h c ν Hyperfine transition frequency e Elementary charge k Boltzmann constant N A K cd SI wheel Defining constants

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1 SI BASE UNITS

2 SI wheel h c Planck constant Speed of light in vacuum Defining constants ν Hyperfine transition frequency e Elementary charge k Boltzmann constant N A Avogadro constant K cd Luminous efficacy

3 National Physical Laboratory The National Physical Laboratory (NPL) is the UK s National Measurement Institute, providing the underpinning measurement capability for UK prosperity and quality of life. From new antibiotics and more effective cancer treatments to unhackable quantum communications and superfast 5G networks, technological advances must be built on a foundation of reliable measurement. NPL is a world-leading research organisation with over 500 scientists and engineers working in a wide range of fields. Our work saves lives, protects the environment, enables citizens to feel safe and secure and supports innovation and international trade. Our measurement advice is objective and independent, trusted by consumers, investors, policymakers and entrepreneurs. NPL is responsible in the UK for units of measurement, within the International System of Units the SI. Through our work and the SI, we help to ensure that measurements are consistent and accurate for every aspect of life. Follow us on social media npl.co.uk npldigital national physical laboratory (NPL)

4 Measurement in our lives Measurement is at the heart of all science and engineering. It is only when we can measure something that scientists can study it and engineers can improve it. And since science and engineering play an important role in our lives, measurement matters for everyone. Measurement affects our daily lives - when our medical care depends critically on measurements of concentrations of chemicals in blood or the intensity of X-rays - when a satellite navigation system guides us along a road and it depends on the time measured by ultra-precision clocks on satellites - when we buy a part that just fits : a nut fits a bolt or a Lego brick sticks perfectly to another brick - when we buy paint and then buy some more a year later and the colour matches. In all these situations, and thousands more, we are enjoying the benefits of a global system of measurement. Measurement and units Measurement is the quantitative comparison of something against a reference. A measurement result is expressed as a value (a number) together with one or more units of measurement, for example: a car travelling at a speed of 10.4 metres per second (m/s). When a measured value is given along with its one or more units, this tells us both the dimension (such as mass, length or time) and the scale of the measured value. npl.co.uk

5 The International System of Units How can we ensure a length measurement in the UK and a length measurement in another country, such as Japan, are consistent? How do we know that measurements done in different years or decades can be compared? We do this by using the globally agreed International System of Units, known as the SI (from the French, Système International d Unités). The SI sets out what the agreed units of measurement are, how they are defined and how they are realised in practice. The widespread adoption of the SI allows science, industry and trade to measure physical objects and phenomena by using the same units, so that the results can be compared meaningfully, worldwide. The SI was formally agreed in 1960 and is directed from the International Bureau of Weights and Measures (BIPM), a laboratory situated in diplomatically protected territory in Sèvres, just outside Paris. At the BIPM, scientists from all over the world meet to agree on definitions of precisely what we mean by each of the SI base units. Typically, these scientists work at national measurement institutes, which are responsible for providing the benefits of the SI in their individual countries. In the UK, this is one of the key roles of NPL. 05

6 What are the base units of the SI? The SI covers units for every type of measurement, but at the heart of the SI is a set of seven units known as the base units. They are the kilogram, the metre, the second, the ampere, the kelvin, the mole and the candela. Unit Symbol Quantity kilogram kg mass metre m length second s time ampere Aelectric current kelvin K temperature mole mol amount of substance candela cdluminous intensity The seven base units have been chosen so that combinations of these can be used to express all other measurement units, known as derived units. For example: npl.co.uk - We can combine base units of length: metre metre metre or cubic metres (m 3 ) to give a unit of volume. - The unit of force, the newton (N), is formed from combining base units of mass, length and time: kilogram metre per second squared (kg m/s 2 ).

7 How have the units of measurement been defined? Historically, units of measurement were defined by physical objects or properties of materials. For example, the metre was defined by the length between lines engraved on a metal bar, and the kilogram is still defined as the mass of a carefully specified cylinder of platinum iridium metal called the international prototype kilogram (IPK). In these cases, the definition was also the physical form the realisation of the unit. However, these physical representations can be unstable they can change over time or in different environments. So, over the years, the definitions have been improved to be more stable and reproducible and to better meet the needs of research and technological applications. During the last century, scientists measured constants of nature, such as the speed of light and the Planck constant, with increasing accuracy. They discovered that these were more stable than physical objects. It became clear that these constants of nature could offer a new and more stable foundation for the SI. How can constants of nature provide definitions of the SI base units? Constants of nature, such as the speed of light, are unchanging and we can give them exact values. Because of this, these constants provide the most exact and stable way to define all of the SI base units into the future. This type of definition is possible because constants of nature themselves have units. For example, the constant e, which is the elementary charge on an electron, can be expressed using units of amperes and seconds. In this way, e is directly related to those two SI base units. So, by using seven carefully chosen constants of nature, we can define all the base units of the SI by using combinations of those constants. 07

