**Measurements and processes of the redefinition of 4 SI units**

Dr. Michael de Podesta

National Physical Laboratory

https://www.npl.co.uk/people/michael-de-podesta

Michael graduated with a BSc from Sussex University in 1981 and then in 1985 completed a DPhil in the electronic properties of metals at cryogenic temperatures. After postdoctoral work at Bristol University, he was appointed a lecturer at the University of London in 1987, and joined NPL in 2000.

Michael is a chartered physicist, a member of the Institute of Physics, and in 2009 was awarded an MBE for services to Science.

Dr Michael de Podesta’s wide-ranging research interests concern all aspects of temperature measurement: from building the most accurate thermometer ever made; to developing industrial sensors capable of surviving harsh conditions; to measuring the temperature underneath the wheel of a train travelling at over one hundred miles per hour; to representing NPL on the steering committee of the International Surface Temperature Initiative.

Michael is an active science communicator and writes a blog at ‘protons for breakfast’

On the 20^{th} May 2019, four of the seven base units of the SI (the kilogram, Kelvin, ampere and mole) were redefined. Significantly this change ushered in a subtle but profound shift in how we measure the world around us. Instead of using human-defined ‘yardsticks’, we will base our system of measurement on the most stable entities we have ever encountered – the constants of nature. In the talk, Dr de Podesta discussed the rationale for the change, and some of the details regarding the Kelvin, kilogram and ampere.

**My notes from the lecture** (if they don’t make sense then it is entirely my fault)

https://en.wikipedia.org/wiki/2019_redefinition_of_the_SI_base_units

https://www.npl.co.uk/insights/changes-international-system-of-units

https://www.nist.gov/si-redefinition/turning-point-humanity-redefining-worlds-measurement-system

https://www.bipm.org/en/news/new-si.html

https://www.sciencedaily.com/releases/2018/11/181116115556.htm

How do we get to know anything?

1) Measure the local environment

2) Compare with your neighbour; village; town; city etc.

https://www.npl.co.uk/about-us/national-metrology-institute

Measurement is the key to understanding.

Measurement makes science scientific – not maths

A candle

Looking at it doesn’t tell you much

Light the wick and measure what is going on

There appears to be about a 2mg per second decrease in mass

This is a dynamic process

70 watts produced. This is 10 times more energy than dynamite

Measure its temperature. On the day the measurement was 965^{o}C

Makes you think about the physics

Measurement is a quantitative comparison

Before the recent changes, you had the standard SI objects. Copies of these are made but these incur errors and if these are in turn copied these errors get bigger.

There are 7 base Si units. There is a worldwide comparison with the originals – the standard originals. SI units are the only coherent ones.

Useful that there are only 7. Everyone uses them. Humanity’s language of measurement. Even the US uses them.

The SI units are decided by committees

With units, you create multiples, submultiples. You create copies and reassemble.

The standard does two jobs – it defines what we mean and allows measurement which is a comparison against the standard.

The base units allow us to produce derived units such as speed.

Units need to be used by everyone – other people convenience not just ours.

The problem with the old view of the base SI units is that they could be damaged or changed.

Three of them had already been sorted out.

**Metre** – International prototype metre bar

https://en.wikipedia.org/wiki/Metre

Creating the metre-alloy in 1874 at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray. Composed of an alloy of 90% platinum and 10% iridium, measured at the melting point of ice.

The problem with relying on a metre of metal is that its length changes with temperature.

To reduce uncertainty, the 17th CGPM in 1983 replaced the definition of the metre fixing the length of the metre in terms of the second and the speed of light:

The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.

2002 – The International Committee for Weights and Measures (CIPM) considers the metre to be a unit of proper length and thus recommends this definition be restricted to “lengths ℓ which are sufficiently short for the effects predicted by general relativity to be negligible with respect to the uncertainties of realisation”.

**Candela**

https://en.wikipedia.org/wiki/Candela

Prior to 1948, various standards for luminous intensity were in use in a number of countries. These were typically based on the brightness of the flame from a “standard candle” of defined composition, or the brightness of an incandescent filament of specific design. One of the best-known of these was the English standard of candlepower. One candlepower was the light produced by a pure spermaceti candle weighing one-sixth of a pound and burning at a rate of 120 grains per hour. Germany, Austria and Scandinavia used the Hefnerkerze, a unit based on the output of a Hefner lamp.

In 2018 (and ratified in 2019) The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 10^{12} hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. The arbitrary (1/683) term was chosen so that the new definition would precisely match the old definition. Although the candela is now defined in terms of the second (an SI base unit) and the watt (a derived SI unit), the candela remains a base unit of the SI system, by definition.

