Base unit of measurement

Last updated March 27, 2024

A base unit of measurement (also referred to as a base unit or fundamental unit) is a unit of measurement adopted for 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. The SI base units, or Systeme International d'unites, consists of the metre, kilogram, second, ampere, kelvin, mole and candela.

Background

In the language of measurement, physical 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 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.

International System of Units

In the International System of Units (SI), there are seven base units: kilogram, metre, candela, second, ampere, kelvin, and mole. Several derived units have been defined, many with special names and symbols.

In 2019 the seven SI base units were redefined in terms of seven defining constants. Therefore the SI base units are no longer necessary but were retained because for historical and practical reasons.^[3] See 2019 redefinition of the SI base units.

Natural units

A set of base dimensions of quantity is a minimal set of units such that every physical quantity can be expressed in terms of this set. The traditional base dimensions are mass, length, time, charge, and temperature, but in principle, other base quantities could be used. Electric current could be used instead of charge or speed could be used instead of length. Some physicists have not recognized temperature as a base dimension since it simply expresses the energy per particle per degree of freedom which can be expressed in terms of energy (or mass, length, and time).^[4] Duff argues that only dimensionless values have physical meaning and all dimensional units are human constructs.^[5]

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 base quantities by one. The ontological issue is whether these fundamental constants really exist as dimensional or dimensionless quantities. This is equivalent to treating length as the same as time or understanding electric charge as a combination of quantities of mass, length, and time which may seem less natural than thinking of temperature as measuring the same material as energy (which is expressible in terms of mass, length, and time).

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 base 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, ε₀.

One could eliminate either the metre or the 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 eliminate the ampere by setting either the vacuum permittivity ε₀ or the elementary charge e to a dimensionless number.
One could eliminate the mole as a base unit by setting the Avogadro constant N_A to 1. This is natural as it is a technical scaling constant.
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 the Boltzmann constant k_B is a technical scaling constant and could be set to a fixed dimensionless number.
Similarly, one could eliminate the candela, as that is defined in terms of other physical quantities via a technical scaling constant, K_cd.
That leaves one base dimension and an associated base unit, but there are several fundamental constants left to eliminate that too – for instance, one could use G, the gravitational constant, m_e, the electron rest mass, or Λ, the cosmological constant.

The preferred choices vary by the field in physics. Using natural units leaves every physical quantity expressed as a dimensionless number, which is noted by physicists disputing the existence of incompatible base quantities.^[5]^[6]^[7]

Related Research Articles

The ampere, often shortened to amp, is the unit of electric current in the International System of Units (SI). One ampere is equal to 1 coulomb (C) moving past a point per second. It is named after French mathematician and physicist André-Marie Ampère (1775–1836), considered the father of electromagnetism along with Danish physicist Hans Christian Ørsted.

The centimetre–gram–second system of units is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways in which the CGS system was extended to cover electromagnetism.

In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities and units of measurement and tracking these dimensions as calculations or comparisons are performed. The term dimensional analysis is also used to refer to conversion of units from one dimensional unit to another, which can be used to evaluate scientific formulae.

<span class="mw-page-title-main">Physical quantity</span> Measurable property of a material or system

A physical quantity is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is the algebraic multiplication of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol. Quantities that are vectors have, besides numerical value and unit, direction or orientation in space.

A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.

The International System of Units, internationally known by the abbreviation SI, is the modern form of the metric system and the world's most widely used system of measurement. Coordinated by the International Bureau of Weights and Measures it is the only system of measurement with an official status in nearly every country in the world, employed in science, technology, industry, and everyday commerce.

The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which all other SI units can be derived. The units and their physical quantities are the second for time, the metre for length or distance, the kilogram for mass, the ampere for electric current, the kelvin for thermodynamic temperature, the mole for amount of substance, and the candela for luminous intensity. The SI base units are a fundamental part of modern metrology, and thus part of the foundation of modern science and technology.