8 Why do we need to change the SI? As science advances, ever more accurate measurements are both needed and achievable. But this improving accuracy must happen through measurement standards and their definitions. The kilogram is the last SI base unit that is still defined in terms of a human-made artefact, the international prototype kilogram (IPK). By definition, the IPK always weighs one kilogram exactly. However, studies of closely similar copies tell us that the mass of the IPK is almost certainly changing minutely. This implies that there has been a tiny but known change in the values of all masses. For mass, and for all units of measurement, we need to rule out this type of problem. There are two key ways that the SI will change to create a more stable and future proof basis for measurement: 1. Taking physical artefacts out of the definitions of the base units Seven base units of the SI will be defined in terms of constants of nature, with no defining artefacts or materials. Moving away from artefact-based definitions will remove uncertainty, avoiding the risk that definitions could become unstable over time. For the best standards for measurements, we need stable definitions that are valid everywhere and at all times. The planned redefinitions will make this possible. 2. Separating definition from realisation For the first time, the definitions of all the SI base units will be separate from their realisations. Instead of definitions becoming outdated as we find better ways to realise units, definitions will stay future-proof. For the redefined SI base units, the definitions will be exact, with no uncertainty. The uncertainty associated with past definitions won t disappear it will move across to the realisations, where it can be reduced as measurements improve. npl.co.uk

9 The 2019 revision of the SI The global metrology community agreed to a revision to the SI at the 26th General Conference on Weights and Measures in November This decision means that, for the first time, all seven of the base units are defined in terms of constants of nature such as the speed of light, the Planck constant and the Avogadro constant. Using seven defining constants as the basis for the SI means that the definitions of all the base units will stay stable into the future. The revision brings in new definitions of the ampere, kilogram, kelvin (and, consequently, degree Celsius) and mole. Although these changes won t be felt in everyday life, they represent a profound change of perspective, as all the base units of the SI will be defined in terms of constants of nature the most stable quantities we have ever encountered. The new definitions affect four of the base units: The kilogram The ampere The kelvin in terms of the Planck constant (h) in terms of the elementary charge (e) in terms of the Boltzmann constant (k) The mole in terms of the Avogadro constant (N A ) 09

10 What does this mean in practice? Making this revision across the whole SI is a profound change in approach that will underlie all measurements in science and more widely. These changes will be used by scientists and engineers who are making measurements at the extremes, but in everyday life it will appear that not much has changed. The redefinition of the units is like replacing the weak foundations of a house with new foundations that are exactly the same size, but stronger. The difference won t be visible on the surface, but substantial changes will have been made to underpin the structure for the long term. The changes in the SI will ensure that the SI definitions stay robust for the future, ready for advancements in science and technology. When will the proposed changes come into effect? The revision of the SI will come into effect on World Metrology Day, 20 May 2019, when more than 80 countries will celebrate how measurement affects our daily lives. npl.co.uk

11 Definitions kilogram page 12 metre page 14 second page 16 ampere page 18 kelvin page 20 mole page 22 candela page 24

12 The kilogram Definition before May 2019 The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. We realise this by comparing the gravitational force on an object with the gravitational force on standard weights. The gravitational force on the standard weights is worked out by comparison (via several intermediate stages) with the gravitational force on the IPK. The kilogram kg is the SI unit of mass Definition after May 2019 It will be defined by taking the fixed numerical value of the Planck constant, h to be when expressed in the unit J s, which is equal to kg m 2 s 1, where the metre and the second are defined in terms of the speed of light, c, and Δν. We will compare the gravitational force on an object against an electromagnetic force, using an instrument known as a Kibble balance. The electromagnetic force can be calculated in terms of h, the Planck constant. npl.co.uk

13 Did you know? A 10 cm cube of water at 4 C has a mass of a kilogram and a metre cube has a mass of a tonne (approximately). Weight is a force (measured in newtons) and is mass multiplied by the gravitational field strength and direction. Weight depends on where you are on the Moon, you could jump six times higher than on Earth (your mass is the same, but you weigh much less). Application NPL provides traceability for measurement of active components of drugs that can weigh from less than a millionth of a kilogram to oil sea platforms that can weigh over 200 million kilograms. A balance comparing the weight of a tonne of feathers and a tonne of lead will change according to temperature and atmospheric pressure, due to the different buoyancy effects of the air displaced by the objects. In shops, solids are sold by weight, liquids by volume and ice cream by both. 13

