IU14. IUPAC Interdivisional Committee on Nomenclature and Symbols (IDCNS)

Report to the 1999 IUPAP General Assembly

Report on recent Committee activities on behalf of IUPAP by Brian W Petley September 1998

1. Introduction

Metrology is a part of science that, at root, relies heavily on international agreement and convention. Examples are the definitions of the SI units and the SI as a whole, the vocabulary of measurement, and the method of reporting Type B uncertainties (including systematic uncertainties).

Advances in science and technology make it necessary to introduce new agreements. It is important that IUPAP plays its part in their production so as to safeguard the interests of those it represents, particularly since many Applied Physicists are subject to practices adopted by other organisations. IUPAP can only, of course, represent the interests of physicists when it is invited to do so and there will naturally be many cases where this is not possible.

As implied by part of the title of commission C2, there are three aspects to the measurement system: symbols, units, and nomenclature and these involve several different organisations.

The Consultative Committee for Units (CCU) was set up by the International Committee for Weights and Measures (CIPM). This committee is the main technical Committee advising the General Conference on Weights and Measures (CGPM). The CGPM is the organisation on which all countries that have signed the metre convention are represented. It has the responsibility for decisions concerning the SI units. The International Standards Organisation (ISO) has the responsibility for symbols, and nomenclature (Committee ISO:TC12 being the Committee concerned with this activity). This includes the names and symbols of the quantities used by physicists.

These Committees have led to a new Committee, the Joint Committee for Guides on Metrology. (JCGM). The purpose of the JCGM committee is to continue the production of recommendations in the form of Metrological Guides. These recommend practices that are commonly agreed between the participating organisations.

The participating organisations such as the ISO, OIML, IEC, then incorporate the Guides into their standards and procedures which often go on to become mandatory in the countries that these organisations represent. Some requirements are to be found in the contracts for research required of physicists in Universities - it is very easy, for example, for a contractor to slip in the phrase 'the research must be performed in accordance with ISO 9000' into a contract.

The first Guides were produced under the aegis of the ISO. Participating organisations include BIPM, ISO, IEC, IFCC, IUPAC, IUPAP, OIML. They have proved remarkably successful. These Guides are the International Vocabulary on Basic Terms in Metrology (the ISO: VIM), and the Guide to the Expression of Uncertainty in Measurement (the ISO: GUM).

The JCGM met in 1997 to constitute itself as a committee. The Committee has taken responsibility for future editions of the GUM and VIM, and also in the production of any further Guides where common agreement can be reached between the participating organisations.

The initial task of the JCGM is to produce revised editions of the GUM and VIM. Two Working groups have been set up, one to consider revisions of the VIM and another to consider the revision of the GUM. One advantage of the JCGM is that the ISO will now be able to produce ISO Standards which are based on the Guides and which will cascade into other ISO Standards before being adopted as national standards in countries throughout the world.

Taken together these organisations have a strong influence on the way that physicists make and report their measurements - so obviously strong IUPAP participation in their activities is desirable. Such participation, of course, involves compromise for physicists cannot expect others to be prepared to change their terminology unless they too are prepared to modify their own position. Equally, there is a huge range of requirements encompassing what physicists 'want' of the measurement system. It must be recognised that no system of units and quantities will satisfy all physicists all of the time.

2. The Joint Committee for Guides in Metrology (JCGM)

BWP has attended the meetings of the JCGM and many of the meetings of the earlier ISO Committee. Two JCGM Working Groups have been set up, one for the GUM and one for the VIM. The Working Group on uncertainties is constituted in a different way.

The Working Group on the VIM has held two meetings, in April and September 1998. BWP has attended both on behalf of IUPAP. The initial progress has been disappointingly slow, partly because the first few definitions affect so many subsequent ones. The definition of 'quantity' has caused particular difficulty. Physical quantity is also likely to have a different meaning in the future. There may be advantages for physicists if a physical quantity becomes a quantity used by physicists.

It is clear that there is a bedding down process as the new and earlier committee members re-think the purpose of the VIM and try to incorporate the reactions of users of the first edition. Some recursion of the decisions may be still necessary.

