1 1. J. Wilkins, An Essay towards a Real Character and a Philosophical Language, Royal Society , London (1668). measures took as its starting point a single universal measure—the meter—and used it to define length, volume, and mass. The meter came from a perceived constant of nature: one ten-millionth of the distance along Earth’s meridian through Paris from the North Pole to the equator. 2 2. K. Adler, The Measure of All Things, Simon & Schuster , New York (2002). 3 The International System of Units (SI), 8th edition (2006), 3. International Bureau of Weights and Measures (BIPM),(2006), http://www.bipm.org/en/si/si_brochure platinum artifact standards for length and mass measurement “for all time, for all people” was born. Although the present International System of Units (SI, from the French Système International d’Unités) was officially established in 1960, its origin goes back to the creation of the metric system during the French Revolution. Following an idea proposed a century earlier by John Wilkins,the new system of weights andtook as its starting point a single universalmeter—and used it to define length, volume, and mass. The meter came from a perceived constant of nature: one ten-millionth of the distance along Earth’s meridian through Paris from the North Pole to the equator.Definitions for the units of volume and mass followed, with the liter being 0.001 mand the kilogram the mass of 1 liter of distilled water at 4 °C. Subsequently, in 1799, twoartifact standards for length andbased on those definitions were deposited in the Archives de la République in Paris. In the words of the Marquis de Condorcet, a new system of“for all time, for all people” was born.

Seventy-six years later, the signing of the Meter Convention in 1875 established three international organizations: the General Conference on Weights and Measures (CGPM), the International Committee for Weights and Measures (CIPM), and the International Bureau of Weights and Measures (BIPM). They were formally tasked with maintaining the SI and continue to do so.

The SI is a living, evolving system, changing as new knowledge and measurement needs arise, albeit sometimes slowly when measured against the rapid pace of scientific progress. For example, in the 18th and 19th centuries when natural philosophers and scientists tried to apply the system of length, mass, and time—with time defined by astronomical observations—to quantify newly discovered phenomena such as magnetism and electricity and the concept of energy, they also discovered the need for new units of measure. The likes of Carl Friedrich Gauss, Wilhelm Weber, James Clerk Maxwell, and Lord Kelvin, pioneers in the new science, helped to expand the system and developed the conceptual framework of a coherent system with base mechanical units from which to create derived units as needed. The system included clear explanations of how to realize the base units through measurement, and the coherent derived units were products of powers of the base units with a prefactor of 1.

1 3 The International System of Units (SI), 8th edition (2006), 3. International Bureau of Weights and Measures (BIPM),(2006), http://www.bipm.org/en/si/si_brochure fundamental constants of nature on which all SI units will be realized. Gone are the base units and their definitions. The timeline in figureshows that despite numerous changes, the SI still has this fundamental framework, with 7 base units (and associated definitions for realizing them) and 22 derived units with special names and symbols.However, international consensus is building to once again advance the SI to reflect contemporary understanding of the physical world. The new framework of the future SI will no longer define seven base units and coherently derived units; instead, it will adopt exact values for sevenof nature on which all SI units will be realized. Gone are the base units and their definitions.