14 The metre Definition The metre is the length of the path travelled by light in vacuum during a time interval of 1/ of a second. We measure distances by comparing objects or distances with standard lengths. Historically, we used pieces of metal or the wavelength of light from standard lamps as standard lengths. Since the speed of light in vacuum, c, is constant, in the SI, we use the distance that light travels in a given time as our standard. For long distances (e.g. Earth to Moon), we simply measure the time light takes to travel the distance using an accurate timer; for shorter distances (when the time is too short to measure accurately enough), we use laser-based systems, where we count the number of wavelengths of the laser light that correspond to the length we want to measure. The definition will be updated to a new format of wording in The metre m is the SI unit of length npl.co.uk

15 Did you know? Application The word metre can be traced to the Greek verb μετρέω (metreo), which means to measure, count or compare. The metre was originally defined as one ten-millionth of the distance on the Earth s surface from the north pole to the equator, on a line passing through Paris. Expeditions from 1792 to 1799 determined this length by measuring the distance from Dunkirk to Barcelona, with an accuracy of about 0.02%. In , physicist Hippolyte Fizeau measured the speed of light using a rotating cogwheel. In 2009, NPL and the BBC used a kitchen blender to recreate Fizeau s experiment. We can traceably measure distances from a few picometres ( m, one trillionth of a metre) to the Voyager 1 spacecraft (already over m away). The Large Hadron Collider particle accelerator in Switzerland is installed in 30 km of underground tunnels to make it work, the steering magnets must be positioned to an accuracy of one tenth of a millimetre every 100 m. 15

16 The second Definition The second is the duration of periods of radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. We measure time in terms of the resonant frequency of caesium atoms. We tune the frequency of a microwave oscillator until it matches the caesium resonant frequency. This frequency is the same for every caesium atom. We define one second to be the time corresponding to exactly oscillations of the microwaves tuned to caesium atoms. The definition will be updated to a new format of wording in The second s is the SI unit of time npl.co.uk

17 Did you know? Time doesn t run at the same rate everywhere. NPL built the first accurate caesium atomic clock in 1955 (over 60 years ago). NPL is building clocks that will be accurate to one second in the lifetime of the universe (14 billion years). Fibre optic cables carry time signals from NPL s atomic clocks to financial institutions in the City of London. Application Satellite navigation systems find locations using signals from atomic clocks on board satellites. Accurate timestamping of financial transactions is important to help prevent trading irregularities and to keep an audit trail. 17

18 The ampere Definition before May 2019 An ampere is a constant electric current that, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to newtons per metre of length. So, the ampere is defined using the forces between wires carrying electric currents. The laws of physics worked out in the 19th century tell us how large these forces will be if we know exactly the geometry of the wires. To create a standard ampere in the lab, we need precisely constructed coils of wire, as well as standards of mass, length and time. The ampere A is the SI unit of electric current Definition after May 2019 It will be defined by taking the fixed numerical value of the elementary charge e to be when expressed in the unit coulomb, which is equal to A s, where the second is defined in terms of Δν. The new ampere definition exploits the fact that electric current is generally made up of a flow of billions of identical charged particles called electrons. We can create a standard ampere by using special nano scale electric circuits that control the flow of electrons. npl.co.uk

19 Did you know? The ampere is named after André-Marie Ampère, who established the equation connecting the size of a magnetic field to the electric current that produces it. A typical lightning strike has a current of 20,000 A. There are 300,000 a year in the UK, but only 15% reach the ground. A wristwatch typically needs only one millionth of an ampere of current from its battery (1 µa). Application Electricity (moving electrical charge) is a key way to carry energy. Our electricity bills charge us on current voltage time. Electrical measurements are everywhere, found in the readout of almost every type of sensor (e.g. light, heat, force) that exists. Accurate measurements support everything from telecommunications and security to automotive and aerospace technologies. As far as we can tell, every single electron in the universe is exactly identical and they all carry exactly the same electrical charge. 19

20 The kelvin Definition before May 2019 The kelvin is the fraction 1/ of the thermodynamic temperature of the triple point of water. We measure the temperature of an object by comparing it with a standard temperature, the temperature of the triple point of water. This standard temperature is exactly K. Unusually in the SI, we also define another unit of temperature, called the degree Celsius ( C). This is related to the kelvin by subtracting from the numerical value of the temperature expressed in kelvin. t(in C) = T(in K) The reason for this is to make it easier to use in a wide variety of applications that had previously used the now obsolete centigrade scale. The kelvin K is the SI unit of thermodynamic temperature Definition after May 2019 One kelvin will be defined by taking the fixed numerical value of the Boltzmann constant, k, to be exactly when expressed in the unit J K 1, which is equal to kg m 2 s 2 K 1, where the kilogram, metre and second are defined in terms of the Planck constant, h, c, and the hyperfine transition frequency, Δν. After this redefinition, we will be measuring the temperature in terms of the energy of molecular motion. The degree Celsius will be related to kelvin in the same way as it was before May npl.co.uk