**Second**

https://en.wikipedia.org/wiki/Second

There have only ever been three definitions of the second: as a fraction of the day, as a fraction of an extrapolated year, and as the microwave frequency of a caesium atomic clock, and they have realized a sexagesimal division of the day from ancient astronomical calendars.

The problem with the original definition was working out what a day was. Also even the best mechanical, electric motorized and quartz crystal-based clocks develop discrepancies, and virtually none are good enough to realize an ephemeris second. Far better for timekeeping is the natural and exact “vibration” in an energized atom. The frequency of vibration (i.e., radiation) is very specific depending on the type of atom and how it is excited. Since 1967, the second has been defined as exactly “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 caesium-133 atom” (at a temperature of 0 K). This length of a second was selected to correspond exactly to the length of the ephemeris second previously defined. Atomic clocks use such a frequency to measure seconds by counting cycles per second at that frequency. Radiation of this kind is one of the most stable and reproducible phenomena of nature. The current generation of atomic clocks is accurate to within one second in a few hundred million years.

Atomic clocks now set the length of a second and the time standard for the world.

Four of the SI units have been recently re-defined using natural constants as the previous measurements were not stable.

The natural constants include: h = planck’s constant; c = speed of electromagnetic waves in a vacuum; k = Boltzmann constant; e = elementary charge; N_{A} = Avogadro constant; Δυ_{cs }= caesium hyperfine frequency; K_{cd} = luminous efficacy of a defined visible radiation

The process of re-defining the 4 base units was administered by the BIPH

https://www.bipm.org/en/about-us/

https://www.youtube.com/playlist?list=PL-vj-3_a7wTAoKqKQxT1UWMKTrWpHS5EW

It was begun in 2007 and measurements were continuously made until 2019.

The process was run by the International Committee for Weights and Measures (CIPM) https://www.bipm.org/en/committees/cipm/

The agenda was set by CGPM General Conference on Weights and Measures (CGPM) https://www.bipm.org/en/worldwide-metrology/cgpm/

Resolution 12: CGPM 2007 https://www.bipm.org/utils/en/pdf/24_CGPM_Resolution_1.pdf

Make new definitions indistinguishable from previous definitions

Dependence of base unit definitions on physical constants with fixed numerical values and on other base units that are derived from the same set of constants

h = planck’s constant; c = speed of electromagnetic waves in a vacuum; k_{B} = Boltzmann constant; e = elementary charge; N_{A} = Avogadro constant; Δυ_{cs }= caesium hyperfine frequency; K_{cd} = luminous efficacy of a defined visible radiation

have exact values meaning that derived units are exact too

Previously the volt had base units of kg, m, s and A (Kgm^{2}S^{-3}A^{-1}). Now its base units would be Δυ_{cs}, c, h and e

So the new system will have base units and derived units in terms of natural constants

So in 2019 we have removed the uncertainty in the end of use definitions, artefacts and materials. It has blurred the distinction between base and derived units,

**Details**

**Ampere**

https://en.wikipedia.org/wiki/Ampere

Prior (1881): The ampere was originally defined as one tenth of the unit of electric current in the centimetre–gram–second system of units. That unit, now known as the abampere, was defined as the amount of current that generates a force of two dynes per centimetre of length between two wires one centimetre apart. The size of the unit was chosen so that the units derived from it in the MKSA system would be conveniently sized.

Current (2019): The flow of 1/ 1.602176634 x 10^{−19} times the elementary charge e per second.

**Kelvin**

https://en.wikipedia.org/wiki/Kelvin

Prior (1743): The centigrade scale is obtained by assigning 0 °C to the freezing point of water and 100 °C to the boiling point of water.

In 1848, William Thomson, who later was made Lord Kelvin, wrote in his paper, On an Absolute Thermometric Scale, of the need for a scale whereby “infinite cold” (absolute zero) was the scale’s null point, and which used the degree Celsius for its unit increment. Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale. Kelvin’s value of “−273” was the negative reciprocal of 0.00366—the accepted expansion coefficient of gas per degree Celsius relative to the ice point, giving a remarkable consistency to the currently accepted value.

The problem with using the boiling and freezing point of water is that they change with pressure.

In 2018, Resolution A of the 26th CGPM adopted a significant redefinition of SI base units which included redefining the Kelvin in terms of a fixed value for the Boltzmann constant of 1.380649 x 10^{−23} JK^{-1}, given the definition of the kilogram, the metre and the second.

**Mole**

https://en.wikipedia.org/wiki/Mole_(unit)

The history of the mole is intertwined with that of molecular mass, atomic mass unit, Avogadro number and related concepts.