How to make a system of units Section: Choose Top of page ABSTRACT How to make a system of u... << Small step or giant leap? Impact and consequences What about the ampere? Getting the word out REFERENCES CITING ARTICLES A system of units to express all physical measurements must take into consideration all physical quantities and the equations that relate those quantities—namely, the accepted laws of physics. A simple example is F = ma = mdv/dt = md2x/dt2, (1) where force F, mass m, acceleration a, velocity v, length x, and time t are all quantities and the relations are Newton’s second law of motion and basic dynamics. 4 45, 129 (2008). 4. For an elementary algebraic test of a complete and nonredundant set of quantum base quantities, see P. J. Mohr, Metrologia, 129 (2008). https://doi.org/10.1088/0026-1394/45/2/001 equation 1 were all we knew about the physical world (six quantities, three constraints), choosing either force or mass and any two of the remaining five quantities would give us an independent set of three base quantities. Carefully choosing a subset of independent base quantities allows one to derive the remaining quantities as functions of the chosen subset through the accepted laws of physics. The selection of base quantities is not unique; but they must be complete and nonredundant.For example, if1 were all we knew about the physical world (six quantities, three constraints), choosing either force or mass and any two of the remaining five quantities would give us an independent set of three base quantities. However, we are not yet done. To fully define the system of units, we must assign a specific reference quantity to each base quantity. The reference quantity can be a specific artifact, as is the case for the base quantity of mass in the present SI—the international prototype of the kilogram (IPK). Alternatively, in the energy equivalence relations E = hν = mc2 = eV = kT, (2) the Planck constant h, the speed of light c, the elementary charge e, and the Boltzmann constant k can also be reference quantities since they are invariants with specific values. The present SI has seven base quantities: time, length, mass, electric current, thermodynamic temperature, amount of substance, and luminous intensity. The specific reference quantities are the definitions shown in table I . In other words, the reference quantities in the present SI are the definitions of the base units: the second, meter, kilogram, ampere, kelvin, mole, and candela. Table Table 1. Present SI base quantities, base units, and definitions Base quantity Base unit Definition Time second The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. Length meter The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second. Mass kilogram The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. Electric current ampere The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per meter of length. Thermodynamic temperature kelvin The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. Amount of substance mole The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12; the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. Luminous intensity candela The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. Table I. ν(133Cs) hfs , c, h, e, k, the Avogadro constant N A , and the luminous efficacy K cd . However, to provide continuity and ease of transition, their values will be expressed in terms of the present SI units instead of in potentially confusing new base units. Table The new SI will also have seven base quantities: frequency, velocity, action, electric charge, heat capacity, amount of substance, and luminous intensity. The specific reference quantities will be the exact values of a set of defining constants: the ground-state hyperfine splitting of the cesium-133 atom ΔCs), the Avogadro constant, and the luminous efficacy. However, to provide continuity and ease of transition, their values will be expressed in terms of the present SI units instead of in potentially confusing new base units. Table II shows the new base quantities and the associated defining constants with their definitions. Table Table 2. New SI base quantities, defining constants, and definitions Base quantity Defining constant Definition Frequency Δν(133Cs) hfs The unperturbed ground-state hyperfine splitting frequency of the cesium-133 atom Δν(133Cs) hfs is exactly 9 192 631 770 hertz. Velocity c The speed of light in vacuum c is exactly 299 792 458 meter per second. Action h The Planck constant h is exactly 6.626X × 10−34 joule second. Electric charge e The elementary charge e is exactly 1.602X × 10−19 coulomb. Heat capacity k The Boltzmann constant k is exactly 1.380X × 10−23 joule per kelvin. Amount of substance N A The Avogadro constant N A is exactly 6.022X × 1023 reciprocal mole. Luminous intensity K cd The luminous efficacy K cd of monochromatic radiation of frequency 540 × 1012 hertz is exactly 683 lumen per watt. The symbol X in the numerical values indicates additional digits to be set upon redefinition of the SI. The term “defining constant” is used in the broader sense to include invariants of nature such as the hyperfine splitting frequency of the cesium-133 atom and the luminous efficacy. Table II.

