International System of Units (SI), Fundamentally Revised

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SI, Fundamentally Revised

  • From SI Brochure, 9th edition (2019)
    • “The definition of the SI units is established in terms of a set of seven defining constants. The complete system of units can be derived from the fixed values of these defining constants, expressed in the units of the SI. These seven defining constants are the most fundamental feature of the definition of the entire system of 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,”
The Underlying Argument
  • The traditional base units of SI (second, meter, kilogram, ampere, kelvin, candela, mole) are defined in terms of seven physical constants (called the “defining constants”).
  • Every SI derived unit (e.g. force, energy, electric charge) is defined in terms of the traditional base units.
  • Therefore, every SI unit is defined in terms of physical constants.
The Defining Constants
  • The hyperfine transition frequency of cesium-133 
    • ∆𝜈Cs = 9,192,631,770 Hz (hertz)
  • Speed of light in a vacuum
    • c = 299,792,458 m/s (meters per second)
  • Planck constant
    • h = 6.626 070 15 × 10-34 J s (joule seconds)
  • Elementary charge 
    • e = 1.602176634 × 10-19 C (coulombs)
  • Boltzmann constant
    • k = 1.380649 × 10-23 J/K (joules / kelvin)
  • Avogadro constant
    • NA = 6.02214076 x 1023 mol-1 (particles per mole) 
  • Luminous efficacy of monochromatic radiation of frequency 540 × 1012 hertz 
    • Kcd = 683 lm/W (lumens per watt)
Traditional Base Units
  • Second s
    • Time
  • Meter m
    • Length
  • Kilogram kg
    • Mass
  • Ampere A
    • Electric Current
  • Kelvin K
    • Thermodynamic Temperature
  • Candela cd  (can-DEE-la or can-DELL-ah)
    • Luminous Intensity
  • Mole mol
    • Amount of Substance
Traditional Derived Units, Examples
  • Speed = m/s (meters per second)
    • Speed is the rate of change of location
  • Acceleration = m/s2 (meters per second, per second)
    • Acceleration is the rate of change of velocity
  • Force = Newton (N) = kg x m/s2 (mass x acceleration)
    • One newton is the force required to make an object of one kilogram accelerate one meter per second per second.
  • Energy, Work, Amount of Heat = Joule (J) = (kg x m/s2) x m (force x distance)
    • One joule is the work done by a force of one newton acting over a distance of one meter. 
    • Work = force times distance = (kg x m/s2) x m = kg x m2/s2
  • Power = Watt(W) = J/s (joules per second)
    • Power is the rate at which energy is used or produced
  • Pressure = N/m2 (perpendicular force per unit area)
  • Electric Charge = Coulomb (C) = s x A (seconds x amperes)
    • A coulomb is the quantity of electric charge transported in one second by a current of one ampere.
  • Electric Potential = Volt (V) = J/C (joules per coulomb)
  • Frequency = Hertz (Hz) = s-1 (per second)
  • Luminous Flux = Lumen (lm) = cd sr (candela x steredian)
    • A lumen is the amount of light streaming outward through a solid angle of one steradian from a point a light of one candela.
Traditional Base Units Derived from Defining Constants

Second

Meter

Kilogram

Ampere

Kelvin

Mole

Candela

Road to Revised SI
National Institute of Standards and Technology (NIST)