IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 8, AUGUST 2012 2125
Measurements for the Future—A Complete SI FromPhysical Constants
Bryan P. Kibble
Abstract—Basing the SI units entirely on the values of funda-mental physical constants involves extremely difficult metrology. Itis desirable that the reproducibilities of a newly defined kilogramand of a thermodynamic temperature scale are at least equal tothose of the present artifact kilogram and the water triple-pointtemperature. This paper discusses the benefits of an updatedSI, the principal difficulties in attaining it, and why the effortexpended is justified.
Index Terms—Measurement, measurement standards, stan-dards, uncertainty, watt balance.
I. INTRODUCTION
THE IMPORTANCE of dependable measurements in theeveryday worlds of manufacture, engineering, and science
is well appreciated, but maybe, the foundation on which thesemeasurements are based is less so.
Even less recognized is the role that the research underpin-ning the SI plays in influencing, monitoring, and improving thisdependability. Paradoxically, the more successful metrologistsare at providing the base units of measurement, the moreinvisible to the everyday world their work becomes. However,this invisibility is desirable; for example, whenever a change ofdefinition of a base unit is implemented, to avoid confusion, wemust do our best to ensure that numerical values for a measuredquantity in the new unit are the same as those expressed interms of the old unit. Only the uncertainties of measurementsshould change and, in the course of time, become smaller.The reproducibility of the present artifact kilogram, i.e., , asingle platinum–iridium mass looked after with the greatestcare, appears to be a few parts in a hundred million on atime scale of decades. This is certainly adequate for all presentneeds, but redefinition in terms of a physical constant has moreadvantages, and to obtain these, it may be even acceptable tocountenance a slightly worse reproducibility in the short term.
The chief advantage would be the resulting very accuratevalues of related physical constants. Table I lists the uncer-tainties of some of these constants if h were to be given
Manuscript received November 28, 2011; revised June 5, 2012; acceptedJune 6, 2012. Date of publication June 29, 2012; date of current versionJuly 13, 2012. The Associate Editor coordinating the review process for thispaper was T. Lipe.
B. P. Kibble, retired, was with the National Physical Laboratory, TeddingtonTW11 0LW, U.K. He consults for the Physikalisch-Technische Bundesanstalt,38116 Braunschweig, Germany.
Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIM.2012.2204162
TABLE IUNCERTAINTIES, IN PARTS IN 109, OF SOME PHYSICAL CONSTANTS NOW
(WITH THE ARTIFACT PROTOTYPE DEFINED TO BE EXACTLY 1 KG)AND AS PROPOSED IN THE FUTURE, IF h, NAe, AND THE BOLTZMANN
CONSTANT k WERE TO HAVE EXACTLY DEFINED VALUES
(WIKIPEDIA, NEW SI DEFINITIONS).
an exact value. Only the kilogram and μ0 would have theiruncertainty increased from zero to the finite values indicated.Similar uncertainties result if the mass of a specified atom(carbon 12, which can be very accurately related to the siliconatoms actually measured) and therefore NA were to be ascribedan exact value rather than h. Details have been publishedelsewhere [1], and values of the constants are available athttp://physics.nist.gov/constants.
The three properties required of a unit are that it should bemore stable than anything we might want to measure in termsof it, that it forms part of an integrated system of other unitsand that, in principle, it could be independently created froma prescription by anyone anywhere. For example, the metercan be created to any required accuracy by laser frequencymeasurement and interferometry at any competent laboratoryjust from the defined second and speed of light c. The secondand c, by virtue of their connection to other physical constants,ensure that meter is part of a coherent SI.
It is on the third requirement for independent creation that thepresent kilogram is wanting; national copies had to be made ofthe prototype kilogram , be periodically certified at the BureauInternational des Poids et Mesures (BIPM), and dispatchedto the national laboratory, because is far too importantto leave the custody of the BIPM. To protect it further, therecalibration of the copies held at BIPM only takes place every50 years or so.
2126 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 8, AUGUST 2012
Note that there is a distinction between the abstract definitionof a unit and its concrete representation for actual use. Forexample, the infinite-parallel-conductors definition of ampere isno use for practical measurements of current, which depend onvoltage measurements and resistance measurements traceableto exact defined values of KJ(= 2e/h) and RK = (h/e2), re-spectively. As the exact values to be ascribed to these constantsfor them to be consistent with the ampere definition have had tobe experimentally measured, they are only in close agreementwith the ampere definition; at present, they cannot define the SIampere. Instead, they only represent ampere, and if the SI valueis important, as in interrelating values of the physical constants,they come with their experimentally measured relative uncer-tainties of 2× 10−7 and 1× 10−7, respectively.
