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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, natural units are physical units of measurement
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
 defined in such a way that certain selected universal physical constants are normalized to unity; that is, their numerical value becomes exactly 1 when measured in some system of natural units.

ral units are intended to elegantly simplify
Nondimensionalization

Nondimensionalization is the partial or full removal of Units of measurements from a mathematical equation by a suitable substitution of variables....
 particular algebraic expressions appearing in physical law or to normalize
Normalizing constant

The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics....
 some chosen physical quantities that are properties of universal elementary particle
Elementary particle

In particle physics, an elementary particle or fundamental particle is a wiktionary:particle not known to have substructure; that is, it is not known to be made up of smaller particles....
s and that may be reasonably believed to be constant.






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In physics
Physics

Physics is the natural science which examines basic concepts such as energy, force, and spacetime and all that derives from these, such as mass, charge, matter and its Motion ....
, natural units are physical units of measurement
Measurement

Measurement is the process of assigning a number to an attribute according to a rule or set of rules. The term can also be used to refer to the result obtained after performing the process....
 defined in such a way that certain selected universal physical constants are normalized to unity; that is, their numerical value becomes exactly 1 when measured in some system of natural units.

Introduction

Natural units are intended to elegantly simplify
Nondimensionalization

Nondimensionalization is the partial or full removal of Units of measurements from a mathematical equation by a suitable substitution of variables....
 particular algebraic expressions appearing in physical law or to normalize
Normalizing constant

The concept of a normalizing constant arises in probability theory and a variety of other areas of mathematics....
 some chosen physical quantities that are properties of universal elementary particle
Elementary particle

In particle physics, an elementary particle or fundamental particle is a wiktionary:particle not known to have substructure; that is, it is not known to be made up of smaller particles....
s and that may be reasonably believed to be constant. However, what may be believed and forced to be constant in one system of natural units can very well be allowed or even assumed to vary in another natural unit system.

Natural units are natural because the origin of their definition comes only from properties of nature
Nature

File:Jungle in Punjab.JPGNature, in the broadest sense, is equivalent to the natural world, physical universe, material world or material universe....
 and not from any human construct. Planck units
Planck units

Planck units are units of measurement named after the German physicist Max Planck, who first proposed them in 1899. They are an example of natural units, i.e....
 are often, without qualification, called "natural units," when in fact they are only one of several systems of natural units, albeit the best known such system. Planck units might be considered unique in that the set of units are not based on properties of any prototype
Prototype

A prototype is an original type, form, or instance of something serving as a typical example, basis, or standard for other things of the same category....
, object, or particle
Subatomic particle

A subatomic particle is an elementary particle or composite particle particle smaller than an atom. Particle physics and nuclear physics are concerned with the study of these particles, their interactions, and non-atomic QCD matter....
 but are solely derived from the properties of free space
Free space

In classical physics, free space is a concept of electromagnetic theory, corresponding to a theoretically perfect vacuum, and sometimes referred to as the vacuum of free space....
.

As with any set of base units or fundamental units the base units of a set of natural units will include definitions and values for length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
, mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
, time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
, temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
, and electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
. Some physicists do not recognize temperature as a fundamental physical quantity, since it simply expresses the energy per degree of freedom of a particle, which can be expressed in terms of energy (or mass, length, and time). Virtually every system of natural units normalizes Boltzmann constant
Boltzmann constant

The Boltzmann constant is the physical constant relating energy at the particle level with temperature observed at the bulk level. It is the gas constant R divided by the Avogadro constant NA:...
 to k=1, which can be thought of as simply a way of defining the unit temperature.

In addition, some physicists recognize electric charge as a separate fundamental dimension of physical quantity, even if it has been expressed in terms of mass, length, and time in unit systems such as the electrostatic cgs system. Virtually every system of natural units normalizes the permittivity of free space to ε0=(4π)-1, an expression which can be thought of as defining the unit charge. This suggests that the controversial adoption, first in CGS units and subsequently in SI
Si

Si, si, or SI may refer to :...
 units, of Georgi
Georgi

Georgi is a surname.Notable people with the surname include:* Johann Gottlieb Georgi , German geographer and chemist* Yvonne Georgi , German dancer, choreographer, and ballet mistress...
's preference for expressing Coulomb's law
Coulomb's law

Coulomb's law, sometimes called the Coulomb law, is an equation describing the electrostatic force between electric charges. It was developed in the 1780s by French physicist Charles Augustin de Coulomb and was essential to the development of the classical electromagnetism....
 in the "rationalized" form F= (4πε0)-1q1q2r-2, rather than as F=kq1q2r-2, may not have been the most natural choice after all.