3. The Consultative Committee for Units

BWP has also attended the recent meetings of the Consultative Committee on Units as the IUPAP representative. The views and decisions of the CCU are forwarded to the Consultative Committee on Weights and Measures (CIPM) and, where necessary, thence to the General Conference on Weights and Measures (CGPM). The final stage is their incorporation in a publication: The International System of Units published by the International Bureau of Weights and Measures (BIPM). The seventh edition of this has been published recently. This publication forms the seed document for all of the international organisations that are concerned with the SI units.

3.1 The 7th edition of the SI units brochure.

The recommendations of the CCU after adoption in the by the CIPM have been incorporated in the 7th edition of the SI units Brochure. The previous editions deprecated the use of cgs units. Notable changes in the 7th Edition of the SI Brochure, from the IUPAP viewpoint, are that it incorporates the IUPAP view that the continued use of cgs units should be permitted as long as physicists and others give their values in SI units the first time that they are used. A difficulty in negotiating this concession was that IUPAP is credited as being the lead organisation to call for the introduction of SI units to replace cgs units. Younger physicists are being increasingly taught physics using SI units and are often unsure as to the size of quantities expressed in cgs units.

The IUPAP request concerning the atomic mass unit has also been adopted in the Brochure as the definition in footnote (c) to table 7, where it is made clear that the atoms are in their ground state and at rest. Following negotiations with IUPAC, there will be a likely consequent change to the definition of the mole in due course. The new edition of the Brochure goes part of the way towards this. Since the mole is much more a unit associated with chemistry it is being left to IUPAC to pursue taking this change to the final stage. This will be in a few years time when all of the definitions of the SI base units are expressed in a common format.

The ISO strongly favours the abolition of the use of the full stop to indicate the decimal point and favours the universal use of the comma. However about half the world currently used the full stop. The potentially controversial situation has been eased somewhat by the use of the decimal point in the english language part of the SI Brochure, and the comma in the french language part. This should permit english language journals such as Metrologia to revert to the use of the decimal point.

The radian and steradian have now been incorporated into the derived units. A symbol for the dimensionless unit 1 would allow the use of SI prefixes for counting, much as we see use of the gigabyte etc in computing. In the 7th edition of the SI Brochure the neper and bel are shown as dimensionless units approved for use alongside the SI (see below).

3.2 The September 1998 meeting of the CCU.

(i) A development, which at first sight was of little direct relevance to physicists, was the result of a strong request by the IFCC for a named unit, the katal, for the derived SI unit mol per second.

The case for its introduction was based on the need to introduce it from the viewpoint of human safety; for nurses particularly have been finding it difficult to compound and convey quantities involving combinations three or more SI units. On this basis the CCU forwarded a recommendation for its adoption to the CIPM.

(ii) The bel and neper have long been used by physicists as dimensionless units, particularly in the technology domain, as 'units' to convey that logarithmic quantities are being used. These are used particularly in acoustics and electromagnetism. BWP circulated a note to the Commission Secretaries concerning this in order to formulate a IUPAP view, and was very grateful for the supportive replies received.

Although a 'logical' case can be presented for either the bel or neper to be the coherent SI units (but not both), the IEC and ISO strongly favoured the neper as the base quantity, and this was the view that prevailed at the CCU. The bel and decibel will continue to be used, and indeed these are the quantities that the majority of users would prefer to see as the SI units.

(ii) A continued source of annoyance to unit purists has been the continued use of percent, ppm, ppb, and ppt. There is also the general problem of conveying large or small values of dimensionless quantities in conversation. This has been raised over a number of years at the CCU. There is the attendant reality that the microradian and the decibel are widely used to express dimensionless quantities, and their use in and alongside the SI has long been tacitly accepted, this created a precedent for the CCU Recommendation (1) given below.

