Natural units - Citizendia

In physics, natural units are physical units of measurement defined in terms of universal physical constants, such that some chosen physical constants each have a numerical value of exactly 1, when expressed in terms of a particular set of natural units. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Measurement is the process of estimating the magnitude of some attribute of an object such as its length or weight relative to some standard ( unit of measurement) such as A physical Constant is a Physical quantity that is generally believed to be both universal in nature and constant in time

Natural units are intended to elegantly simplify particular algebraic expressions appearing in physical law or to normalize some chosen physical quantities that are properties of universal elementary particles and that may be reasonably believed to be constant. Nondimensionalization is the partial or full removal of units from a Mathematical equation by a suitable substitution of Variables. In mathematics the word expression is a term for any well-formed combination of mathematical symbols In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made 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 and not from any human construct. Nature, in the broadest sense is equivalent to the natural world, physical universe, material world or material universe. Planck units are often, without qualification, called "natural units" but are only one system of natural units among other systems. Planck units are Units of measurement named after the German physicist Max Planck, who first proposed them in 1899 Planck units might be considered unique in that the set of units are not based on properties of any prototype, object, or particle but are based only on properties of free space. 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 A subatomic particle is an elementary or composite Particle smaller than an Atom. In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes

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, mass, time, temperature, and electric charge. A set of fundamental units is a set of units for physical quantities from which every other unit can be generated 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 is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Some physicists have not recognized temperature as a fundamental dimension of 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 the Boltzmann constant to k=1, which can be thought of as simply another expression of the definition of the unit temperature. Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics 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. The centimetre-gram-second system ( CGS) is a system of physical units. Virtually every system of natural units normalizes the permittivity of free space to ε₀=(4π)^-1, which can be thought of as an expression of the definition of the unit charge. Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical

1 Candidate physical constants used in natural unit systems
2 Planck units
3 Stoney units
4 "Schrödinger" units
5 Atomic units (Hartree)
6 Electronic system of units
7 Quantum electrodynamical system of units (Stille)
8 Geometrized units
9 N-body units
10 SI units
11 See also
12 External links

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. , m_e and m_p cannot both be defined as the unit mass in a single system).

Constant	Symbol	Dimension
speed of light in vacuum	${ c } \$	L T^-1
Gravitational constant	${ G } \$	M^-1L³T^-2
Dirac's constant or "reduced Planck's constant"	$\hbar=\frac{h}{2 \pi}$ where ${h} \$ is Planck's constant	ML²T^-1
Coulomb force constant	$\frac{1}{4 \pi \epsilon_0}$ where ${ \epsilon_0 } \$ is the permittivity of free space	Q^-2 M L³ T^-2
Elementary charge	$e \$	Q
Electron mass	$m_e \$	M
Proton mass	$m_p \$	M
Boltzmann constant	${ k } \$	ML²T^-2Θ^-1

Dimensionless physical constants such as the fine-structure constant

$\alpha \ \equiv \frac{e^2}{\hbar c (4 \pi \epsilon_0)} = \frac{1}{137.03599911}$

cannot take on a different numerical value no matter what system of units are used. 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 For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing 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, $\hbar$ , e, or 4πε₀, can be normalized (leaving the remaining physical constant to take on a value that is a simple function of α, alluding to the fundamental nature of the fine-structure constant) but not all 4.

Planck units

Main article: Planck units

Quantity	Expression	Metric value
Length (L)	$l_P = \sqrt{\frac{\hbar G}{c^3}}$	1. Planck units are Units of measurement named after the German physicist Max Planck, who first proposed them in 1899 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 61609735×10^-35 m
Mass (M)	$m_P = \sqrt{\frac{\hbar c}{G}}$	21. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object 7664598 μg
Time (T)	$t_P = \sqrt{\frac{\hbar G}{c^5}}$	5. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of 3907205×10^-44 s
Electric charge (Q)	$q_P = \sqrt{\hbar c (4 \pi \epsilon_0)}$	1. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. 87554573×10^-18 C
Temperature (Θ)	$T_P = \sqrt{\frac{\hbar c^5}{G k^2}}$	1. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature 4169206×10³² K