Small step or giant leap? Section: Choose Top of page ABSTRACT How to make a system of u... Small step or giant leap? << Impact and consequences What about the ampere? Getting the word out REFERENCES CITING ARTICLES 5 116, 797 (2011). 5. B. N. Taylor, J. Res. Natl. Inst. Stand. Technol., 797 (2011). https://doi.org/10.6028/jres.116.022 ν(133Cs) hfs , c, and K cd , the four remaining definitions would be: As can be seen in tables I and II , the present and future definitions of the SI have similarities, especially when one compares the present base quantities of time and length with the new base quantities of frequency and velocity. The definitions are fully equivalent, as is also the case for luminous intensity. That equivalence is because the present SI has already incorporated invariants of nature as part of its foundation, thanks to the 1967 and 1983 redefinitions of the second and meter, respectively. In fact, if the IPK were temporarily granted the status of an invariant of nature, all of the present base unit definitions could be recast into the form of the new SI.After ΔCs), and, the four remaining definitions would be: ‣ The mass of the international prototype of the kilogram, m(K), is exactly 1 kilogram. ‣ The magnetic permeability, μ 0 , is exactly 4π × 10−7 newton per ampere squared. ‣ The triple point of water, T TPW , is exactly 273.16 kelvin. ‣ The molar mass of carbon-12, M(12C), is exactly 0.012 kilogram per mole. Because the SI has been continually evolving with new knowledge and technological advances, it might appear that the impending change is just another incremental improvement with an exchange of “invariants” in which m(K), µ 0 , T TPW , and M(12C) are replaced by h, e, k, and N A . However, the change brings major advantages, the most conspicuous being the replacement of the IPK artifact, with its inherent problems of accessibility, lack of an explicit link to an invariant of nature, and questionable long-term stability. fundamental constants, measurements traceable to the SI will no longer be confined to a particular realization or experiment, such as a direct comparison between secondary mass standards and the IPK. The present definition of the meter as “the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second” demonstrates the scalability of an explicitly defined constant. At the small length scale, state-of-the-art x-ray interferometry measurements have determined the lattice spacing of isotopically enriched silicon-28 crystals 6 et al. , Metrologia 48, S37 (2011). 6. E. Massa, Metrologia, S37 (2011). https://doi.org/10.1088/0026-1394/48/2/S06 uncertainty that is less than 10−18 m (relative uncertainty of 5 parts in 109). At the large length scale, the lunar laser ranging experiment can measure the Earth–Moon distance with an absolute uncertainty approaching 1 mm (relative uncertainty less than 1 part in 1011) by timing the roundtrip flight of a laser pulse from Earth to the Moon and back. 7 76, 076901 (2013). 7. T. W. Murphy, Rep. Prog. Phys., 076901 (2013). https://doi.org/10.1088/0034-4885/76/7/076901 platinum artifact. By explicitly defining the values of a set oftraceable to the SI will no longer be confined to a particular realization or experiment, such as a direct comparison between secondary mass standards and the IPK. The present definition of the meter as “the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second” demonstrates the scalability of an explicitly defined constant. At the small length scale, state-of-the-art x-ray interferometryhave determined the lattice spacing of isotopically enriched silicon-28 crystalswith an absolutethat is less than 10m (relativeof 5 parts in 10). At the large length scale, the lunar laser ranging experiment canthe Earth–Moon distance with an absoluteapproaching 1 mm (relativeless than 1 part in 10) by timing the roundtrip flight of a laser pulse from Earth to the Moon and back.Both experiments depend on the fixed value of the speed of light, implicitly through the x-ray wavelength in the case of interferometry and explicitly in the case of lunar laser ranging. Neither experiment suffers from needing to relate the results to a standard at a specific length scale, as would be the case if the definition of the meter were still the distance between two notches on aartifact. The new SI will have an increased scalability and accessibility through the chosen set of constants because they appear in various research fields and physical theories, including special relativity, quantum mechanics, quantum electrodynamics, atomic physics, and condensed-matter physics. For example, given an exact value of h, mass at the 1-kg level can be measured on a watt balance with a relative uncertainty of 2 parts in 108 (see the box below). Or frequency measurements of atom recoil from the absorption and emission of photons can give mass at the level of 10−25 kg (a single atom) with a relative uncertainty of 2 parts in 109. fundamental constants to define a system of units, the selection of h, e, k, and N A for the new SI was made in careful consideration of practicality, reproducibility, accessibility, and the precision at which measurements can be made today. Comparisons of Josephson voltage standards and of quantized Hall resistance standards linked to the values of h and e (see figure 2 uncertainties 8 46, R13 (2009). 8. B. M. Wood, S. Solve, Metrologia, R13 (2009). https://doi.org/10.1088/0026-1394/46/6/R01 , 9 et al. , New J. Phys. 13, 093026 (2011). 9. T. J. B. M. Janssen, New J. Phys., 093026 (2011). https://doi.org/10.1088/1367-2630/13/9/093026 18 and 1011, respectively. Conversely, the gravitational constant G—which might seem a reasonable choice for a fundamental constant more directly linked to the traditional base mechanical units—is inherently difficult to measure (see the article by Clive Speake and Terry Quinn on While there is great freedom in the choice of the set ofto define a system of units, the selection of, andfor the new SI was made in careful consideration of practicality, reproducibility, accessibility, and the precision at whichcan be made today. Comparisons of Josephson voltage standards and of quantized Hallstandards linked to the values ofand(see figure) have relativeof a few parts in 10and 10, respectively. Conversely, the gravitational constant—which might seem a reasonable choice for amore directly linked to the traditional base mechanical units—is inherently difficult to(see the article by Clive Speake and Terry Quinn on page 27 ).