In the case of kilogram, the abstract definition merely iden-tifies the artifact and accords the exact value of 1 kg to it,whatever its mass happens to be at the time. Its realizationconsists of comparing it with other mass standards by weighing,and uncertainty is associated with this process.
The establishment of a unit for temperature measurements isalso unsatisfactory but for a different reason. The aim is to setup a scale of thermodynamic temperature, based on a definedvalue ascribed to the Boltzmann constant kB . A suitably simplesystem is needed, and traditionally, this has been the statisticalthermodynamic properties of an ideal gas. An ideal gas doesnot exist, but the inert gases are a very good approximationand their departure from the behavior of an ideal gas canbe investigated and allowed for. As with the electrical units,continuity with the temperature scale is now in use, which isbased on the value of 273.16 K for the triple point of water,is required. This entails, first, measuring a value of kB , whichis consistent with this value; second, defining kB to exactlyhave this value; and, third, setting up a temperature scale formeasuring other temperatures based on the new defined valueof kB .
The relative accuracy needed for the measurement of kB , sothat there are no noticeable step changes in the numerical valuesof temperatures expressed in terms of the old and new scales,is of the order of 1× 10−6. At present, measurements of thevelocity of sound claim this accuracy, while measurements ofthe dielectric constant or the refractive index of inert gases yieldrelative one-standard-deviation uncertainties of about 8× 10−6
and, happily, the results agree within this uncertainty. However,it is clearly desirable that a measurement by an independentmethod, as in the previously mentioned case of the kilogramwork and which is independent of the properties of an inert gas,should be carried out.
II. NOISE THERMOMETRY
Thermometry based on the electrical Johnson–Nyquist noisegenerated in a resistor [2], [3] is just such a method. It is inde-pendent of the resistor construction, shape, size, composition,or physical state.
The mean square value V 2 within bandwidth B of voltageV across the terminals of resistance R in thermodynamicequilibrium at temperature T is, to a sufficient approximation,4kBTRB. All sources of energy dissipation associated with the
conductor must be represented in its resistance. For example,under ac conditions, dielectric, magnetic, and eddy-currentlosses need to be included in the ac dissipative resistance ofthe conductor. Special resistors of such simple constructionthat these influences can be reliably calculated have beenmade, and by comparison with them, the variation with thefrequency of the observed resistor within the bandwidth can bemeasured. Alternatively, methods have been recently devised,whereby the inherent frequency independence of the quantumHall resistance can establish the frequency dependence of otherresistors [4].
Noise thermometry possesses the great advantages of sim-plicity of the concept and applicability over a wide range oftemperatures so that a continuous thermodynamic temperaturescale can be established, but it has a major drawback. Thenoise voltage generated is exceedingly small. It is only a fewnanovolts for reasonable values of resistance, a practical obser-vational bandwidth of up to a megahertz and at temperatures upto hundreds of kelvin. Low-noise preamplifiers, which observeand measure these voltages, have themselves noise of a fewnanovolts. This can be separately measured and subtracted [5],but the accuracy establishing a thermodynamic temperaturescale needs the technique of autocorrelation. In this technique,the resistor is observed by two similar preamplifiers in parallel,and their separate outputs are examined by a correlation cir-cuit. Since the noise fluctuations of the separate amplifiers arecompletely uncorrelated, they average to zero, while the noisefluctuation in the resistor is completely correlated in the twochannels and is correctly measured. A further practical diffi-culty occurs, even using this technique, if extraneous electricalinterference is allowed to enter both channels and is therebyalso correlated and measured in the error. It can be reduced tonegligible proportions by the coaxial techniques of interferencerejection described in [6].
