National Physical Laboratory

What is the minimum number of base units that is required? (FAQ - Quantum)

A difficult question perhaps impossible. In what way the minimum? Some would say seven have been introduced into the SI because seven are needed. It has also been argued that with the use of fundamental constants only one unit is needed - Say time is the base unit, then length is measured in light-seconds etc

At a more practical level, the number that are required depends on the scientific discipline.

Discipline Units involved
Geometry length
Kinematics length, time
Mechanics length, mass, time
Electricity length, mass, time, current
Electro-optics length, mass, time, current, luminous intensity
Electro-chemistry length, mass, time, current, amount of substance
Thermodynamics length, mass, time, current, temperature, amount of substance

Systems such as the SI are man made and hence chose the number of units based on human requirements. From a philosophical point of view one could try and reduce the number of units. The natural system of units is based on fundamental constants and their number depends on the theoretical framework that is being considered. From the point of view of pure physics the number of units could be reduced for example temperature could be considered a conversion factor between mechanical and thermal energy, so although useful in practice in principal the kelvin could be eliminated. Similarly amount of substance and luminous intensity could be demoted to derived units in a world of gedanken measurements.

Advances in physics could increase or reduce the number of units required. For example if it were found that space is not isotropic then length would become a more complex quantity requiring three units. A more complete physics of the universe may have fewer free parameters and hence reduce the number of units.

But how far can the units be reduced? In quantum field theory plus general relativity there are three constants c, h/2π (h-bar), e that provide natural units plus an arbitrary choice of a mass that cannot be theoretically linked to other masses, so four base units (velocity, action, charge and mass) are needed. In string theory it has been argued that only two constants (c and λs, the string length) and hence two base units are required. A more concise theory yet, M theory for example, may require only one.

Last Updated: 25 Mar 2010
Created: 9 Aug 2007

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