(iv) A further matter discussed was the extension of the range of SI prefixes beyond the range 10-24 to 1024. There were two proposal were considered one from a CCU Working Group, and the other from the AAPT. The first built on the existing SI prefixes and the second required changing the CIPM decision concerning the prefixes for 10-24 and 1024. The Chairman of the CCU reported that the proposed extensions had been widely circulated by him, and that there had been no strong demand for extending the range. The CCU therefore decided not to extend the range of SI unit for the present by reason of the presently limited application. It was considered also that adopting further prefixes for larger and smaller prefixes would permit everyday quantities to be readily be expressed in absurd ways which might affect the reputation of the SI.

(v) The SI units have been defined over a long period, and it has not been necessary to standardise their form. However there is an increasing drive to standardise wherever desirable for scientific and technological convenience and in order to make the international measurement system as logical and consistent as possible. The CCU had discussed this earlier but decided not to take action. However the usefulness of a standard form has been of interest particularly to the ISO and IEC. A draft proposal to standardise the form of the SI units was discussed at the September meeting of the CCU.

Any decisions will have to be extensively discussed with the CIPM Committees that advise on the various units. It is expected that several of the definitions of the SI base units will have to be modified at future dates: the definition of the second may incorporate a statement concerning the temperature of the black body radiation, the definition of the prototype kilogram may be replaced, the definition of the mole may be revised to incorporate the statement that the carbon-12 atoms are it rest etc, the definition of the kelvin does not specify the isotopic composition of the water.

(vi) There was also a proposal to change the symbols for the deca, hecta, and kilo, so that all prefixes larger than unity would be use capital letters. However there are inevitable difficulties because some capital roman letters already have two meanings. The proposal did not receive sufficient support, partly because there would be a clash by using the same symbol as is used for SI units Henry and Kelvin - admittedly the use of mm to denote the millimetre does not appear to cause problems.

The recommendations forwarded by the CCU to the CIPM are given below. As is usual their justification has been clearly stated and, for those finally adopted, the considerations would be recorded in future editions of the SI Brochure along with earlier decisions for the SI.

4. Draft Resolutions forwarded by the CCU to the CGPM (subject to editorial corrections)

Recommendation U1 (1998) special name for the SI unit mole per second, the katal, for the expression of catalytic activity.

The Consultative Committee for Units


the importance for human health and safety of facilitating the use of SI units in the fields of medicine and biochemistry,

that a non SI unit called "unit", symbolised U, equal to mmol×min-1, which is not coherent with the SI, has been in widespread use in medicine and biochemistry since 1964 for expressing catalytic activity,

that the absence of a special name for the SI unit mole per second has led to results of clinical measurements being given in various local units,

that the use of SI units in medicine and clinical chemistry is strongly recommended in these fields,

that the International Federation of Clinical Chemistry and Laboratory Medicine has asked the CCU to recommend the special name katal, symbol kat, for the SI unit mole per second, that while the proliferation of special names represents a danger for the SI, exceptions are made in matters related to human health and safety (15th CGPM, 1975, Resolutions 8 and 9, 16th CGPM, 1979, Resolution 5)


that the name katal, symbol kat, has been used for the SI unit mole per second for over thirty years to express catalytic activity, recommends the adoption of the special name katal, symbol kat, for the SI unit mole per second for use in the fields of medicine and biochemistry for the expression of catalytic activity.

4.1 Recommendation for the neper and the bel

Recommendation U2 (1998)

The neper and the bel

The Consultative Committee for Units


that the natural logarithm is used to define logarithmic decrement, field level and power level in the system of quantities on which the SI is based,

that quantities and quantity equations on which the SI is based become simplified when the natural logarithm is used,

that in particular, for complex quantities the only useful logarithm is the natural logarithm,

that with the use of the natural logarithm the radian and neper become coupled and thus the same status in the SI,

that the 20th CGPM (1995, Resolution 8) decided to interpret the then supplementary units as dimensionless derived units and consequently to eliminate the class supplementary units as a separate class in the SI,

that the CIPM through the SI brochure, 7th edition (1998) has accepted the neper, symbol NP, as a special name for the coherent SI unit one, for expressing the values of logarithmic quantities, and also the bel, symbol B, as a practical unit for expressing the values of such quantities, that there is a need to complete the internal consistency of the SI by formally adopting the special name and symbol for the unit one, for expressing the values of dimensionless quantities in areas such as acoustics and electrotechnology, recommends the adoption of the special name neper, symbol Np, for the SI dimensionless derived unit one, for expressing the values of logarithmic quantities such as logarithmic decrement, field level, or power level, and the confirmation of the decision by the CIPM to accept for use with the International System, the non-coherent unit bel, symbol B, and its commonly used submultiple the decibel, symbol dB.