Candidate physical constants used in natural unit systems

The candidate physical constants to be normalized are chosen from those in the following table. Note that only a smaller subset of the following can be normalized in any one system of units without contradiction in definition (e.g., me and mp cannot both be defined as the unit mass in a single system).

Constant Symbol Dimension
speed of light
Speed of light

The speed of light in an free space is an important physical constant usually written as c, with a value of 299,792,458 metres per second....
 in vacuum		 L
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 T
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
-1
Gravitational constant
Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
 M
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
-1L3T-2
Planck's constant (reduced) ML2T-1
Coulomb force constant
Coulomb's law

Coulomb's law, sometimes called the Coulomb law, is an equation describing the electrostatic force between electric charges. It was developed in the 1780s by French physicist Charles Augustin de Coulomb and was essential to the development of the classical electromagnetism....
 where is the permittivity of free space Q
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
-2 M L3 T-2
Elementary charge
Elementary charge

The elementary charge, usually denoted e, is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron....
 Q
Electron mass M
Proton mass M
Boltzmann constant
Boltzmann constant

The Boltzmann constant is the physical constant relating energy at the particle level with temperature observed at the bulk level. It is the gas constant R divided by the Avogadro constant NA:...
 ML2T-2T
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
-1


Dimensionless physical constant
Dimensionless physical constant

In physics, a dimensionless physical constant is a universal physical constant whose numerical value is the same under all possible systems of units....
s such as the fine-structure constant
Fine-structure constant

In physics, the fine-structure constant, usually denoted is the characterizing the strength of the electromagnetic interaction. A fundamental physical constant and a dimensionless quantity, its numerical value is the same in all system of units....




cannot take on a different numerical value no matter what system of units is used. Judiciously choosing units can only normalize physical constants that have dimension. Since α is a fixed dimensionless number not equal to 1, it is not possible to define a system of natural units that will normalize all of the physical constants that comprise α. Any 3 of the 4 constants: c, , e, or 4πε0, can be normalized (leaving the remaining physical constant to take on a value that is a simple function of α, attesting to the fundamental nature of the fine-structure constant) but not all 4.

Planck units


Quantity Expression Metric value
Length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 (L)		 1.61609735×10-35 m
Mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 (M)		 21.7664598 µg
Time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 (T)		 5.3907205×10-44 s
Electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 (Q)		 1.87554573×10-18 C
Temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 (Θ)		 1.4169206×1032 K


Planck units hold pride of place among systems of natural units, because they do not invoke any properties (specifically, the charge
Elementary charge

The elementary charge, usually denoted e, is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron....
, mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
, or orbital radius
Bohr radius

In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central atomic nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy....
) of any elementary particle
Elementary particle

In particle physics, an elementary particle or fundamental particle is a wiktionary:particle not known to have substructure; that is, it is not known to be made up of smaller particles....
. For example, the proton
Proton

The proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H+....
 and electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
 are equally sensible choices, and thus are equally arbitrary. But their masses differ
Proton-to-electron mass ratio

In physics, the proton-to-electron mass ratio, μ or β, is simply the rest mass of the proton mass divided by that of the electron mass....
 considerably, a fact having nontrivial implications for all other systems of natural units, because these all invoke one or more properties of protons or electrons.

By contrast, the physical constants that Planck units normalize are all properties of free space
Free space

In classical physics, free space is a concept of electromagnetic theory, corresponding to a theoretically perfect vacuum, and sometimes referred to as the vacuum of free space....
. In particular, the definition of Planck units does not invoke the elementary charge
Elementary charge

The elementary charge, usually denoted e, is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron....
, whose numerical value, when measured in units of Planck charge
Planck charge

In physics, the Planck charge , is one of the base units in the system of natural units called Planck units. It is a quantity of electric charge defined in terms of fundamental physical constants....
, is the square root of the fine-structure constant
Fine-structure constant

In physics, the fine-structure constant, usually denoted is the characterizing the strength of the electromagnetic interaction. A fundamental physical constant and a dimensionless quantity, its numerical value is the same in all system of units....
 α. Hence any observed variation over space or time in the value of α is attributed to variation in the elementary charge.

