One of our regular contributors, Ronnie Cohen, has followed up on Martin Vlietstra’s article about the “new kilogram”, with a summary of the forthcoming changes to SI. It proved difficult to create some of the symbols used by SI in the text editor used by Metric Views, and readers who require the full story may wish to visit https://www.bipm.org .

On 16 November 2018, the member states of the International Bureau of Weights and Measures (BIPM) voted to redefine four of the seven base units of the SI in terms of constants. These new definitions come into force on 20 May 2019. The list of redefined base units and their fixed numerical values are:

- the kilogram, redefined by the Planck constant
- the ampere, redefined by the elementary charge
- the kelvin, redefined by the Boltzmann constant
- the mole, redefined by the Avogadro constant

This means that the kilogram and other kilogram-based definitions of other units no longer depend on the mass of physical artifact locked in a vault in Paris.

The General Conference on Weights and Measures (CGPM) agreed to the following definitions for the fixed numerical values of the constants used to define the SI base units:

- the unperturbed ground state hyperfine transition frequency of the caesium 133 atom is 9 192 631 770 Hz
- the speed of light in vacuum c is 299 792 458 m/s
- the Planck constant h is 6.626 070 15 × 10
^{–34}J s - the elementary charge e is 1.602 176 634 × 10
^{–19}C - the Boltzmann constant k is 1.380 649 × 10
^{–23}J/K - the Avogadro constant N
_{A}is 6.022 140 76 × 10^{23}mol^{–1} - the luminous efficacy of monochromatic radiation of frequency 540 × 10
^{12}Hz, K_{cd}, is 683 lm/W

The following table compares the old and new definitions of the SI base units:

Quantity | Unit Name | Old Definition | New Definition |
---|---|---|---|

time | second | 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. | The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom to be 9 192 631 770 when expressed in the unit Hz, which is equal to s-^{1}. |

length | metre | The length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second. | The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m/s, where the second is defined in terms of the caesium atom. |

mass | kilogram | A unit of mass equal to the mass of the international prototype of the kilogram. | The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10-^{34} when expressed in the unit J s, which is equal to kg m^{2/}s, where the metre and the second are defined in terms of c and the caesium frequency. |

electric current | ampere | A constant current which, 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 2 x 10^{–7 }N/m. |
The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 ×10-^{19} when expressed in the unit C, which is equal to A s, where the second is defined in terms of the caesium atom frequency. |

thermodynamic temperature | kelvin | The fraction 1/273.16 of the thermodynamic temperature of the triple point of water. | The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 ×10-^{23} when expressed in the unit J/K, which is equal to kg m^{2/}s^{2/}K, where the kilogram, metre and second are defined in terms of h, c and the caesium atom frequency. |

amount of substance | mole | 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 mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 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.
The amount of substance, symbol |

luminous intensity | candela | Luminous intensity, in a given direction, of a source that emits monochromatic radiation at a frequency of 540 x 10^{12} hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. |
The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 10^{12} Hz, K_{cd}, to be 683 when expressed in the unit lm/W, which is equal to cd sr/W, or cd sr kg-^{1} m-^{2} s^{3}, where the kilogram, metre and second are defined in terms of h, c and the caesium atom frequency. |

The second, metre and candela keep their basic definitions but are expressed in different words. The other SI base units get fundamental changes to their definitions.

Phew!

Technically, The ampere is no longer a base unit. The coulomb as it is defined directly directly from the elemental charge. The ampere is thus a derived unit equal to exactly one coulomb per second. 1 A = 1 C/s

It is also true that Planck’s constant defines the joule second and since the second is previously defined it defines the joule, making the joule the base unit. The kilogram can be defined from the relationship energy is force times distance and force is mass times acceleration or E =mad (1 J = 1 kg.m^2/s^2), which yields m = E/ad or that 1 kg = 1 J.s^2/m^2. The kilogram is a derived not.

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@Daniel – All SI units are now defined from the seven SI constants. The new SI brochure maintains the concept of base units and derived units “because it is useful and historically well established”.

SI Brochure – 9th Edition:

“2.3 Definitions of the SI units

Prior to the definitions adopted in 2018, the SI was defined through seven base units from which the derived units were constructed as products of powers of the base units. Defining the SI by fixing the numerical values of seven defining constants has the effect that this distinction is, in principle, not needed, since all units, base as well as derived units, may be constructed directly from the defining constants. Nevertheless, the concept of base and derived units is maintained because it is useful and historically well established, noting also that the ISO/IEC 80000 series of Standards specify base and derived quantities which necessarily correspond to the SI base and derived units defined here.”

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