The other major consequence of the exceedingly small ob-servable noise voltage and its statistical nature is that it mustbe integrated over long periods to obtain part-per-million res-olution. To attain the target resolution of 2 ppm for measuringkB , 60-day integration time is required, assuming a measure-ment bandwidth of 500 kHz. This is clearly unrealistic, giventhe difficulty of holding the observed temperature sufficientlyconstant over this time, the risk of interruptions of variouskinds, and the need to repeat the observation many times toinvestigate possible sources of systematic error. One possibleway forward is to increase the number of measurement channelsconnected in parallel to the resistor and add the outputs oftheir individual correlators. The needed integration time is thenreduced in proportion to the number of measurement channels;ten correlated measurement channels in parallel should lead toa much more realistic five-day integration time [7].
Another possibility is to increase the measurement band-width, but this is technically difficult. Also, since the actualvalue of the resistor is irrelevant, provided it can be adequatelymeasured, a choice of value that better matches the noise figureof the preamplifiers can be made. Ref. [8] is a review of thesituation.
To base a thermodynamic temperature scale on Johnsonnoise thermometry, the observed voltage noise must be
KIBBLE: MEASUREMENTS FOR THE FUTURE—A COMPLETE SI FROM PHYSICAL CONSTANTS 2127
measured in terms of similar statistically fluctuating voltagesindependently created by a random statistical process applied toa voltage whose amplitude is known in electrical SI units. Twoways of doing this are being used. In the first, synthesis of a ran-dom waveform is directly made by a programmable Josephsonvoltage array [9], whereas in the second, an orthodox digital-to-analog converter has its dc reference voltage calibrated, also interms of a Josephson array [10].
III. HISTORY
The emergence of watt balances has greatly improved thelink between electrical and mechanical SI units. To understandtheir working principle, consider a magnetic flux Φ, whichthreads a coil of wire carrying current I . The interaction energyE = I · Φ, and consequently, the force on the coil in the ver-tical, i.e., x, direction Fx = ∂E/∂x = I∂Φ/∂x = Mg whenbalanced against mass M subject to the earth’s gravitationalacceleration g. Now, suppose that, in a separate measurement,the coil is vertically moved with velocity u = dx/dt, inducingvoltage U = ∂Φ/∂t = (∂Φ/∂x) · (dx/dt).
Eliminating ∂Φ/∂x and measuring I as the voltage dropU ′ that it produces across resistance R yield Mgu = UU ′/R,thereby equating the mechanical and electrical SI units ofpower. The geometrical properties of flux and coil embodiedin ∂Φ/∂x are eliminated and do not need to be measuredat all, provided that they remain unaltered between the twomeasurements. It is primarily this great simplification that givesthis approach more than a hundred times the accuracy of currentbalances, which previously linked the mechanical and electricalSI units. If U and U ′ are measured in terms of KJ and Rin terms of RK , the electronic charge e cancels, and a directconnection between M and h results. Therefore, only a definedvalue of h is needed to fix the SI kilogram and the enhancedaccuracy of the order of a few tens of parts per billion currentlybeing obtained is nearly sufficient to contemplate redefinition.
This very general derivation of the principle of a watt balancereveals the considerable advantages of the technique. Becausethe measurement has the two quite separate parts of weighingand moving, the power equated is virtual rather than real. Thatis to say, there is no displacement involved when the force ofweighing is measured, and there is no flow of current takingplace when the voltage induced by moving is measured. There-fore, real forces and energy expenditures, such as those causedby friction or Joule heating in the coil, or interaction with themagnetic permeability of the coil and former with the magneticflux, do not affect the result. Because any nonhomogeneousproperties of the coil conductor do not enter into the derivation,neither the exact current distribution in the cross section ofthe coil conductor nor its shape is relevant. In short, wholeclasses of systematic error do not affect the result. The thermalexpansion of the coil is also eliminated by choosing a circularcoil geometry interacting with a radial magnetic flux.
Furthermore, the quantities needing measurement are theminimum number necessary for equating electrical and me-chanical powers. For example, only one set of vertical dis-placement measurements need to be made to measure the coilvelocity. Also, by a stroke of good fortune, the quantities are all
of a size suitable for making one part in 109 measurements.Typically, the current in the coil is about 10 mA, which ismeasured as the voltage drop of about 1 V that it produces whenflowing through a 100 Ω resistor in series with the coil. Thevoltage induced when the coil moves is also about 1 V, and themoving velocity corresponds to about 5000 optical fringes persecond, easily within the nanosecond gating capability of anelectronic counter. The relative accuracy of free-fall gravime-ters also approaches a part in 109.
