Information about Natural Units
In physics, natural units are physical units of measurement defined in terms of universal physical constants in such a manner that some chosen physical constants take on the numerical value of one when expressed in terms of a particular set of natural units. 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. 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. Planck units are often, without qualification, called "natural units" but are only one system of natural units among other systems. 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.
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. 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. 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 normalize the permittivity of free space to ε0=(4π)-1, which can be thought of as an expression of the definition of the unit charge.
Dimensionless physical constants such as the fine-structure constant
cannot take on a different numerical value no matter what system of units are 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, alluding to the fundamental nature of the fine-structure constant) but not all 4.
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). Being so, the Planck units are defined independently of the elementary charge which comes out to be the square root of the fine-structure constant, √α if measured in terms of Planck units. 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.
Proposed by George Stoney in 1881. Stoney units fix the elementary charge and allow Planck's constant to float. They can be obtained from Planck units with the substitution:
The name coined by Michael Duff[1]. They can be obtained from Planck units with the substitution:
First proposed by Douglas Hartree to simplify the physics of the Hydrogen atom. Michael Duff[2] calls these "Bohr units". 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, 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,
. They can be obtained from "Schrödinger" units with the substitution:
Michael Duff[3] calls these "Dirac units". They can be obtained from Stoney units with the substitution:
Similar to the electronic system of units except that the proton mass is normalized rather that the electron mass. Also a conceivable variation in the value of α would be considered to be due to a variation in Planck's constant.
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 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:
N-body units are a completely self-contained system of units used for N-body simulations of self gravitating systems in astrophysics. 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 underlying assumption is that the system of N objects (stars) satisfies the virial theorem. 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)
[4].
They were taken up by Haldan Cohn (1979)
[5]
and later widely advertised and generalized by Douglas Heggie and Robert Mathieu (1986)
[6].
In particle physics, an elementary particle or fundamental particle is a not known to have substructure; that is, it is not known to be made up of smaller particles.
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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. 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. 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 normalize the permittivity of free space to ε0=(4π)-1, which can be thought of as an expression of the definition of the unit charge.
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 in vacuum |  | L T-1 |
| Gravitational constant |  | M-1L3T-2 |
| Dirac's constant or "reduced Planck's constant" |  where  is Planck's constant | ML2T-1 |
| Coulomb force constant |  where  is the permittivity of free space | Q-2 M L3 T-2 |
| Elementary charge |  | Q |
| Electron mass |  | M |
| Proton mass |  | M |
| Boltzmann constant |  | ML2T-2Θ-1 |
Dimensionless physical constants such as the fine-structure constant
cannot take on a different numerical value no matter what system of units are 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, alluding to the fundamental nature of the fine-structure constant) but not all 4.
Planck units
| Quantity | Expression | Metric value |
|---|---|---|
| Length (L) |  | 1.61609735×10-35 m |
| Mass (M) |  | 21.7664598 μg |
| Time (T) |  | 5.3907205×10-44 s |
| Electric charge (Q) |  | 1.87554573×10-18 C |
| Temperature (Θ) |  | 1.4169206×1032 K |
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). Being so, the Planck units are defined independently of the elementary charge which comes out to be the square root of the fine-structure constant, √α if measured in terms of Planck units. 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) |  |
| Mass (M) |  |
| Time (T) |  |
| Electric charge (Q) |  |
| Temperature (Θ) |  |
Proposed by George Stoney in 1881. Stoney units fix the elementary charge and allow Planck's constant to float. They can be obtained from Planck units with the substitution:
.
"Schrödinger" units
| Quantity | Expression |
|---|---|
| Length (L) |  |
| Mass (M) |  |
| Time (T) |  |
| Electric charge (Q) |  |
| Temperature (Θ) |  |
The name coined by Michael Duff[1]. They can be obtained from Planck units with the substitution:
.
Atomic units (Hartree)
| Quantity | Expression |
|---|---|
| Length (L) |  |
| Mass (M) |  |
| Time (T) |  |
| Electric charge (Q) |  |
| Temperature (Θ) |  |
First proposed by Douglas Hartree to simplify the physics of the Hydrogen atom. Michael Duff[2] calls these "Bohr units". 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, 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,
. They can be obtained from "Schrödinger" units with the substitution:
.
Electronic system of units
| Quantity | Expression |
|---|---|
| Length (L) |  |
| Mass (M) |  |
| Time (T) |  |
| Electric charge (Q) |  |
| Temperature (Θ) |  |
Michael Duff[3] calls these "Dirac units". They can be obtained from Stoney units with the substitution:
- .
- .
Quantum electrodynamical system of units (Stille)
| Quantity | Expression |
|---|---|
| Length (L) |  |
| Mass (M) |  |
| Time (T) |  |
| Electric charge (Q) |  |
| Temperature (Θ) |  |
Similar to the electronic system of units except that the proton mass is normalized rather that the electron mass. Also a conceivable variation in the value of α would be considered to be due to a variation in Planck's constant.