Stoney units


Quantity Expression Metric Value
Length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 (L)		 1.38068×10-36 m
Mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 (M)		 1.85921×10-9 kg
Time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 (T)		 4.60544×10-45 s
Electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 (Q)		 1.60218×10-19 C
Temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 (Θ)		 1.21028×1031 K


George Johnstone Stoney
George Johnstone Stoney

George Johnstone Stoney was an Ireland physicist most famous for introducing the term electron as the "fundamental unit quantity of electricity"....
 was the first physicist to introduce the concept of natural units. He presented the idea in a lecture entitled "On the Physical Units of Nature" delivered to the British Association in 1874. Stoney units fix the elementary charge
Elementary charge

The elementary charge, usually denoted e, is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron....
 and allow Planck's constant (only discovered after Stoney's proposal) to float. They can be obtained from Planck units
Planck units

Planck units are units of measurement named after the German physicist Max Planck, who first proposed them in 1899. They are an example of natural units, i.e....
 with the substitution: . This removes Planck's constant from the definitions and the value it takes on in Stoney units is the reciprocal of the fine-structure constant
Fine-structure constant

In physics, the fine-structure constant, usually denoted is the characterizing the strength of the electromagnetic interaction. A fundamental physical constant and a dimensionless quantity, its numerical value is the same in all system of units....
, 1/a. Hence any observed variation over space or time in the value of a is attributed to variation in Planck's constant.

"Schrödinger" units


Quantity Expression Metric Value
Length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 (L)		 2.59276×10-32 m
Mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 (M)		 1.85921×10-9 kg
Time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 (T)		 1.18516×10-38 s
Electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 (Q)		 1.602176487×10-19 C
Temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 (Θ)		 6.44490×1026 K


The name was coined by Michael Duff
Michael Duff

Michael James Duff is Principal of the Faculty of Physical Sciences and Abdus Salam Chair of Theoretical Physics at Imperial College London....
. They can be obtained from Planck units
Planck units

Planck units are units of measurement named after the German physicist Max Planck, who first proposed them in 1899. They are an example of natural units, i.e....
 with the substitution: . This removes the speed of light
Speed of light

The speed of light in an free space is an important physical constant usually written as c, with a value of 299,792,458 metres per second....
 from the definitions and the value it takes on in Schrödinger units is the reciprocal of the fine-structure constant
Fine-structure constant

In physics, the fine-structure constant, usually denoted is the characterizing the strength of the electromagnetic interaction. A fundamental physical constant and a dimensionless quantity, its numerical value is the same in all system of units....
, 1/α. Hence any observed variation over space or time in the value of a is attributed to variation in the speed of light,

Atomic units (Hartree)


Quantity Expression
Length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 (L)
Mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 (M)
Time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 (T)
Electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 (Q)
Temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 (Θ)


First proposed by Douglas Hartree
Douglas Hartree

Douglas Rayner Hartree PhD, Fellow of the Royal Society was an England mathematician and physicist most famous for the development of numerical analysis and its application to atomic physics....
 to simplify the physics of the Hydrogen atom
Hydrogen atom

A hydrogen atom is an atom of the chemical element hydrogen. The Electric charge neutral atom contains a single positively-charged proton and a single negatively-charged electron bound to the nucleus by the Coulomb force....
. Michael Duff
Michael Duff

Michael James Duff is Principal of the Faculty of Physical Sciences and Abdus Salam Chair of Theoretical Physics at Imperial College London....
 calls these "Bohr units". The unit energy
Energy

In physics, energy is a scalar physical quantity that describes the amount of Work_ that can be performed by a force. Energy is an attribute of objects and systems that is subject to a conservation law....
 in this system is the total energy of the electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
 in the first circular orbit of the Bohr atom and called the Hartree energy
Hartree energy

A hartree is the atomic units of energy and is named after physicist Douglas Hartree.The hartree energy is equal to the absolute value of the electric potential energy of the hydrogen atom in its ground state....
, Eh. The unit velocity is the velocity of that electron, the unit mass is the electron mass, me, and the unit length is the Bohr radius
Bohr radius

In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central atomic nucleus. The model says that the electrons orbit only at certain distances from the nucleus, depending on their energy....
, . They can be obtained from "Schrödinger" units with the substitution: . This removes the speed of light
Speed of light

The speed of light in an free space is an important physical constant usually written as c, with a value of 299,792,458 metres per second....
 (as well as the gravitational constant
Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
) from the definitions and its numerical value in atomic units is the reciprocal of the fine-structure constant
Fine-structure constant

In physics, the fine-structure constant, usually denoted is the characterizing the strength of the electromagnetic interaction. A fundamental physical constant and a dimensionless quantity, its numerical value is the same in all system of units....
, 1/α. Hence any observed variation over space or time in the value of a is attributed to variation in the speed of light.