Velocity fluctuations caused by ambient vibration result inabout 0.1% noise superimposed on the induced voltage ofmoving. These velocity fluctuations are not in fact a problembecause they are completely correlated with the voltage fluctu-ations they produce. Therefore, the integration of velocity andvoltage over a time interval eliminate the fluctuations from theirratio.
The remaining difficulty is that scalar electrical power is re-lated to the scalar product of the force vector mg and velocity u.Therefore, u should be aligned with g, i.e., have only a verticalcomponent, and there should be no significant rotational veloci-ties either. Furthermore, the path taken by the moving coil mustpass exactly through the position it occupied for weighing.
In practice, these alignment requirements of typically 5×10−5 rad and 1 μm can, with great care, be met, although thecoil is an unrestrained object rather than something mounted ona coordinate measuring machine.
The original purpose of a watt balance was to replace theampere balance [11]. The ampere balance was a practicalapparatus for realizing the ampere’s abstract definition in termsof the very small force per meter that an ampere producesbetween two parallel conductors. Instead of a current, the wattbalance measured an electrical power, E = I2R.I was easilydeduced as the SI value of R could be measured with more thanadequate accuracy from calculable capacitor and frequency, anassociated chain of ac bridges and a resistor of such simpleconstruction that its difference between its ac and dc valuescould be dependably calculated [6].
Following crude proof-of-principle apparatuses, the U.K.National Physical Laboratory and the USA National Bureauof Standards (now renamed the National Institute of Standardsand Technology) both constructed versions differing in detailwhich immediately yielded results nearly a hundred timesbetter than the current balances in various national measure-ment laboratories. Simultaneously, the Josephson and quantumHall effects were developed to maintain values of voltage andresistance standards, respectively, with unprecedented repro-ducibility. Consequently, the Comite International des Poidset Mesures was able to authorize that, from January 1, 1990,this new derivation of the ampere could be represented byexact values attributed to KJ and RK governing these effects.The decision to create representations of units had a precedentin the distinction between the so-called “absolute” electricalunits and the much more reproducible and practical “Inter-national Units” devised at the end of the 19th century, butas in that instance, it should only be viewed as a temporarystopgap.
The subtlety of the situation should be noted; although thevalues of KJ and RK were chosen to be as near as could be
2128 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 8, AUGUST 2012
measured in SI units by watt balances and calculable capacitors,they could not be used to redefine the SI volt and ohm despitetheir far superior reproducibililty, because the coherence of theSI still depended on the link to the kilogram via the definitionof ampere.
The situation can be resolved by changing the definition ofthe kilogram from the unique platinum–iridium artifact kept atthe Bureau International des Poids et Mesures to a definition interms of h, as aforementioned.
An alternative definition of kilogram, in terms of the massof an atom, has the attraction of easily understood simplicity.All that is needed is to count the number of similar atoms in amacroscopic piece of material whose mass is approximately thesame as . This is tantamount to a determination of NA. Theproblem of counting out the very large number (of the orderof 1023) of atoms has been solved. Silicon atoms are chosenbecause silicon can be refined into a near-perfect crystal. Thenumber of atoms in a macroscopic crystal can be calculatedby observing X-ray Moire fringes as the crystal planes passby when a crystalline plate is moved along between two otherstationary pieces of identical crystal. The distance moved and,hence, the lattice spacing are measured by optical interferom-etry. The number of crystal planes and, therefore, the numberof atoms in a larger piece of about 1-kg mass can be thencalculated if the volume of this mass is also measured by opticalinterferometry [12].
Unfortunately, despite the appealing simplicity of this ap-proach to a kilogram definition, there are severe practicaldifficulties. The Moire fringes require extremely accurate me-chanical alignment and translational accuracy to be observable.The interferometry is very demanding, the kilogram of siliconhas to be made and polished into a near-perfect sphere (becausea sphere has no sharp edges along which an uncertain numberof atoms would be missing), and a large number of diametersmust be measured to calculate its volume. The atoms at itssurface react with the atmosphere to form oxides, and thethickness of a few molecules of this surface layer has to bemeasured by ellipsometry. All these problems are so difficultand expensive to solve that they have proven to be beyondthe resources of any one National Measurement Laboratory,and a worldwide consortium of several major laboratories hasevolved to finish the work, each one concentrating on just someof the aforementioned problems.