The first table of standard atomic weight (atomic mass) was published by John Dalton (1766–1844) in 1805, based on a system in which the relative atomic mass of hydrogen was defined as 1. These relative atomic masses were based on the stoichiometric proportions of chemical reaction and compounds, a fact that greatly aided their acceptance: It was not necessary for a chemist to subscribe to atomic theory (an unproven hypothesis at the time) to make practical use of the tables. This would lead to some confusion between atomic masses (promoted by proponents of atomic theory) and equivalent weights (promoted by its opponents and which sometimes differed from relative atomic masses by an integer factor), which would last throughout much of the nineteenth century.

1900: A stoichiometric quantity which is the equivalent mass in grams of Avogadro’s number of molecules of a substance.

2019: The amount of substance of exactly 6.02214076 x 10^{23} elementary entities. This number is the fixed numerical value of the Avogadro constant, N_{A}, when expressed in the unit mol^{−1 }and is called the Avogadro number.

**Kilogram**

https://en.wikipedia.org/wiki/Kilogram

1793: The grave was defined as being the mass (then called weight) of one litre of pure water at its freezing point.

1889: The mass of a small squat cylinder of ~47 cubic centimetres of platinum-iridium alloy kept in the Pavillon de Breteuil, France. Also, in practice, any of numerous official replicas of it.

A replica of the prototype kilogram on display at Cité des Sciences et de l’Industrie, featuring the protective double glass bell.

The problem with using a block of metal is that it doesn’t normally have a mass of 1kg. It needs to be carefully cleaned (with the skin of a goat!!!!!!!!!). The mass actually drifts with time, 1 part in 10^{10} per year.

2019: The kilogram is defined by setting the Planck constant h exactly to 6.62607015 x 10^{−34} J⋅s (J = kg⋅m^{2}⋅s^{−}^{2}), given the definitions of the metre and the second. Then the formula would be kg = h/6.62607015 x 10^{−34}⋅m^{2}⋅s^{−}^{1}

How was the 1kg block of metal replaced?

Kibble balance is a project to develop an “electronic kilogram”. The vacuum chamber dome, which lowers over the entire apparatus, is visible at the top in the above left picture. Above right shows the NIST-4 Kibble balance, which began full operation in early 2015, measured Planck’s constant to within 13 parts per billion in 2017, which was accurate enough to assist with the 2019 redefinition of the kilogram.

https://en.wikipedia.org/wiki/Kibble_balance

A Kibble balance or watt balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize the new definition of the kilogram unit of mass based on fundamental constants, termed an electronic or electrical kilogram.

The name watt balance comes from the fact that the weight of the test mass is proportional to the product of current and voltage, which is measured in units of watts. In June 2016, two months after the death of the inventor of the balance, Bryan Kibble, metrologists of the Consultative Committee for Units of the International Committee for Weights and Measures agreed to rename the device in his honour.

The Kibble balance is a more accurate version of the ampere balance, an early current measuring instrument in which the force between two current-carrying coils of wire is measured and then used to calculate the magnitude of the current. In this new application, the balance will be used in the opposite sense; the current in the coils will be measured using the new standard definition of the Planck constant to “measure mass without recourse to the IPK or any physical object.” The balance determines the weight of the object; then the mass can be calculated by accurately measuring the local Earth’s gravity (the net acceleration combining gravitational and centrifugal effects) with a gravimeter. Thus the mass of the object is defined in terms of a current and a voltage —an “electronic kilogram.”

A conducting wire of length L that carries an electric current I perpendicular to a magnetic field of strength B experiences a Lorentz force equal to the product of these variables. In the Kibble balance, the current is varied so that this force counteracts the weight W of a standard mass m. This principle is derived from the ampere balance. W is given by the mass m multiplied by the local gravitational acceleration g. Thus, W = mg = BLI.

The Kibble balance avoids the problems of measuring B and L in a second calibration step. The same wire (in practice, a coil) is moved through the same magnetic field at a known speed v. By Faraday’s law of induction, a potential difference U is generated across the ends of the wire, which equals BLv. Thus

U = BLv.

The unknown product BL can be eliminated from the equations to give

UI = mgv.

With U, I, g, and v accurately measured, this gives an accurate value for m. Both sides of the equation have the dimensions of power, measured in watts in the International System of Units; hence the original name “watt balance”.

Mass m is UI/gv

The Avogadro project

https://www.youtube.com/watch?v=ZMByI4s-D-Y

The International Avogadro Coordination (IAC) project formally began as an international effort whose scope was to determine the Avogadro constant N_{A} with a relative uncertainty equal to or less than 2 × 10^{−8} using an isotopically enriched silicon crystal.

Take a perfect crystal sphere of 28Si measure its dimensions (using a laser), Find its structure using X-ray crystallography, work out the number of atoms, use spectroscopic analysis, find the mass of the sphere and examine its surface.

So 1kg is measured in terms Δυ_{cs}, c and h.