<span class="mw-page-title-main">Metric system</span> Metre-based systems of measurement

The metric system is a decimal-based system of measurement. The current international standard for the metric system is the International System of Units, in which all units can be expressed in terms of seven base units: the metre, kilogram, second, ampere, kelvin, mole, and candela.

Dimensionless quantities, also known as quantities of dimension one are implicitly defined in a manner that prevents their aggregation into units of measurement. Typically expressed as ratios that align with another system, these quantities do not necessitate explicitly defined units. For instance, alcohol by volume (ABV) represents a volumetric ratio. Its derivation remains independent of the specific units of volume used; any common unit may be applied. Notably, ABV is never expressed as milliliters per milliliter, underscoring its dimensionless nature.

Buckingham <span class="texhtml mvar" style="font-style:italic;">π</span> theorem Theorem in dimensional analysis

In engineering, applied mathematics, and physics, the Buckingham $π$ theorem is a key theorem in dimensional analysis. It is a formalisation of Rayleigh's method of dimensional analysis. Loosely, the theorem states that if there is a physically meaningful equation involving a certain number n of physical variables, then the original equation can be rewritten in terms of a set of p = n − k dimensionless parameters $π$ ₁, $π$ ₂, ..., $π$ _p constructed from the original variables, where k is the number of physical dimensions involved; it is obtained as the rank of a particular matrix.

The atomic units are a system of natural units of measurement that is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They were originally suggested and named by the physicist Douglas Hartree. Atomic units are often abbreviated "a.u." or "au", not to be confused with similar abbreviations used for astronomical units, arbitrary units, and absorbance units in other contexts.

A geometrized unit system or geometrodynamic unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, c, and the gravitational constant, G, are set equal to unity.

Quantity or amount is a property that can exist as a multitude or magnitude, which illustrate discontinuity and continuity. Quantities can be compared in terms of "more", "less", or "equal", or by assigning a numerical value multiple of a unit of measurement. Mass, time, distance, heat, and angle are among the familiar examples of quantitative properties.

A system of units of measurement, also known as a system of units or system of measurement, is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, regulated and defined for the purposes of science and commerce. Instances in use include the International System of Units or SI, the British imperial system, and the United States customary system.

The ohm is the unit of electrical resistance in the International System of Units (SI). It is named after German physicist Georg Ohm. Various empirically derived standard units for electrical resistance were developed in connection with early telegraphy practice, and the British Association for the Advancement of Science proposed a unit derived from existing units of mass, length and time, and of a convenient scale for practical work as early as 1861.

The vacuum magnetic permeability, also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ₀. Its purpose is to quantify the strength of the magnetic field emitted by an electric current. Expressed in terms of SI base units, it has the unit kg⋅m⋅s⁻²·A⁻². It can be also expressed in terms of SI derived units, N·A⁻².

The Unified Code for Units of Measure (UCUM) is a system of codes for unambiguously representing measurement units. Its primary purpose is machine-to-machine communication rather than communication between humans.

In 2019, four of the seven SI base units specified in the International System of Quantities were redefined in terms of natural physical constants, rather than human artifacts such as the standard kilogram. Effective 20 May 2019, the 144th anniversary of the Metre Convention, the kilogram, ampere, kelvin, and mole are now defined by setting exact numerical values, when expressed in SI units, for the Planck constant, the elementary electric charge, the Boltzmann constant, and the Avogadro constant, respectively. The second, metre, and candela had previously been redefined using physical constants. The four new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met. These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: c, G, ħ, and k_B. Expressing one of these physical constants in terms of Planck units yields a numerical value of 1. They are a system of natural units, defined using fundamental properties of nature rather than properties of a chosen prototype object. Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity.

A coherent system of units is a system of units of measurement used to express physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, including numerical factors, as the corresponding equations directly relating the quantities. It is a system in which every quantity has a unique unit, or one that does not use conversion factors.