9.2.2. Recommmended changes to Table 3, consequent on 4.1.

Table 3. SI derived units with special names and symbols

SI derived unit

Derived quantity Name Symbol Expressed in terms of other SI units Expressed in terms of SI base units

logarithmic decrement, field level, power level neper Np ln e = 1(a)

(a) For the logarithmic decrement the expression for the unit is L = (ln d×T)d×T= e = 1 Np =1; for field level the expression is Lf = (ln F/Fo) F/Fo = e = 1 Np = 1; and for power level the expression is

Lp = (1/2) (ln P/Po) P/Po = e2 = 1 Np = 1.

4.2 Special name for the SI unit one.

Recommendation U3:

Special name for the SI unit one, the U or the uno() for use with the SI prefixes

The Consultative Committee for Units,


that the use of SI prefixes with the SI units allows the use of units of the SI with a magnitude much greater or less than that of the SI units,

that while the use of SI prefixes compromises the coherence of the sI, it has undoubtedly added to its practical value and contributed to its widespread use,

that there is at present no convenient way of using the SI prefixes to express values for dimensionless quantities for which there is no special name,

that it can be unsaticfactory to use for this purpose powers of ten expressed in the form 10n,

that in consequence, expressions such as "per mille", "ppm", "ppb", and "ppt" which are language dependent and in some cases ambiguous in their meaning have come into widespread use, and that this is to be deprecated,


the adoption of the special name U or uno, symbol U, (to be decided) for the number one, for use in combination with the SI prefixes to express the values of dimensionless quantities which are much greater or less than one.

4.2.1 Draft entry for Table 6 of the SI Brochure.

Draft entry for table 6, with footnote (j) :

Name Symbol Value in SI units

<U or uno>(j) U 1 U = 1

(j) This unit is introduced to allow the use of SI prefixes to express the values of quantities that involve a dimensionless quantity and have values much greater than or much less than one, thus obviating the need to use powers of ten. See Section 3.3.

Draft entry 3.3:

3.3 The <U or uno.

The unit of dimensionless quantities, quantities of dimension one, the <U or uno>, may be combined with the SI prefixes to give a unit for dimensionless quantities having values much greater or less than one. The unit <U or uno>, symbol U, is equal to one.

Examples: a mass fraction w = 2 ´10-6 = 2 mU

a number concentration C = 3 ´ 1012 dm-3 = 3 TU dm-3

the relative uncertainty of the Planck constant is ur = 4 ´10-7 = 0.4 U.

These examples are sometimes written using expressions such as ppm, ppb, and ppt, but the use of the unit <U or uno> in combination with a prefix is to be preferred.

5. ISO TC12

BWP also attended an initial meeting of ISO: TC 12 to consider the projected production by the ISO of an international standard on the methods of presenting data in graphical and tabular form. As with terminology, and reporting uncertainties, physicists encounter restriction of their freedom when they seek to publish or otherwise report the results of their labours. Even from this initial meeting and without taking up a IUPAP position, it is already apparent that there will inevitably be some physicists who are unhappy with the final result. There appear to be two main forms presently used by physicists throughout the world to labl headings in tables or the axes in graphs:

(i) to use the form: physical quantity/unit; and

(ii) to use the form: physical quantity (unit).

It is already clear that those advocating form (ii) via inputs to all of the participating organisations will face an uphill struggle unless strong logical arguments can be deployed - tradition counts for little.

6. Conclusion

(i) Continued representation by IUPAP on such bodies as the above is essential if the views of physicists are to be safeguarded. This is particularly important because absence from participating in an earlier decision by the CCU, IEC, or ISO, may make IUPAP objection to a later decision extremely difficult.