Impact and consequences Section: Choose Top of page ABSTRACT How to make a system of u... Small step or giant leap? Impact and consequences << What about the ampere? Getting the word out REFERENCES CITING ARTICLES The impact of defining h, e, k, and N A as exact will extend substantially beyond providing a basis for a system of units. Many other fundamental constants will simultaneously become exact due to the inherent relationships among them through the accepted laws of physics. Another important consequence will be exact conversion factors, with no uncertainty, for expressing energy in units of joule, kilogram, inverse meter, hertz, kelvin, or electron volt. No longer will unit conversion cause an additional uncertainty component to appear—for example, when a researcher reports the mass of some particle in kilograms when in fact the measurement was in eV or hertz. In addition, many of the other fundamental constants will have substantially reduced uncertainties. fundamental constants and conversion factors. (See the article by Peter Mohr and Barry Taylor, Physics Today, uncertainties of a select group of fundamental constants in the present SI, based on the 2010 CODATA recommendations, 10 84, 1527 (2012). 10. P. J. Mohr, B. N. Taylor, D. B. Newell, Rev. Mod. Phys., 1527 (2012). https://doi.org/10.1103/RevModPhys.84.1527 uncertainty of most of the constants. Due to new relevant data since the 2010 adjustment, the uncertainties are expected to further decrease for the upcoming 2014 CODATA adjustment. The International Council for Science’s Committee on Data for Science and Technology (CODATA) periodically provides the scientific and technological communities with a self-consistent set of internationally recommended values forand conversion factors. (See the article by Peter Mohr and Barry Taylor, March 2001, page 29 .) Table III , listing theof a select group ofin the present SI, based on the 2010 CODATA recommendations,and in the new SI, shows the dramatic decrease inof most of the constants. Due to new relevant data since the 2010 adjustment, theare expected to further decrease for the upcoming 2014 CODATA adjustment. Table Table 3. Changing uncertainties for fundamental constants Quantity Symbol Present SI u r × 109 New SI u r × 109 International prototype of the kilogram m(K) 0 44 Permeability of free space µ 0 0 0.32 Permittivity of free space ε 0 0 0.32 Triple point of water T TPW 0 910 Molar mass of carbon-12 M(12C) 0 0.70 Planck constant h 44 0 Elementary charge e 22 0 Boltzmann constant k 910 0 Avogadro constant N A 44 0 Molar gas constant R 910 0 Faraday constant F 22 0 Stefan–Boltzmann constant σ 3600 0 Electron mass m e 44 0.64 Atomic mass unit m u 44 0.70 Mass of carbon-12 m(12C) 44 0.70 Josephson constant K J 22 0 von Klitzing constant R K 0.32 0 Fine-structure constant α 0.32 0.32 E = mc2 energy equivalent J↔kg 0 0 E = hc/λ energy equivalent J↔m–1 44 0 E = hν energy equivalent J↔Hz 44 0 E = kT energy equivalent J↔K 910 0 1 J = 1 (C/e) eV energy equivalent J↔eV 22 0 Relative uncertainties, u r , for some fundamental constants and energy equivalents are given in parts in 109. Present relative uncertainties are based on the 2010 CODATA adjustment of the fundamental constants. 10 84, 1527 (2012). 10. P. J. Mohr, B. N. Taylor, D. B. Newell, Rev. Mod. Phys., 1527 (2012). https://doi.org/10.1103/RevModPhys.84.1527 u r of m(K) in the present SI is 0 only by definition. The new SI relative uncertainties assume fixed values of the Planck constant h, elementary charge e, Boltzmann constant k, and Avogadro constant N A . Table III. When the CGPM approves the redefinition of the SI, the CODATA Task Group on Fundamental Constants will perform two special evaluations of the fundamental constants. The first will be similar to its periodic determinations, but with the goal of determining the best values of the defining constants h, e, k, and N A . The second will be to determine the values and greatly reduced uncertainties of the remaining constants based on the newly exact defining constants. The framework of the new SI, with exact defining constants, will have significant consequences for national metrology institutes and practical metrology. The value of T TPW will not change, but a relative uncertainty component on the order of 1 × 10−6 or less will be added. The value of M(12C) will not change, but a relative uncertainty component on the order of 7 × 10−10 or less will be added. The value of m(K) will not change, but a relative uncertainty on the order of 2 × 10−8 or less will be added. The IPK will become just another artifact with no special position in the SI. Anyone with the ability to make appropriate measurements related to the defining constants will be able to realize the kilogram.

