs constantes qui suivent n’a pas de l’incertitude
associée:
• pour la fréquence de la radiation non perturbée correspondant à la transition entre les deux
niveaux hyperfins de l'état fondamental de l'atome de césium 133 ΔνCs elle est 9 192 631 770 Hz,
• pour la vélocité dans le vide de la lumière c elle est 299 792 458 m s–1,
• pour la constante de Planck h elle est 6,626 XX ×10−34 J s,
... ” [similarly for the rest] 7
In this way, by anticipating the fact that the new is the previous SI with modifications, one resolves
the circularity that would be induced by indicating in it numerical values and thus their units,8
because the latter are unchanged, so they are known—and all numerical values are now stipulated,
like previously only those of ΔνCs, c, NA and Kcd .
Then the Resolution does not need to indicate anything else, except the new definition of the base
units, which can also be simplified:
“Les définitions des sept unités de base du système pratique d’unités de mesure en vigueur sont
abrogées et les définitions équivalentes qui suivent sont adoptées:
• La durée du second est égale à la durée totale du nombre de périodes corréspondantes à la valeur
de la fréquence de radiation ΔνCs de l’atome de césium 133 adoptée auparavant;
• La longueur du metre corresponds à la valeur adoptée de la vélocité dans le vide de la lumière c
avec la durée du second adoptée auparavant;
• La mass du kilogram corresponds à la valeur adoptée de la constante de Planck h avec la
longueur du metre et durée du second adoptées auparavant;
... “ [similarly for the rest in the same order] 7
Therefore the base units maintain only the function that the base quantities have in their present
definition in the VIM, clause 1.4 [VIM].
Finally, the Resolution should indicate the capacity delegated to the CIPM in the implementation of
the changes of the SI:
“La 26me Réunion de la Conférence Générale invite le CIPM à établir des instructions pour les
méthodes de référence courantes permettant d’atteindre aux valeurs numériques indiquées
auparavant avec une incertitude maximale de consigne en ce qui concerne les réalisations
primaires, ainsi que à ajourner périodiquement la mise en pratique de chaque unité de base avec
des méthodes correspondantes avec la meilleure approximation aux méthodes de référence.”
Everything else, including the rational of these changes and choices, should go into the 9th Edition
of the SI Brochure, which, as usual, must follow the same structure of the Resolution, and here
comes the rest of the above comments.
7
Assuming that they will similarly derive from those spelled as in Draft 2016b, or later—e.g., concerning
the mole [IUPAC].
8
The numerical value of the constants cannot be expressed until the units are chosen. By choosing the values
presently available, one implicitly also fixed the present units: this “continuity” [CGPM 2011] means
conversion factor kold,new = 1.000 …x(y), where the position of the digit x affected by the uncertainty y is the
one determined by the present experimental uncertainties—see Section 2 (a).
8
arXiv-phys 15 February 2017
References
[Bronnikov et al.2015] Bronnikov K.A., Ivashchuk V.D., Kalinin M.I., Khruscho V.V. v,
Kononogov S.A. and Melnikov V.N., On new definitions of SI base units. Why is the ‘atomic’
kilogram preferable, Measurement Techniques (english), May 2015, DOI 10.1007/s11018-0150674-6; arXiv:1410.7906v1 29 October 2014
[CCU 2015] CCU, New SI, Draft of 9th edition of the SI Brochure, issued on December 11 2015, in
Draft Documents on http://www.bipm.org/en/measurement-units/new_si/ (January 4, 2016).
[CCU 2016] http://www.bipm.org/en/measurement-units/new-si/#communication
[CGPM 2011] Resolution 1, 24th Meeting CGPM 2011, http://www.bipm.org/en/CGPM/db/24/1
[CODATA] http://physics.nist.gov/cuu/Constants/index.html , http://www.bipm.org/extra/codata /
[IUPAC] Definition of the mole (IUPAC Provisional Recommendation 201X), Recommendation
11-Jan-2017, R. Marquardt, J. Meija, Z. Mester, M. Towns, R. Weir, R. Davis and J. Stohner,
http://iupac.org/recommendation/definition-of-the-mole/
[L. Mari and F. Pavese 2016] L. Mari, F. Pavese, A conceptual roadmap for setting up a system of
units in the ‘New SI’ context. arXiv Physics.ed-ph 1604.00982, pp. 6; Journal of Physiscs Conf.
Series 772 (2016) 012011. doi:10.1088/1742-6596/772/1/012011
[Mari et al. 2017] L. Mari, P. Blattner, F. Pavese, Improving the understandability of the next
edition of the International System of Units (SI) by focusing on its conceptual structure,
arXiv:1604.00982v2 2 Jan 2017
[Metre Convention] http://www.bipm.org/en/worldwide-metrology/metre-convention/
[MRA] CIPM. Mutual recognition of national measurement standards and of calibration and
measurement certificates issued by national metrology institutes (MRA), 1999.
BIPM, Sèvres, http://www.bipm.org
[Newell 2014] D.B. Newell, A more fundamental International System of Units, Physics Today
67(7), 35 (2014); doi:10.1063/PT.3.2448. View online: http://dx.doi.org/10.1063/PT.3.2448
[Pavese 2014] F. Pavese, How much does the SI, namely the proposed ‘new SI’, conform the spirit
of the Metre Treaty?, ACQUAL 19 (2014) 307-314
[Pavese 2016a] F. Pavese, The New SI: some critical features and a critical review of the CCU 2016
Draft of the SI Brochure, Measurement (2016) online since 22 July 2016; 98 (2017) 325–338, with
Supplementary Information. Doi:10.1016/j.measurement.2016.07.058
[Pavese 2016b] F. Pavese, Some conceptual problems in the CCU 2016 draft of the New SI, Journal
of Physiscs Conf. Series 772 (2016) 012011. Doi:10.1088/1742-6596/772/1/012011
[Pavese 2016] F. Pavese, A. Charky, Some important features of the proposed new definition of the
International System of Units (SI) that the users should know about before 2018, IJMQE 7 (2016)
403–413 (http://www.metrology-journal.org/articles/ijmqe/abs/2016/04/contents/contents.html ,
free access)
[Quincey and Brown 2016] P. Quincey, R.J.C. Brown, The changing role of base units within the
revised SI: an opportunity to take dimensional analysis back to its roots, AQUAL 21 (2016)417–
420
[SI 8th] http://www.bipm.org/en/measurement-units/ , http://www.bipm.org/en/publications/sibrochure/
[VIM] BIPM (2008). International Vocabulary of Metrology—Basic and General Concepts and
Associated Terms (VIM) 3rd edn. http://www.bipm.org/en/publications/guides/
9