(ii) In consideration of (i), it is recommended that IUPAP makes every effort to respond positively to invitations to be independently represented on other international bodies. The closer IUPAP can get to the fountain-head of decisions by other organisations the more effective it can be.

(iii) IUPAP is but one of many bodies concerned with the production and use of the international system of quantities and units. Compromises must necessarily be made if a universal system is to prevail. It is clear, for example, that the mole, which finds little application in physics, is essential to chemistry. The reasons why the SI has the form that it does today are given in the SI Brochure. It is helpful for the perceived defects in the International System of Units (SI units) and the system of quantities on which it is based.

(iv) It is not always easy to discover whether physicists agree or disagree with proposals made by other international organisations and it is very helpful if IUPAP Commissions can convey their opinions about Symbols, units and nomenclature to the designated IUPAP representative. Reactions by physicists usually cover the range 'indifference' to 'caring passionately'.

No one system of units is satisfactory for the whole of range presently covered by physics. Thus, one obviously cannot use a metre defined in terms of the speed of light to check the constancy of the latter. Neither can one check Ohm's Law using electrical units derived by methods that assume its constancy. Physicists therefore must have the freedom to use particular units or unit systems for particular purposes. However, at some stage we all have to communicate the results of our discoveries both to our colleagues who are investigating much the same part of physics and to others who do not know our local shorthand jargon - which sometimes is a transient one. It does not seem unreasonable to request that where local units are used, for the convenience of other physicists and other scientists and technologists, the value of the local unit is given in terms of the corresponding SI the first time that it is used.

IUPAP is credited with calling for the adoption of the SI, something that we can use to advantage. However, the gradual changes over the years since its adoption may have made it more suitable for use in some parts of physics and less suitable for others. Physicists and IUPAP may have to play greater attention to the latter aspect in the future, and even specify whether they recommend use of the whole or part of the SI.


Concerning the neper.

Brian W Petley

IUPAP representative

I note that the neper is on the agenda for discussion at the next meeting of the CCU. I suggest a final look before we leap. We may be creating precedents which will erode the beauty and decimal nature of the SI, and also be difficult to redress. 'Where will the changes to the SI end?', is an often heard and recurrently expressed concern. ' Why do they have to keep tinkering with the SI?' is another concern often expressed by physicists and other users.

Although exponential quantities occur widely in science and technology, many users do not appear to have any need express them in terms of a logarithmic unit. For the first fifty years of its existence, the SI has not included the neper, bel , decibel, bit, or byte (neither, of course, did the cgs system). Introducing the neper opens the door to all of these. Although science and technology have progressed, since the SI was adopted, this historical absence argues for proceeding slowly before introducing too many major changes to the SI. It is important for the teaching of SI usage that the reasons for decisions for changes to the SI are logically and properly explained to the present and future generation of users. To do otherwise makes the decisions of the CGPM appear to be autocratic and arbitrary, rather than being firmly logical, and democratic, and based on sound scientific principles.

So far the SI has proved to be an adaptable system which is suitable for commerce, science, and technology. Scientists, of necessity, need more than one unit system. Particular unit systems are introduced in order to simplify the discussion of specific problems. These systems can be confusing where they have been locally rather than internationally defined. At some point we have to consider whether, by trying to make the SI units more suitable for technology, we may succeed in making them much less suitable for use in science. We may be in danger of moving the SI in that direction.


(i) I propose that, at its next meeting, the CCU reviews and discusses the desirability, or otherwise, of producing recommendations and a report outlining the justification for introducing the neper, the rules for using it, how it affects the logical development of the SI, and the precedents that it creates.

In justification of this proposal, I attach a first attempt to articulate some of the aspects of the above, and which might be addressed in such a report.

(ii) I propose that the CCU considers whether it might be prudent to consider waiting for user reaction to the present edition of the SI Brochure, before proceeding further with the neper.