Electronic system of units


Quantity Expression
Length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 (L)
Mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 (M)
Time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 (T)
Electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 (Q)
Temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 (Θ)


Michael Duff
Michael Duff

Michael James Duff is Principal of the Faculty of Physical Sciences and Abdus Salam Chair of Theoretical Physics at Imperial College London....
 calls these "Dirac units". They can be obtained from Stoney units via the substitution: . They can be also obtained from atomic units
Atomic units

Atomic units form a system of units convenient for atomic physics, electromagnetism, and quantum electrodynamics, especially when the focus is on the properties of electrons....
 with the substitution: . As is the case with Stoney units, any observed variation over space or time in the value of a is attributed to variation in Planck's constant.

Quantum electrodynamical system of units (Stille)


Quantity Expression
Length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 (L)
Mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 (M)
Time
Time

Time is a component of the measurement used to sequence events, to compare the durations of events and the intervals between them, and to quantify the motions of objects....
 (T)
Electric charge
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 (Q)
Temperature
Temperature

In physics, temperature is a physical property of a Physical system that underlies the common notions of hot and cold; something that feels hotter generally has the greater temperature....
 (Θ)


The electron mass can replace that of the proton
Proton

The proton is a subatomic particle with an electric charge of +1 elementary charge. It is found in the nucleus of each atom but is also stable by itself and has a second identity as the hydrogen ion, H+....
. Any observed variation over space or time in the value of a is attributed to variation in .

Geometrized units


The geometrized unit system is not a completely defined or unique system. In this system, the base physical units are chosen so that the speed of light
Speed of light

The speed of light in an free space is an important physical constant usually written as c, with a value of 299,792,458 metres per second....
 and the gravitational constant
Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
 are set equal to unity leaving latitude to also set some other constant such as the Boltzmann constant
Boltzmann constant

The Boltzmann constant is the physical constant relating energy at the particle level with temperature observed at the bulk level. It is the gas constant R divided by the Avogadro constant NA:...
 and Coulomb force constant
Coulomb's law

Coulomb's law, sometimes called the Coulomb law, is an equation describing the electrostatic force between electric charges. It was developed in the 1780s by French physicist Charles Augustin de Coulomb and was essential to the development of the classical electromagnetism....
 equal to unity: If the reduced Planck constant is also set equal to unity, then geometrized units are identical to Planck units
Planck units

Planck units are units of measurement named after the German physicist Max Planck, who first proposed them in 1899. They are an example of natural units, i.e....
.

N-body units


Quantity Expression
Length
Length

Length is the long dimension of any object. The length of a thing is the distance between its ends, its linear extent as measured from end to end....
 (R)
Mass
Mass

In physical science, mass refers to the degree of acceleration a body acquires when subject to a force: bodies with greater mass are accelerated less by the same force....
 (M)


N-body units are a completely self-contained system of units used for N-body simulation
N-body simulation

An N-body simulation is a simulation of massive particles under the influence of physical forces, usually gravity and sometimes other forces....
s of self gravitating systems in astrophysics. In this system, the base physical units are chosen so that the total mass (M), the gravitational constant
Gravitational constant

The gravitational constant, denoted G, is an empirical physical constant involved in the calculation of the gravitation between objects with mass....
 (G) and the virial radius (R) are set equal to unity. The underlying assumption is that the system of N objects (stars) satisfies the virial theorem
Virial theorem

In mechanics, the virial theorem provides a general equation relating the average over time of the total kinetic energy, , of a stable system, bound by potential forces, with that of the total potential energy, , where angle brackets represent the average over time of the enclosed quantity....
. The consequence of standard N-body units is that the velocity dispersion of the system is and that the dynamical -crossing- time scales as . The first mention of standard N-body units was by Michel Hénon (1971) . They were taken up by Haldan Cohn (1979) and later widely advertised and generalized by Douglas Heggie and Robert Mathieu (1986).

See also

  • anthropic units
    Anthropic units

    The ability to characterize, quantitative, and measurement objects in the physical world is an essential milestone towards the development of complex human civilizations....
  • fundamental unit
    Fundamental unit

    A set of fundamental units is a set of Units of measurement for physical quantity from which every other unit can be generated.In the language of measurement, quantities are quantifiable aspects of the world, such as time, distance, velocity, mass, momentum, energy, and weight, and units are used to describe their measure....
  • dimensional analysis
    Dimensional analysis

    Dimensional analysis is a conceptual tool often applied in physics, chemistry, and engineering to understand physical situations involving certain physical quantities....
  • physical constant
    Physical constant

    A physical constant is a physical quantity that is generally believed to be both universal in nature and constant in time. It can be contrasted with a mathematical constant, which is a fixed numerical value but does not directly involve any physical measurement....
    s


External links

  • (National Institute of Standards and Technology) is a convenient source of data on the commonly recognized constants.
  • A comparative overview/tutorial of various systems of natural units having historical use.