$c = 1 \$

$G = 1 \$

$\hbar = 1 \$

$\frac{1}{4 \pi \epsilon_0} = 1$

$k = 1 \$

$e = \sqrt{\alpha} \$

The physical constants that Planck units normalize are properties of free space and not properties (such as charge, mass, size or radius) of any object or elementary particle (that would have to be arbitrarily chosen). In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes In Particle physics, an elementary particle or fundamental particle is a particle not known to have substructure that is it is not known to be made Being so, the Planck units are defined independently of the elementary charge which, if measured in terms of Planck units, comes out to be the square root of the fine-structure constant, √α. The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing In Planck units a conceivable variation in the value of the dimensionless α would be considered to be due to a variation in the elementary charge.

Stoney units

Quantity	Expression
Length (L)	$l_S = \sqrt{\frac{G e^2}{c^4 (4 \pi \epsilon_0)}}$
Mass (M)	$m_S = \sqrt{\frac{e^2}{G (4 \pi \epsilon_0)}}$
Time (T)	$t_S = \sqrt{\frac{G e^2}{c^6 (4 \pi \epsilon_0)}}$
Electric charge (Q)	$q_S = e \$
Temperature (Θ)	$T_S = \sqrt{\frac{c^4 e^2}{G (4 \pi \epsilon_0) k^2}}$

$c = 1 \$

$G = 1 \$

$e = 1 \$

$\frac{1}{4 \pi \epsilon_0} = 1$

$k = 1 \$

$\hbar = \frac{1}{\alpha} \$

Proposed by George Stoney in 1881. 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 is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Stoney units fix the elementary charge and allow Planck's constant to float. The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. They can be obtained from Planck units with the substitution:

$\hbar \leftarrow \alpha \hbar = \frac{e^2}{c (4 \pi \epsilon_0)}$ . Planck units are Units of measurement named after the German physicist Max Planck, who first proposed them in 1899

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, 1/α. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing In Stoney units a conceivable variation in the value of the dimensionless α would be considered to be due to a variation in Planck's constant.

"Schrödinger" units

Quantity	Expression
Length (L)	$l_{\psi} = \sqrt{\frac{\hbar^4 G (4 \pi \epsilon_0)^3}{e^6}}$
Mass (M)	$m_{\psi} = \sqrt{\frac{e^2}{G (4 \pi \epsilon_0)}}$
Time (T)	$t_{\psi} = \sqrt{\frac{\hbar^6 G (4 \pi \epsilon_0)^5}{e^{10}}}$
Electric charge (Q)	$q_{\psi} = e \$
Temperature (Θ)	$T_{\psi} = \sqrt{\frac{e^{10}}{\hbar^4 (4 \pi \epsilon_0)^5 G k^2}}$

$e = 1 \$

$G = 1 \$

$\hbar = 1 \$

$\frac{1}{4 \pi \epsilon_0} = 1$

$k = 1 \$

$c = \frac{1}{\alpha} \$

The name was coined by Michael Duff [1]. 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 is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature This article is about Physicist and string theorist Michael Duff They can be obtained from Planck units with the substitution:

$c \leftarrow \alpha c = \frac{e^2}{\hbar (4 \pi \epsilon_0)}$ . Planck units are Units of measurement named after the German physicist Max Planck, who first proposed them in 1899

This removes the speed of light from the definitions and the value it takes on in Schrödinger units is the reciprocal of the fine-structure constant, 1/α. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing In Schrödinger units a conceivable variation in the value of the dimensionless α would be considered to be due to a variation in the speed of light.