(iii) Reminder: I assume that at some stage, the CCU will draft a shortened case for the neper in the CGPM form: 'in consideration of x, y, z,. the neper is introduced as a dimension-less derived SI unit for logarithmic quantities.' The strength or weakness of the case for the neper and the associated constraints may be more clearly revealed when it is expressed in this form.

[Note, the attached Appendix is written to meet the CCU submission deadline and may still contain some unnoticed errors].


A note on the neper and the bel, etc, and the method of

writing the numerical value of a physical quantity.

Brian W Petley

IUPAP representative on the CCU

1. Summary.

There seems to be an on-going technological user need for the use of the terms such as neper and bel, and beyond these there are other 'units'such as the bit, and the byte. There are potentially a number of problems raised by their introduction to the SI. There might be an alternative solution to that of formally regarding them as dimension-less SI units. The way in which this solution might be effected is outlined.

2. Introduction: aspects of the neper and the SI

(i) the SI is regarded as a decimal system of units which is firmly based on the use of decimal multiples and sub-multiples of the basic unit; the use of decimal numbers is so widespread that it has not been thought necessary to specify this very explicitly;

(ii) in view of (i), one would logically expect an SI logarithmic unit which was firmly based on numbers to base ten: a consideration which suggests the bel rather than the neper as the introduced unit; it is certainly unexpected that the neper rather than the bel is proposed as the coherent SI unit.

(iii) the SI is intended to be a logically consistent system for universal use, having unique units; the usage of the SI units and prefixes is universal; (a) the neper and bel are used in particular areas, and (b) there is a different logarithmic relationship for power ratios and voltage ratios: named logarithmic quantities are neither unique nor universal. In order to illustrate (b), it is apparent that users do not find it necessary to invoke a unit such as the neper, or bel, in order to convey such logarithmic quantities as a half-life, or a pH, respectively. The need for a named logarithmic unit is consequently a localised one. Why should some technological areas require this unit and not others?

(iv) There are also problems relating to sustaining the concept of coherence. In the decimal SI, whenever an SI unit is defined, the numerical value is unity in the equation:

physical quantity = {numerical value)}´ [unit(s)]. In the case of the neper we have Q = ex Qo , and there is no requirement for Qo to be either an SI base unit, or a derived SI unit.

(v) It is apparent that in the current usage of the neper, bel, and decibel, major communication problems are experienced, not only because we have P = 10x/10 Po for power ratios and use

V = 10x/20 Vo for voltage ratios, but also through Qo not being a specific reference quantity or unit; thus the milliwatt, the watt, other reference powers, or the thermal noise power, etc, are widely used as reference levels in power measurements. Users should, of course, state the reference levels, but they frequently do not. The CGPM can issue edicts that users should do so, but there is a considerable risk such an edict will be ignored. The CGPM has experience of this with the confusion between weight and mass - adding the neper and other quantities may well add further confusion and misuse, and so corrupt the usage of SI units.

(vi) In the SI there is a very clear distinction between the numerical value and the unit. Terms such as neper, bel, and others, begin to erode this distinction. We illustrate in the next section how these can be portrayed as being part of a common set of user problems concerning the communication of the form of the numerical value. Thus, there are similarities between SI prefixes, radian, steradian, neper, bit and byte, etc. This argues for attempting to introduce a consistent method of solving them.

(vii) It is clear that we are increasingly moving towards replacing the fundamental relation:

physical quantity = {numerical value}´ [unit],

by another fundamental relation:

physical quantity = numerical value} ´ [dimension-less unit] ´ [dimensioned unit].

We need to be able to make it very clear as to when in the SI a dimension-less quantity is to be assigned a formal name, and when it is not.

(viii) The properties of dimension-less units are rather different from dimensioned quantities. These must be carefully explained in the SI Brochure if the SI is to be portrayed as a logically consistent decimal system, and also if the very useful concept of the method of dimensions is also to be sustained. Thus, in the case of the radian, we see that there are problems when we express sin q as a power series sin q = q - q3/3 + etc, for it is clear that in this case the dimensionality of the radian behaves very differently from the metre, etc. Adding to user difficulties, in expressions containing angular frequency w, the dimensional nature of the radian would usually be retained in terms such as w, w2, w3. The dimensionality of the radian is both arbitrary and ephemeral

(ix) We have already tempered the notion of coherence in the SI by permitting the relation:

y hertz = 2p y radian/second.

