# Base unit (measurement)

(Redirected from Fundamental units)

A base unit (also referred to as a fundamental unit) is a unit adopted for measurement of a base quantity. A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others.

In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, temperature, energy, and weight, and units are used to describe their magnitude or quantity. Many of these quantities are related to each other by various physical laws, and as a result the units of a quantities can be generally be expressed as a product of powers of other units; for example, momentum is mass multiplied by velocity, while velocity is measured in distance divided by time. These relationships are discussed in dimensional analysis. Those that can be expressed in this fashion in terms of the base units are called derived units (fr).

## International System of Units

In the International System of Units, there are seven base units: kilogram, metre, candela, second, ampere, kelvin, and mole.

## Natural units

There are other relationships between physical quantities that can be expressed by means of fundamental constants, and to some extent it is an arbitrary decision whether to retain the fundamental constant as a quantity with dimensions or simply to define it as unity or a fixed dimensionless number, and reduce the number of explicit fundamental constants by one.

For instance, time and distance are related to each other by the speed of light, c, which is a fundamental constant. It is possible to use this relationship to eliminate either the unit of time or that of distance. Similar considerations apply to the Planck constant, h, which relates energy (with dimension expressible in terms of mass, length and time) to frequency (with dimension expressible in terms of time). In theoretical physics it is customary to use such units (natural units) in which c = 1 and ħ = 1. A similar choice can be applied to the vacuum permittivity or permittivity of free space, ε0.

• One could eliminate any of the metre and second by setting c to unity (or to any other fixed dimensionless number).
• One could then eliminate the kilogram by setting ħ to a dimensionless number.
• One could then further eliminate the ampere by setting either the permittivity of free space ε0 (alternatively, the Coulomb constant ke = 1/(4πε0)) or the elementary charge e to a dimensionless number.
• One could similarly eliminate the mole as a base unit by reference to Avogadro's number.
• One could eliminate the kelvin as it can be argued that temperature simply expresses the energy per particle per degree of freedom, which can be expressed in terms of energy (or mass, length, and time). Another way of saying this is that Boltzmann's constant kB could be expressed as a fixed dimensionless number.
• Similarly, one could eliminate the candela, as that is defined in terms of other physical quantities.
• That leaves one base dimension and an associated base unit, but we still have plenty of fundamental constants left to eliminate that too – for instance one could use G, the gravitational constant, me, the electron rest mass, or Λ, the cosmological constant.

A widely used choice, in particular for theoretical physics, is given by the system of Planck units, which are defined by setting ħ = c = G = kB = ke = 1.

That leaves every physical quantity expressed as a dimensionless number, so it is not surprising that there are also physicists who have cast doubt on the very existence of incompatible fundamental quantities.[1][2][3]