References

1 2 "ISO 80000-1:2009". International Organization for Standardization. Archived from the original on 2019-07-02. Retrieved 2019-09-15.
↑ Taylor, Barry N.; Thompson, Ambler (2008). The International System of Units (SI). Washington, D.C.: U.S. Department of Commerce. p. 56 (10th CGPM, 1954, Resolution 6).
↑ "9th edition of the SI Brochure". BIPM. 2019. Archived from the original on 19 April 2021. Retrieved 20 May 2019.
↑ Quincey, Paul; Brown, Richard J C (2017-08-01). "A clearer approach for defining unit systems". Metrologia. 54 (4): 454–460. arXiv: 1705.03765 . doi:10.1088/1681-7575/aa7160. ISSN 0026-1394.
1 2 Michael Duff (2015). "How fundamental are fundamental constants?" . Contemporary Physics. 56 (1): 35–47. arXiv: 1412.2040 . Bibcode:2015ConPh..56...35D. doi:10.1080/00107514.2014.980093. hdl:10044/1/68485. S2CID 118347723. Archived from the original on 2021-11-22. Retrieved 2020-04-03.
↑ Jackson, John David (1998). "Appendix on Units and Dimensions" (PDF). Classical Electrodynamics. John Wiley and Sons. p. 775. Archived from the original (PDF) on 13 January 2014. Retrieved 13 January 2014. The arbitrariness in the number of fundamental units and in the dimensions of any physical quantity in terms of those units has been emphasized by Abraham, Plank, Bridgman, Birge, and others.
↑ Birge, Raymond T. (1935). "On the establishment of fundamental and derived units, with special reference to electric units. Part I." (PDF). American Journal of Physics. 3 (3): 102–109. Bibcode:1935AmJPh...3..102B. doi:10.1119/1.1992945. Archived from the original (PDF) on 23 September 2015. Retrieved 13 January 2014. Because, however, of the arbitrary character of dimensions, as presented so ably by Bridgman, the choice and number of fundamental units are arbitrary.

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[80000-1:2009-1] 1 2 "ISO 80000-1:2009". International Organization for Standardization. Archived from the original on 2019-07-02. Retrieved 2019-09-15.

[2] Taylor, Barry N.; Thompson, Ambler (2008). The International System of Units (SI). Washington, D.C.: U.S. Department of Commerce. p. 56 (10th CGPM, 1954, Resolution 6).

[Brochure9_2019-3] "9th edition of the SI Brochure". BIPM. 2019. Archived from the original on 19 April 2021. Retrieved 20 May 2019.

[4] Quincey, Paul; Brown, Richard J C (2017-08-01). "A clearer approach for defining unit systems". Metrologia. 54 (4): 454–460. arXiv: 1705.03765 . doi:10.1088/1681-7575/aa7160. ISSN 0026-1394.

[hep-th1412.2040-5] 1 2 Michael Duff (2015). "How fundamental are fundamental constants?" . Contemporary Physics. 56 (1): 35–47. arXiv: 1412.2040 . Bibcode:2015ConPh..56...35D. doi:10.1080/00107514.2014.980093. hdl:10044/1/68485. S2CID 118347723. Archived from the original on 2021-11-22. Retrieved 2020-04-03.

[6] Jackson, John David (1998). "Appendix on Units and Dimensions" (PDF). Classical Electrodynamics. John Wiley and Sons. p. 775. Archived from the original (PDF) on 13 January 2014. Retrieved 13 January 2014. The arbitrariness in the number of fundamental units and in the dimensions of any physical quantity in terms of those units has been emphasized by Abraham, Plank, Bridgman, Birge, and others.

[7] Birge, Raymond T. (1935). "On the establishment of fundamental and derived units, with special reference to electric units. Part I." (PDF). American Journal of Physics. 3 (3): 102–109. Bibcode:1935AmJPh...3..102B. doi:10.1119/1.1992945. Archived from the original (PDF) on 23 September 2015. Retrieved 13 January 2014. Because, however, of the arbitrary character of dimensions, as presented so ably by Bridgman, the choice and number of fundamental units are arbitrary.

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