What about the ampere? Section: Choose Top of page ABSTRACT How to make a system of u... Small step or giant leap? Impact and consequences What about the ampere? << Getting the word out REFERENCES CITING ARTICLES h and e through the Josephson constant, K J = 2e/h, and the von Klitzing constant, R K = h/e2. Figure 2 K J−90 and R K−90 , based on the best available data. 11 26, 69 (1989). 11. T. J. Quinn, Metrologia, 69 (1989). https://doi.org/10.1088/0026-1394/26/1/006 resistance linked to K J−90 and R K−90 . However, the present SI continues to define the ampere as the current in two infinitely long, negligibly thin wires set 1 m apart that will produce a force of 2 × 10−7 N for each meter of length. That is, for a quarter of a century, almost all electrical metrology has used a system of units that is not part of the SI. Defining h and e exactly will bring electrical metrology back into the SI. With the discoveries of the Josephson and quantum Hall effects, it became possible to conceive of quantum electrical standards that relate electrical units toandthrough the Josephson constant,= 2, and the von Klitzing constant,. Figureexplains the operation of two such quantum electrical standards in use at NIST. In 1990 the CIPM adopted exact values for the constants, now labeledand, based on the best available data.Since then, almost all electrical metrology has been traceable to conventional electrical units of voltage andlinked toand. However, the present SI continues to define the ampere as the current in two infinitely long, negligibly thin wires set 1 m apart that will produce a force of 2 × 10N for each meter of length. That is, for a quarter of a century, almost all electrical metrology has used a system of units that is not part of the SI. Definingandexactly will bring electrical metrology back into the SI. K J and R K . Taking into consideration new relevant input data for the 2014 CODATA adjustment of the fundamental constants, 12 12. Special issue, “Watt and Joule Balances, the Planck Constant and the Kilogram,” Metrologia 51(2) (2014). resistance measurements on the order of 1 × 10−7 and 2 × 10−8, respectively. Those changes are within the relative uncertainties of 4 × 10−7 for voltage and 1 × 10−7 for resistance measurements assigned by the CIPM’s Consultative Committee for Electricity (now the Consultative Committee for Electricity and Magnetism) when translating between the 1990 conventional and SI electrical units. 13 26, 47 (1989); 38, 89 (2001). 13. B. N. Taylor, T. J. Witt, Metrologia, 47 (1989); https://doi.org/10.1088/0026-1394/26/1/004 T. J. Quinn, Metrologia, 89 (2001). https://doi.org/10.1088/0026-1394/38/1/11 Another significant impact on electrical metrology will arise from the anticipated assigned values forand. Taking into consideration new relevant input data for the 2014 CODATA adjustment of thethe new fixed values of the Josephson and von Klitzing constants would lead to relative changes in voltage andon the order of 1 × 10and 2 × 10, respectively. Those changes are within the relativeof 4 × 10for voltage and 1 × 10forassigned by the CIPM’s Consultative Committee for Electricity (now the Consultative Committee for Electricity and Magnetism) when translating between the 1990 conventional and SI electrical units. Even though the values of the permeability and permittivity of free space—μ 0 and ε 0 , respectively—will not change upon redefinition, they will no longer be exact. There will be an additional relative uncertainty component on the order of 3 × 10−10 or less to any electrical measurement that is directly linked to μ 0 and ε 0 .