SI base unit

(physics) One of a small number of units in a system of measurement that are defined, independent of other units, by means of a physical standard; equivalently, a unit of a base quantity. Also known as fundamental unit.

Any comprehensive system of units of measure must be founded on a set of units equal in number to the dimensions
[McNish A. G. Phys. Today Vol. 10:4, 19-25 (1957)] addressed, and they must be independent to encompass those dimensions. Length, mass, and time form the primeval set of dimensions and of base units; they have usually been augmented by volt else ampere as a base unit to extend coverage to the electromagnetic domain (though electric charge, represented in the SI by the coulomb, might be seen as the essential pertinent dimension). However, as with these latter, any of the initial trio could be replaced by combinations: for instance speed, the ratio of length to time, could replace either one of those two components.

To serve adequately, each base unit must be founded on reference standards accurately measurable to the precision appropriate to the conceived purposes of the system. In the SI, for time the second is defined as an appropriate multiple of the period of the hyperfine transitions of the caesium atom giving the second; for length the metre is defined as the distance travelled by light in a specified number of seconds; for mass the kilogram is defined by a physical prototype; and the ampere is defined as the electric current strength that maintains a specific force in a specified circumstance. Earlier versions of the metric system used other definitions, and some used the volt instead of the ampere. Yet earlier, the absolute system, ignoring the phenomenon of electric charge, managed with only the first three dimensions, while the metre was defined originally to have a set count along a quadrant of Earth. The gram was the original base unit for mass, defined as the mass of 1 cubic centimetre of water, but it soon became one thousandth of a prototype kilogram.

Ideally the standards should be indestructible and be invariable over time and place; to be practical they should also be reproducible and easily measured, accurately, to the required precision. Ideally they should be defined and measurable independently of each other. While the modern standards defining the second and the metre come close to requirements, those for the kilogram and ampere fall well short.

Most fundamental constants are indestructible, invariant (though see below) and measurable, within sophisticated laboratories, to the level of precision required. Either the Bohr radius else the Compton wavelength could provide a standard for length, from which the speed of light in a vacuum could provide for time, and the Newtonian constant of gravitation for mass. The elementary charge of the proton provides directly for electric charge. All of these, like the period of transition of caesium and the wavelength of light that underlie the definitions of the second and the metre, are seen as natural units.

Given the facility to name derived units as combinations of base units, the crucial question is which are to be the standards, with the secondary question of what multiples of the chosen standards shall be employed as fundamental units (as in the numbers involved in defining the second and the metre, and the practice of dividing the Planck constant by 2 π in some systems).

The SI includes the kelvin for thermodynamic temperature, the candela for luminous intensity, and the mole for the amount of a substance as base units too, and consideration has been given to including units for plane and solid angles with them. Since 1980 the angles have been accepted as not independent but merely derived units, specifically ratios of like-dimensioned measurements, hence dimensionless. The Kalantaroff system avoids mass as a fundamental, augmenting length, time, and electric charge with magnetic flux instead (the metre, second, coulomb, and weber being extant units for these quantities).
[Kinitsky V. A. Amer. J. Phys. Vol. 30, 89-93 (1962)]

Various schemes use selected fundamental physical constants entirely as their standards,
[Tuninsky V. S. Metrologia Vol. 36, 1-7 (1999)] sometimes directly as base units, but otherwise such that the selected constants have value 1, referred to as being normalized, in the pertinent system. The Planck length, mass, and time are base units in our familiar dimensions that are sized to normalize three such constants (though the scheme would need scaling to be practical). The schemes described under atomic units and natural units use selected fundamental physical constants entirely as their standards, indeed directly as base units. McWeeny
[McWeeny R. Nature Vol. 243, 196-8 (1973)] advocated the following as base units:
electron mass (≈ 9.11 × 10^-31 kg),
elementary charge of the proton (≈ 1.60 × 10^-19 C),
Planck constant over 2π (≈ 1.05 × 10^-34 J·s) and
permittivity of free space (≈ 8.86 × 10^-12 m^-3·kg^-1·s²·C²).The first two give valued units of mass and charge directly; the third adds time to the dimensions, the last length.

Ludovici,
[Ludovici B. F. Amer. J. Phys. Vol. 24, 400-7 (1956)] following Dirac,
[Dirac P. A. M. Proc. Roy. Soc. London Ser. A Vol. 165, 199-208 (1938)] saw all atomic units except for elementary charge as not assuredly invariable, especially allowing for the Heisenberg uncertainty principle, so advocated the following as fundamental units:
elementary charge of the proton (≈ 1.60 × 10^-19C),
Newtonian constant of gravitation (≈ 6.67 × 10^-11 m³·kg^-1·s^-2),
permittivity of free space (≈ 8.86 × 10^-12 m^-3·kg^-1·s²·C²) and
permeability of free space (≈ 1.26 × 10^-6 m·kg·C^-2),all unvarying. The first gives a valued unit of charge directly. From that, the product of the next two gives a value for mass. From those two values, the fourth choice gives a value for length, then either of the middle two the value for time.

The f.p.s. system was the main non-metric system. See gravitational system for further variations.

Any of the fundamental units of length, mass, time, electric current, thermodynamic temperature, amount of substance, or luminous intensity in the International System of Units, consisting respectively of the meter, kilogram, second, ampere, kelvin, mole, and candela.

(DOD) Unit of organization in a tactical operation around which a movement or maneuver is planned and performed.

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