One last difficulty has, somewhat unexpectedly, proven to bethe most challenging. Naturally occurring silicon is a mixtureof three isotopes whose masses differ by a few percent. Conse-quently, a very accurate measurement of the relative abundanceof each isotope in the actual crystal used for the measurementis crucial. The latest measurements use silicon enriched so thatit nearly consists of only one isotope, but the production ofkilograms of this material was very expensive, and only twokilogram artifacts have been made from it. Isotopic abundancemeasurements are still needed to give a more accurate over-all result. The latest measurements relying on the Canadianisotopic abundance determination, expressed as the resultingvalue of h for comparison with the watt balance results [sinceh = (mecα
2)/(2R∞NA)], are shown in Figs. 1 and 2 [14].The values of the other constants in the expression are known
Fig. 1. Principle of a watt balance.
with at least a factor of ten less uncertainty of either h or NA
[13]. While this latest situation is very encouraging, there arecredible discrepancies still to be resolved.
The consequence of all these problems is that there is onlyone successful silicon atom-counting result, albeit based onindependent measurements in different laboratories of most ofits constituent parts, in contrast to the several watt balancesin different countries producing or about to produce results.Therefore, it is difficult to envisage, at present, silicon atomcounting fulfilling the “independent creation” requirement byother laboratories or consortiums in the future. The repetitionof this paper is just too demanding. That is not to say that thispaper is less significant. It provides the extra evidence inde-pendent from the results of watt balances needed to considerredefinition of the kilogram. Probably, it will also result insilicon-sphere artifacts of better stability than to representkilogram.
The recent history of the kelvin is bound up in a “natural”artifact by ascribing the exact numerical value of 273.16 K tothe temperature of the triple point of water, and like the siliconatom-counting kilogram, there is an immediate limitation ofreproducibility in terms of the purity and the isotopic contentof the water. However, unlike the kilogram, there is a veryreal problem with establishing a temperature scale. Derivinga mass scale is easy—that two masses are identical can beestablished by substitution weighing, and then, together theyconstitute twice the mass. By the repeated application of thissimple procedure, a linear scale of mass can be built up.Such a procedure, unfortunately, does not exist for temperature.There is no sufficiently simple physical system for whichequal increments of added energy produce equal incrementsof temperature, and moreover, a given temperature cannot bepreserved in the simple manner of a mass standard. Thus,
KIBBLE: MEASUREMENTS FOR THE FUTURE—A COMPLETE SI FROM PHYSICAL CONSTANTS 2129
Fig. 2. Time-ordered measurements of h with 68% confidence error bars. (Triangles) Watt balance results, (circles) silicon results, (cross) the latest Committeeon Data for Science and Technology (CODATA) result from least-square adjustment of the values of relevant constants, and (squares) other techniques. The NRC-11 watt balance and NRC-1128Si results are in excellent agreement and consistent with the NPL-11 and METAS-11 watt balance results and with the Institutefor Reference Materials and Measurements (IRMM) natural silicon result readjusted for the isotope content. They are discrepant with the NIST-98 and NIST-07results.
instead, other reproducible temperatures such as those at whichpure metals melt must be related to that of the water triple pointand a continuous temperature scale produced by interpolationbetween these by using some physical property such as thevariation of resistance of a conductor with temperature. Aproperty like this is assumed to be sufficiently smooth andcontinuous that the intermediate values are determinable withadequate accuracy by fitting a curve through only a few valuesat fixed points. Nature provides fixed points in the form of thewater triple point and the freezing temperatures of various pureelements. The thermodynamic temperature of these fixed pointshas been each measured by gas thermometry.
A partial resolution of this unsatisfactory situation ispresently being sought by basing a thermodynamic temperaturescale on an exact value ascribed to the Boltzmann constant.
IV. PRESENT SITUATION
Measurements intended to replace a unit and then thereaftermaintain it usually proceed in three stages. The first stage es-tablishes a proof of principle and gives reasonable expectationthat the new method will, with enough effort, yield sufficientaccuracy to at least match the reproducibility of the old unit.The second stage entails the elaboration of the first apparatusand procedure to reduce various type-A uncertainties (evaluatedusing statistics) and eliminate type-B uncertainties (evaluatedby other means). This can produce a build-up of complicated“add-ons,” which can make the apparatus too labor intensivefor the future routine maintenance of the unit. In the third stage,there should be a revisitation of the fundamental principles ofthe method to replace some of the complications with a morestraightforward design [15].