Atomic units (Hartree)

Main article: Atomic units

Quantity	Expression
Length (L)	$l_A = \frac{\hbar^2 (4 \pi \epsilon_0)}{m_e e^2}$
Mass (M)	$m_A = m_e \$
Time (T)	$t_A = \frac{\hbar^3 (4 \pi \epsilon_0)^2}{m_e e^4}$
Electric charge (Q)	$q_A = e \$
Temperature (Θ)	$T_A = \frac{m_e e^4}{\hbar^2 (4 \pi \epsilon_0)^2 k}$

$e = 1 \$

$m_e = 1 \$

$\hbar = 1 \$

$\frac{1}{4 \pi \epsilon_0} = 1$

$k = 1 \$

$c = \frac{1}{\alpha} \$

First proposed by Douglas Hartree to simplify the physics of the Hydrogen atom. Atomic units ( au) form a System of units convenient for Atomic physics, Electromagnetism, and Quantum electrodynamics, especially 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 is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Douglas Rayner Hartree PhD, FRS ( March 27, 1897 – February 12, 1958) was an English Mathematician A hydrogen atom is an atom of the chemical element Hydrogen. The electrically neutral Michael Duff [2] calls these "Bohr units". This article is about Physicist and string theorist Michael Duff The unit energy in this system is the total energy of the electron in the first circular orbit of the Bohr atom and called the Hartree energy, E_h. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In Atomic physics, the Bohr model created by Niels Bohr depicts the Atom as a small positively charged nucleus surrounded by Electrons A hartree (symbol E h is the atomic unit of Energy and is named after Physicist Douglas Hartree. The unit velocity is the velocity of that electron, the unit mass is the electron mass, m_e, and the unit length is the Bohr radius, $a_0 = 4 \pi \epsilon_0\hbar^2/m_e e^2 \$ . The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J In the Bohr model of the structure of an Atom, put forward by Niels Bohr in 1913 Electrons orbit a central nucleus. They can be obtained from "Schrödinger" units with the substitution:

$G \leftarrow \alpha G \left( \frac{m_P}{m_e} \right)^2 = \frac{e^2}{4 \pi \epsilon_0 m_e^2} \$ .

This removes the speed of light (as well as the gravitational constant) from the definitions and the value it takes on in atomic units is the reciprocal of the fine-structure constant, 1/α. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing In atomic units a conceivable variation in the value of the dimensionless α would be considered to be due to a variation in the speed of light.

Electronic system of units

Quantity	Expression
Length (L)	$l_e = \frac{e^2}{c^2 m_e (4 \pi \epsilon_0)}$
Mass (M)	$m_e = m_e \$
Time (T)	$t_e = \frac{e^2}{c^3 m_e (4 \pi \epsilon_0)}$
Electric charge (Q)	$q_e = e \$
Temperature (Θ)	$T_e = \frac{m_e c^2}{k}$

$c = 1 \$

$e = 1 \$

$m_e = 1 \$

$\frac{1}{4 \pi \epsilon_0} = 1$

$k = 1 \$

$\hbar = \frac{1}{\alpha} \$

Michael Duff [3] calls these "Dirac units". 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 is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature This article is about Physicist and string theorist Michael Duff They can be obtained from Stoney units with the substitution:

$G \leftarrow \alpha G \left( \frac{m_P}{m_e} \right)^2 = \frac{e^2}{4 \pi \epsilon_0 m_e^2} \$ .

They can be also obtained from Atomic units with the substitution:

$\hbar \leftarrow \alpha \hbar = \frac{e^2}{c (4 \pi \epsilon_0)}$ . Atomic units ( au) form a System of units convenient for Atomic physics, Electromagnetism, and Quantum electrodynamics, especially

Similarly to Stoney units, a conceivable variation in the value of α would be considered to be due to a variation in Planck's constant.

Quantum electrodynamical system of units (Stille)

Quantity	Expression
Length (L)	$l_{\mathrm{QED}} = \frac{e^2}{c^2 m_p (4 \pi \epsilon_0)}$
Mass (M)	$m_{\mathrm{QED}} = m_p \$
Time (T)	$t_{\mathrm{QED}} = \frac{e^2}{c^3 m_p (4 \pi \epsilon_0)}$
Electric charge (Q)	$q_{\mathrm{QED}} = e \$
Temperature (Θ)	$T_{\mathrm{QED}} = \frac{m_p c^2}{k}$

$c = 1 \$

$e = 1 \$

$m_p = 1 \$

$\frac{1}{4 \pi \epsilon_0} = 1$

$k = 1 \$

$\hbar = \frac{1}{\alpha} \$

Similar to the electronic system of units except that the proton mass is normalized rather that the electron mass. 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 is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J Also a conceivable variation in the value of α would be considered to be due to a variation in Planck's constant.