It is confusing to users that this irrational, incoherent relation, is permitted in the SI while the exact relation: z inch = 25.4 z mm, disqualifies the use of a widely used dimensioned unit for use with the SI. In the past this argument was safeguarded by regarding the radian and steradian as a separate class of supplementary dimension-less SI units, a separation that has recently been abandoned.

(x) The introduction of the neper has hitherto been resisted by the CGPM, CIPM, and CCU, for the whole of the existence of the SI. It is neither clear what the basis for these objections was, nor what recent scientific and technological advances and changes have negated, or overcome, these objections. These objections may have been partially documented in the past, and they possibly ought be re-examined in detail.

3. The representation of the numerical values of dimension-less quantities

We may write the quantity Q in terms of a quantity Qo of the same kind in any system of units as:

Q = n(1) ´ Qo The usual form when the reference quantity Qo is an SI unit (3.1)

or alternatively as:

Q = n'(2) ´ 10n(2) Qo This form is used in association with the SI prefixes, when Qo becomes the unit of the quantity concerned in order to restrict the range of values for the number n'(2), to: 10-3 < n'(2) < 103. (3.2)
There are also other forms of representing the number in widespread use, in science, commerce, and technology, such as:

Q = en(3) Qo for which the term neper is used to communicate n(3); similar expressions occur in radioactive decay, but the neper, or another term, is not used as a unit for expressing half-lives. (3.3)

P = 10n(4) Po the form for which the bel is used to communicate n(4) (3.4)

c(H+) = 10-x ´ co the form used to express concentrations in terms of a standard concentration co, the term pH is used to denote x; pH is not regarded as either having an associated unit, or as being measured in bel. (3.5)

P = 10n(4) /10 Po the form for which the term decibel is used to communicate n(4) (3.6)

V = 10x/20 Vo the form used when decibel is used to communicate logarithmic voltage ratios (3.7)

w = 2p f radian: 2p is an irrational number (3.8)

QQo the term bit is used to indicate that binary rather than decimal numbers are being used in digital communication, etc: not yet an SI unit. (3.9)

Q = (1/8) Qo the term byte is used in computing and digital technology to indicate that the binary numbers are grouped (so as to communicate the alphabet, etc): not yet an SI unit There are also other unit-like terms used in communication technology. (3.10)

where, in the above, n(1), n(2),. ., are decimal numbers, i and i''(1) are integers. Also, pi may take the values of either 0, or 1. [It is hoped that switching between units, standard quantities and physical quantities in the above in order to illustrate an apparent commonality of problems, has not been too confusing.]

It appears from the above discussion that the need by users in some areas for the terms neper, bel, bit, etc, all arose as part of the representation of the numerical values in a system of quantities in which particular standard reference quantities (units) were used, and not as part of an associated unique system of units. Moreover, they simply denote the form of expression of the numerical value, not the standard reference quantity, or the unit.

Just because numerical values and units share additive and commutative properties, it does not follow from this commonality that 'numbers', or numerical values, are necessarily the same as 'units'. We note at this point that it seems illogical to argue that simply performing the mathematical operation of taking the appropriate logarithm of both sides of equations (3.3) and (3.4) should confer a dimensionality on the exponents.

Precedents for use with the SI

In the case of the SI, and following earlier cgs usage, the prefix (that is, the method of denoting (3.2) above) is attached to the unit rather than to the numerical value of the quantity. As equation (3.2) illustrates, the SI prefixes are essentially part of the same class of problems as the neper, etc, for expressing numerical values. Prefixes are, of course, included in the SI - but they are not regarded as being SI units.

This encourages one to argue that:

(i) The adoption of the SI prefixes provide ample precedent for attaching designations such as neper and bel, simply to indicate that the numerical value is not in the usual raw decimal number form.

(ii) A new word, or phrase, may therefore required to denote this category of SI representation.