The first two stages are well illustrated by the developmentof the watt balance for replacing kilogram.
The third stage is often assisted by the relentless advancein technology. In the present instance, there has been recentprogress in making arrays of quantum Hall devices connected inseries or parallel to yield a Hall resistance near any reasonabledesired value [16], [17]. A 100-Ω resistor made in this waywould help watt balance measurements as its value would be di-rectly governed by the von Klitzing constant and its aging rate,current coefficient, and temperature coefficient would be zero.
Very recently, Steele et al. from the National Research Coun-cil (NRC), Ottawa, Canada [14], using the watt balance devel-oped at the National Physical Laboratory (NPL), Teddington,U.K. [18], [19], have reported a watt balance result for h anda contribution to the result derived from silicon atom-countingmeasurements. These results agree to within 1.2 parts in 108.This degree of agreement is probably fortuitous, given that therelative uncertainties of the measurements are 6.6 and 3.2 partsin 108, respectively, but its importance lies in the fact that theagreement resulted from the removal of significant systematic(type-B) errors from each measurement. Discrepancies have avital role to play in metrology because they stimulate the searchfor errors. Naturally, it is vital that the search for errors does notend with agreement that could simply be by chance.
The way would seem to be clear for a kilogram redefinition,but the only other watt balance result of comparable accuracy[18] is discrepant with this value by 26 parts in 108 (see Fig. 2).The search for error must continue.
With regard to noise thermometry, the situation is moredisappointing. Just one group promises a relative accuracyof 6× 10−6 in the near future [7], but this is still short ofthe 1− 2× 10−6 target. The other active group [10] is still
2130 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 61, NO. 8, AUGUST 2012
developing its technique. This does not compare well withthe total worldwide effort put into silicon atom-counting andwatt balances and reflects that the Boltzmann constant isless glamorous and somewhat the poor relation in constantmeasurement.
V. MOTIVATION
In these times of severe budget restrictions, it is particularlyrelevant to be clear why this difficult and esoteric metrologyneeds to be carried out. The “because it is there” answer ofprevious generations no longer impresses the funding sources.It is also difficult to accurately assess the economic and con-venience benefits of a soundly based, coherent, and simple-to-use system of units, but one can appeal to the fact thatthe worldwide mega-Euro activities of technology and scienceare now utterly dependent on it. Furthermore, we have alwayssought to understand the universe that we inhabit, and accuratemeasurement plays a major role. The history of science is full ofexamples from the buoyancy observations of Archimedes to therecent possibility that neutrinos might travel with a velocity thatslightly exceeds the velocity of light. The careful measurementsof anomalies in the spectrum of atomic hydrogen, which led tothe development of the quantum theory of radiation, vacuumfluctuations, and the interactions and the decay of fundamentalparticles in the 1950’s, are particularly pertinent.
In the present context of measurements related to the coher-ence of an SI based on the values of physical constants, searchesfor inconsistencies among these values are very important. Thevalue of the elementary charge e as contained in the Josephsonconstant 2e/h just might not be quite the same as that in thevon Klitzing constant h/e2, and this can be tested by passinga current generated by counting and timing electrons througha quantum Hall device and measuring the voltage across itwith Josephson junctions. This kind of investigation has cometo be known as a “metrological triangle.” Another example iswhether the SI ohm unit as realized by a calculable capacitor,which is directly based on a length measurement in termsof meter, is the same as that derived from the quantum Halleffect, which is intimately related to values of the fine structureconstant α, since h/e2 = μ0c/2α as derived from properties ofthe electron [13]. The failure of these “triangles” to close wouldindicate incompleteness in our understanding of physics at themost fundamental level. Sub-part-per-million measurementsare in hand, which need improvements in what is presentlypossible and which are far from easy, but they complementthose of the Large Hadron Collider and are at least orders ofmagnitude less expensive.
Other aspects of metrology can greatly benefit from theeffort expended in establishing an SI unit. The difficulty ofattaining the desired few parts in 108 accuracy for a wattbalance does not lie in its basic principle but in the largenumber of quantities that must be measured at least a factor often better for their statistically combined uncertainties to reachthis overall target. This necessitates driving the measurementsof mass, gravitational acceleration, resistance, constant, andslowly varying voltages and velocity measurement by the timedpassage of optical interference fringes to or even beyond their
state of the art. Consequently, any institution attempting a wattbalance measurement will inevitably improve its expertise in allthese basic techniques of metrology.