Geometrized units

Main article: Geometrized unit system

$c = 1 \$

$G = 1 \$

The geometrized unit system is not a completely defined or unique system. A geometrized unit system or geometric unit system is a system of Natural units in which the base physical units are chosen so that the Speed of light In this system, the base physical units are chosen so that the speed of light and the gravitational constant are set equal to unity leaving latitude to also set some other constant such as the Boltzmann constant and Coulomb force constant equal to unity:

$k = 1 \$

$\frac{1}{4 \pi \epsilon_0} = 1$

If Dirac's constant (also called the "reduced Planck's constant") is also set equal to unity,

$\hbar = 1 \$

then geometrized units are identical to Planck units. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. Planck units are Units of measurement named after the German physicist Max Planck, who first proposed them in 1899

N-body units

Quantity	Expression
Length (R)	$\frac{1}{R} = \frac{1}{N(N-1)} \sum_{i=1}^{N} \sum_{j=1}^{N} \frac{1}{r_j-r_i}$
Mass (M)	$M = \sum_{i=1}^{N} m_i$

$M = 1 \$

$G = 1 \$

$R = 1 \$

N-body units are a completely self-contained system of units used for N-body simulations of self gravitating systems in astrophysics. 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 is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object An N -body simulation is a simulation of massive particles under the influence of physical forces usually gravity and sometimes other forces In this system, the base physical units are chosen so that the total mass (M), the gravitational constant (G) and the virial radius (R) are set equal to unity. The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass The underlying assumption is that the system of N objects (stars) satisfies the virial theorem. In Mechanics, the virial theorem provides a general equation relating the average total Kinetic energy, \left\langle T \right\rangle of a stable system The consequence of standard N-body units is that the velocity dispersion of the system is $v = 1/\sqrt{2}$ and that the dynamical -crossing- time scales as $t = 2\sqrt{2}$ . The first mention of standard N-body units was by Michel Hénon (1971) [4]. They were taken up by Haldan Cohn (1979) [5] and later widely advertised and generalized by Douglas Heggie and Robert Mathieu (1986) [6].

SI units

The metric system, or International System of Units (SI) as it is currently known, is not a natural system of units. Historically, metric units were not defined in terms of universal physical constants, nor were they defined in such a manner that some chosen set of physical constants would each have a numerical value of exactly 1.

There has been a trend in the last few decades, however, to redefine the units of the SI in terms of universal physical constants. In 1983, the seventeenth CGPM redefined the metre in terms of time and the speed of light, thus fixing the speed of light at exactly 299,792,458 m/s. And in 1990, the eighteenth CGPM adopted conventional values for the Josephson constant and the von Klitzing constant, fixing the conventional Josephson constant at exactly 483,597. 9 ×10⁹ Hz/V, and the conventional von Klitzing constant at exactly 25 812. 807 Ω.

When the conventional values of the Josephson and von Klitzing constants are taken in conjunction with the definition of the meter, one obtains a metric system with units which are not natural, but which are derived from natural units through multiplicative factors. The relationship is illustrated in the following table:

Quantity / Symbol	Planck	Stoney	Schrödinger	Atomic	Electronic	SI
speed of light in vacuum $c \,$	$1 \,$	$1 \,$	$\frac{1}{\alpha} \$	$\frac{1}{\alpha} \$	$1 \,$	$299 792 458 \$
Planck's constant $h \,$	$2\pi \,$	$\frac{2\pi}{\alpha} \$	$2\pi \,$	$2\pi \,$	$\frac{2\pi}{\alpha} \$	$\frac{4 \times 10^{-18}}{(25812.807) (483597.9)^2} \$
Dirac's constant $\hbar=\frac{h}{2 \pi}$	$1 \,$	$\frac{1}{\alpha} \$	$1 \,$	$1 \,$	$\frac{1}{\alpha} \$	$\frac{2 \times 10^{-18}}{\pi (25812.807) (483597.9)^2} \$
elementary charge $e \,$	$\sqrt{\alpha} \,$	$1 \,$	$1 \,$	$1 \,$	$1 \,$	$\frac{2 \times 10^{-9}}{(25812.807) (483597.9)} \$
Josephson constant $K_J =\frac{2e}{h} \,$	$\frac{\sqrt{\alpha}}{\pi} \,$	$\frac{\alpha}{\pi} \,$	$\frac{1}{\pi} \,$	$\frac{1}{\pi} \,$	$\frac{\alpha}{\pi} \,$	$483597.9 \times 10^9 \,$
von Klitzing constant $R_K =\frac{h}{e^2} \,$	$\frac{2\pi}{\alpha} \,$	$\frac{2\pi}{\alpha} \,$	$2\pi \,$	$2\pi \,$	$\frac{2\pi}{\alpha} \,$	$25812.807 \,$
characteristic impedance of vacuum $Z_0 = 2 \alpha R_K \,$	$4 \pi \,$	$4 \pi \,$	$4 \pi \alpha \,$	$4 \pi \alpha \,$	$4 \pi \,$	$2 \alpha (25812.807) \,$
electric constant (vacuum permittivity) $\epsilon_0 = \frac{1}{Z_0 c} \,$	$\frac{1}{4 \pi} \,$	$\frac{1}{4 \pi} \,$	$\frac{1}{4 \pi} \,$	$\frac{1}{4 \pi} \,$	$\frac{1}{4 \pi} \,$	$\frac{1}{2 \alpha (25812.807) (299792458)} \$
magnetic constant (vacuum permeability) $\mu_0 = \frac{Z_0}{c} \,$	$4 \pi \,$	$4 \pi \,$	$4 \pi \alpha^2 \,$	$4 \pi \alpha^2 \,$	$4 \pi \,$	$\frac{2 \alpha (25812.807)}{299792458} \$
Newtonian constant of gravitation $G \,$	$1 \,$	$1 \,$	$1 \,$	$- \,$	$- \,$	$- \,$
electron mass $m_e \,$	$- \,$	$- \,$	$- \,$	$1 \,$	$1 \,$	$- \,$
caesium ground state hyperfine transition frequency	$- \,$	$- \,$	$- \,$	$- \,$	$- \,$	$9\ 192\ 631\ 770 \,$

External links

The NIST website(National Institute of Standards and Technology) is a convenient source of data on the commonly recognized constants. The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. The elementary charge, usually denoted e, is the Electric charge carried by a single Proton, or equivalently the negative of the electric charge carried The Josephson effect is the phenomenon of current flow across two weakly coupled Superconductors, separated by a very thin insulating barrier The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems Impedance of Free Space (also known as Z_0 is a Canadian IDM and Electronica group Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical The vacuum permeability, referred to by international standards organizations as the magnetic constant, and denoted by the symbol μ 0 (also The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J Caesium or cesium (ˈsiːziəm is the Chemical element with the symbol Cs and Atomic number 55 In Quantum mechanics, a stationary state is an Eigenstate of a Hamiltonian, or in other words a state of definite energy In Atomic physics, hyperfine coupling is the weak magnetic interaction between Electrons and nuclei. The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units A set of fundamental units is a set of units for physical quantities from which every other unit can be generated Dimensional analysis is a conceptual tool often applied in Physics, Chemistry, Engineering, Mathematics and Statistics to understand A physical Constant is a Physical quantity that is generally believed to be both universal in nature and constant in time
K.A. Tomilin: NATURAL SYSTEMS OF UNITS; To the Centenary Anniversary of the Planck System A comparative overview/tutorial of various systems of natural units having historical use.

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Contents

Candidate physical constants used in natural unit systems

Planck units

Stoney units

"Schrödinger" units

Atomic units (Hartree)

Electronic system of units

Quantum electrodynamical system of units (Stille)

Geometrized units

N-body units

SI units

See also

External links