21 Did you know? The triple point of water is the unique temperature at which liquid water, solid water (ice) and water vapour, can all co-exist in equilibrium. This temperature was chosen as a standard temperature because it is highly reproducible. A simple glass cell containing pure water can reproduce this temperature to within K ( C). The coldest possible temperature (0 K or C) is called the absolute zero of temperature. At this temperature, molecules would have for most practical purposes lost all of their energy of motion. Application Temperature is important to the operation of almost all industrial processes, from food preparation to the manufacture of microcircuits. Many physical properties of things change with temperature, leading to many different ways to make thermometers. Once calibrated, thermometers use changes in the size of objects, changes in their electrical resistance and changes in colour to find out the temperature. Stainless steel, used in food storage, medical instruments and cutlery, is heated to over 1600 C during manufacture. 21

22 The mole Definition before May 2019 The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in kg of carbon 12. This large number is called the Avogadro number. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles or specified groups of such particles. Amount of substance is the quantity used to express how much chemical material is present in a sample of interest. It defines a very large number of similar, fundamental chemical constituents, such as atoms or molecules. The mole mol is the SI unit of amount of substance Definition after May 2019 The mole will be defined as exactly elementary entities. This number is the fixed numerical value of the Avogadro constant, N A, when expressed in the unit mol 1. This is the reverse of the original definition the Avogadro constant will be exactly known and no longer represented by an exact mass of a specific chemical. Much of chemistry involves weighing chemicals and relating this to the amount of substance present via the mass we expect a mole of a particular chemical to have. This will not change from May 2019, but the new definition will offer the possibility of new methods being used, such as counting individual molecules, to improve accuracy for very small amounts of chemical material. npl.co.uk

23 Did you know? If an atom was the size of a grapefruit, then an Avogadro number of them would have approximately the same volume as the Earth. The Avogadro number is so large that the number of atoms in a mole of carbon is greater than the total number of human cells in every person on Earth. (Human bodies contain around 40 trillion cells, and with about seven billion people on Earth, total cell count is about ) Application Atoms and molecules don t react together in terms of mass-based relationships, but instead in terms of amount of substance based relationships. We often call this stoichiometry. The mole is used to quantify the number of atoms or molecules that can chemically react on a one-to-one (or simple whole number) basis, as this is much more useful than their mass or volume. We don t use the mole to describe things that aren t fundamental entities like atoms, ions and molecules, so it is not just a large number that can be used for, say, a mole of stars. 23

24 The candela Definition The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency hertz and that has a radiant intensity in that direction of 1/683 watts per steradian (a unit of solid angle). The candela is the only SI base unit based on human perception, that is, how bright lights appear to human beings. Historically, the candela was defined in terms of the light given out by a candle, hence the name. The human eye responds differently to different frequencies of light. Under typical daytime lighting conditions, the peak sensitivity is at approximately hertz, which is in the greeny-yellow region of the light spectrum. The contribution of each frequency is weighted depending on the sensitivity of the human eye to that frequency. The definition will be updated to a new format of wording in The candela cd is the SI unit of luminous intensity npl.co.uk

25 Did you know? The only psychophysical SI base unit, the candela converts physical watts to perceived luminance, originally defined as one candlepower (with the candle made of sperm whale wax). Our eyes are more sensitive to green light than to red and blue light. Application The lumen measures total light in all directions from a source it can be seen on light bulb packaging, allowing you to compare the brightness of different lighting technologies (the equivalent wattage of light bulbs tells you how much electrical power is consumed by a tungsten light bulb of similar brightness). 25

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28 npl.co.uk Disclaimer Although every effort is made to ensure that the information contained in this brochure is accurate and up to date, NPL does not make any representations or warranties, whether express, implied by law or by statute, as to its accuracy, completeness or reliability. NPL excludes all liabilities arising from the use of this brochure to the fullest extent permissible by law. NPL reserves the right at any time to make changes to the material, or discontinue the brochure, without notice. The NPL name and logo are owned by NPL Management Limited. Any use of any logos must be authorised in writing. NPL Management Ltd, v3/.5K/4PT/1018