To illustrate the extreme difficulty of just one of thesetechniques as applied to a watt balance, note that comparinga constant voltage source with the output of a programmableJosephson array can, with great care, be accomplished with1× 109 relative accuracy provided that the noise properties ofthe source are small enough, that the effects of thermoelectricvoltages are eliminated, that the voltmeter measuring smallvoltage differences has sufficient linearity and stability of itszero indication, etc. As additional problems, the voltage of theorder of a volt generated by the moving coil of a watt balanceslowly varies at the rate of about a hundred microvolts persecond because of the nonuniformity of the magnetic flux andrapidly by up to a millivolt over a bandwidth of up to a kilohertzbecause the coil velocity is affected by ground vibration. For-tunately, the vibrational velocities and the consequent voltagefluctuations are completely correlated, and their effects can becompletely removed by integration over identical time intervals.Attaining an accuracy of the order of a nanovolt therefore placesgreat demands on the timing arrangements and the linearityand the bandwidth of the voltage difference amplifier. The slowvariation due to magnetic-flux nonuniformity has to be dealtwith by curve fitting to extract the voltage/velocity ratio atthe instants the coil passes through the positions that it occu-pied during weighing. Watt balance operators have succeededin satisfying these demands, despite their extreme difficulty[18]–[20].
The challenges for watt balance proponents are, first, tocomplete the watt balance measurements still in progress; sec-ond, to improve their resolution and consistency; and, third, toprogress toward a version of the apparatus engineered for easierroutine verification of representative artifact kilograms in thefuture. Therefore, the progress depends on the willingness ofthose laboratories working with watt balances to continue torefine their work after redefinition to produce a kilogram basedon quantum standards, which is more reproducible than . Apermanent stability of a few parts in 108 is needed.
I believe that it is a very great benefit to a national mea-surement laboratory to take part in measurements of this kind.Working at the limits of metrology presents the challenge ofusing individual skills to devise new methods and of persistingto obtain the unique correct result of a measurement and itsassociated uncertainty rather than following a procedure laiddown, however intelligently, by others. Unfortunately, wattbalances, silicon atom counting, and inert-gas thermometry arenot affordable by the budgets of most individual institutes, butjoining in a collaborative effort with other institutes shouldbe possible. State-of-the-art noise thermometry, however, doesnot need greatly expensive apparatus or manpower, particularlyif there is already a thermometer calibration section in theinstitute, which realizes the international practical temperaturescale.
There is also the very important possibility of spinoff fromfundamental metrology. Struggling with measurements at theboundary of what is possible is just as likely to result inadvances in technology useful for science and engineering
KIBBLE: MEASUREMENTS FOR THE FUTURE—A COMPLETE SI FROM PHYSICAL CONSTANTS 2131
as a whole as planetary exploration and is again much lessexpensive.
The last vestige of the 19th century metrology and units willdisappear with abandoning the artifact kilogram. They will bereplaced by 21st century SI units more fitting for the quantumand fundamental particle physics, which underpins our presentworld of communication and technology. The world authority,the General Conference on Weights and Measures, has alreadyannounced its intention to do this [21].
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Bryan P. Kibble was born on October 20, 1938,in Berkshire, U.K. He received the B.A. degree inphysics and the D.Phil. degree from Oxford Univer-sity, Oxford, U.K., in 1960 and 1964, respectively.
From 1960 to 1967, he did research in the fieldof atomic spectroscopy. From 1965 to 1967, hewas with the University of Windsor, Windsor, ON,Canada. Until 1967, he was with the National Phys-ical Laboratory, Teddington, U.K., where he wasconcerned with accurate measurements of physicalconstants and realizations of the base SI electrical
units, i.e., watt, farad, ohm, and henry.Dr. Kibble is a Fellow of the Institution of Engineering and Technology (IET)
and the Institute of Physics, which awarded him the Duddel medal in 1985. Hewas a recipient of the SUNAMCO medal in 1992, the IET Achievement Awardin 2000, and the IEEE Joseph Keithley Award in 2009. He retired in 1998 andnow acts as a Consultant in alternating-current impedance measurement withthe Physikalisch-Technische Bundesanstalt, Braunschweig, Germany.