(iii) If the term 'dimension-less unit' is going to be adopted as the preferred name, then it should be made clear to all SI users that dimension-less units have very different properties from dimensioned units and are members of a different class of units - a classification which, logically, should also include the SI prefixes.

4. Consideration of present usage of the neper, bel, and decibel along with SI units

Consider now


where x is a distance and k the quantity that one wishes to specify and convey to someone else. In this case, following tradition, one might well wish to state:

"where k = -15 dB/m"

in order to convey the value of the quantity k. In this form one gets the impression that the decibel is already an agreed SI unit for expressing logarithmic power ratios. If we look more closely it becomes clear that what is really intended to convey is:

"where k = (-15 m-1) dB".

That is one is essentially expressing two quantities simultaneously to other people:

(i) that the numerical form of the dimension-less expression containing k, is that of equation (3.4), and

(ii) that the value of the physical quantity k, is -15 m-1.

Thus, it may be the position of the 'dB' in the expression which causes one to instinctively regard it as an SI unit. In reality, though, we also are simply following the same convention that is used with SI prefixes, namely of attaching it ahead of the unit. The CGPM, CIPM or CCU do not regard SI prefixes as being SI units, they are given a separate designation. It is interesting that in the former case it is more associated with the numerical value than the unit, as may be evidenced by the location of the /.

In current usage the use of the above terms to indicate the logarithmic value of the quantity Q in terms of Qo is, demonstrably, both confused and unsafe. Present users often omit making any reference to the value of the reference quantity Qo. There is no requirement either for Qo to be a coherent SI unit: we have partial coherence. In acoustics, for example, there is often confusion because three different values of the reference quantities for Qo are in widespread use. Such confusion is an obvious potential danger to life and health.

There is no reason to suppose that this sloppy, unsatisfactory, form of usage would stop if the neper, decibel, etc, simply became part of permitted SI terminology [Practical, but usually deprecated , terms such as dB mW are used in recognition of this problem and this, alas, sometimes gets truncated to dBm! However, although we may deprecate it, it is an attempt by the user to solve a perceived metrological problem: one which must be solved if these terms are to be introduced into the SI.]

Where the decibel, etc are permitted, the present (unsafe) onus is on the user to attach the value of Qo to the measured quantity, it is not part of an instrument read-out: as mW, for example would be.

4.1 The radian and steradian

Although peripheral to the present arguments, we should note at this point that the radian and steradian have caused considerable problems for the SI during its first forty years of existence, and that their varying SI designations have reflected this. They too could also be regarded as belonging to the same class of problems of section 3, as in illustrated in equation (3.8).

4.2 Why not combine an apparently a common problem of SI usage into a common class of SI solution?

Our system of units is based on the notion that a physical quantity is the product of a numerical value and a unit. These are two distinct concepts and consequently it is desirable that they should be kept separate. We see from the above arguments that there is the possibility of a common set of alternative solutions to that of extending the concept of dimension-less quantities. This is particularly attractive as far as the method of dimensions is concerned, for it avoids having equations in which some of the 'units' do not appear on both sides of the equation (as we see when we write, for example, sin q = q). Alternatively, one might introduce a better term than 'dimension-less units': one could imagine a section concerning 'SI prefixes and numerical values', in the SI Brochure.

5. Conclusion.

(i) It is preferable for the diversity of users, that the SI is presented as a conceptually simple decimal system of units and associated physical quantities, with a clear distinction between numerical values and units, and between dimensioned quantities and dimension-less quantities.

(ii) In view of their pre-existing widespread misuse, any introduction of terms such as the neper, bel, decibel, bit, and byte, into the official SI must be made with considerable care.

(iii) The precedent of the separate classification adopted for the SI prefixes might be extended in order to find a way to safely introduce the neper, bel, bit, byte, etc, for use with the SI. Thereby avoiding introducing an endless succession of named dimension-less SI units. In suggesting such discussion it has, of course, implicitly been assumed that a sufficiently strong case exists to introduce them into the SI. This need can, and should, be questioned very carefully.

Brian Petley

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