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 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:
N-body units
| Quantity | Expression |
|---|---|
| Length (R) |  |
| Mass (M) |  |
N-body units are a completely self-contained system of units used for N-body simulations of self gravitating systems in astrophysics. 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 underlying assumption is that the system of N objects (stars) satisfies the virial theorem. 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)
[4].
They were taken up by Haldan Cohn (1979)
[5]
and later widely advertised and generalized by Douglas Heggie and Robert Mathieu (1986)
[6].
See also
External links
- The NIST website(National Institute of Standards and Technology) is a convenient source of data on the commonly recognized constants.
- 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.
| Planck's natural units |
| Base Planck units: Planck time | Planck length | Planck mass | Planck charge | Planck temperature |
| Derived Planck units: Planck energy | Planck force | Planck power | Planck density | Planck angular frequency | Planck pressure | Planck current | Planck voltage | Planck impedance | Planck momentum |
Physics is the science of matter[1] and its motion[2][3], as well as space and time[4][5] —the science that deals with concepts such as force, energy, mass, and charge.
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units of measurement have played a crucial role in human endeavour from early ages up to this day. Disparate systems of measurement used to be very common. Now there is a global standard, the International System (SI) of units, the modern form of the metric system.
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Measurement is the estimation of the magnitude of some attribute of an object, such as its length or weight, relative to a unit of measuremnt. Measurement usually involves using a measuring instrument, such as a ruler or scale, which is calibrated to compare the object to some
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In physics, 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.
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Nondimensionalization is the partial or full removal of units from a mathematical equation by a suitable substitution of variables. This technique can simplify and parameterize problems where measured units are involved. It is closely related to dimensional analysis.
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expression must be well-formed. That is, the operators must have the correct number of inputs, in the correct places. The expression 2 + 3 is well formed; the expression * 2 + is not, at least, not in the usual notation of arithmetic.
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For the novel, see .
In particle physics, an elementary particle or fundamental particle is a not known to have substructure; that is, it is not known to be made up of smaller particles.
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Nature, in the broadest sense, is equivalent to the natural world, physical universe, material world or material universe. "Nature" refers to the phenomena of the physical world, and also to life in general.
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In physics, Planck units are physical units of measurement defined exclusively in terms of the five universal physical constants shown in the table below in such a manner that all of these physical constants take on the numerical value of one when expressed in terms of these units.
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A prototype is an original type, form, or instance of some thing serving as a typical example, basis, epitome, or standard for other things of the same category.
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Semantics
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A subatomic particle is an elementary or composite particle smaller than an atom. Particle physics and nuclear physics are concerned with the study of these particles, their interactions, and non-atomic matter composed from them.
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In physics, free space is a concept of electromagnetic theory, corresponding to a theoretical "perfect vacuum".
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Definition
Free space simply means that there is no material or other physical phenomenon..... Click the link for more information.
For the use in number theory, see .
A set of fundamental units is a set of units for physical quantities from which every other unit can be generated...... Click the link for more information.
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. This may be distinguished from height, which is vertical extent, and width or breadth
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Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic
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time.
One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured.
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One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured.
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trillion fold).]]
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. Temperature is one of the principal parameters of thermodynamics.
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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. Temperature is one of the principal parameters of thermodynamics.
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Flavour in particle physics
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The Boltzmann constant (k or kB) is the physical constant relating temperature to energy.
It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this
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It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this
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centimetre-gram-second system (CGS) is a system of physical units. It is always the same for mechanical units, but there are several variants of electric additions. It was replaced by the MKS, or metre-kilogram-second system, which in turn was replaced by the International
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Vacuum permittivity is the electric constant ε0 (also known as the permittivity of free space, or by the term dielectric constant of vacuum), which is a fundamental physical constant.
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speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning "swiftness".[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum.
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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. This may be distinguished from height, which is vertical extent, and width or breadth
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time.
One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured.
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One view is that time is part of the fundamental structure of the universe, a dimension in which events occur in sequence, and time itself is something that can be measured.
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gravitational constant, the universal gravitational constant, Newton's constant, and colloquially Big G. The gravitational constant is a physical constant which appears in Newton's law of universal gravitation and in Einstein's theory of general
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Mass is a fundamental concept in physics, roughly corresponding to the intuitive idea of "how much matter there is in an object". Mass is a central concept of classical mechanics and related subjects, and there are several definitions of mass within the framework of relativistic
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Planck constant (denoted ) is a physical constant that is used to describe the sizes of quanta. It plays a central role in the theory of quantum mechanics, and is named after Max Planck, one of the founders of quantum theory.
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Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:
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- The magnitude of the electrostatic force between two points electric charges is directly proportional to the product of the magnitudes of each
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Vacuum permittivity is the electric constant ε0 (also known as the permittivity of free space, or by the term dielectric constant of vacuum), which is a fundamental physical constant.
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Flavour in particle physics
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