In
physics
Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...
, natural unit systems are
measurement
Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.
In other words, measurement is a process of determining how large or small a physical quantity is as compared to ...
systems for which selected
physical constants have been set to
1 through
nondimensionalization of
physical units. For example, the
speed of light may be set to 1, and it may then be omitted, equating mass and energy directly rather than using as a conversion factor in the typical
mass–energy equivalence equation . A purely natural
system of units has all of its dimensions collapsed, such that the physical constants completely define the system of units and the relevant physical laws contain no conversion constants.
While natural unit systems simplify the form of each equation, it is still necessary to keep track of the non-collapsed dimensions of each quantity or expression in order to reinsert physical constants (such dimensions uniquely determine the full formula).
Systems of natural units
Summary table
where:
* is the
fine-structure constant ( ≈ 0.007297)
* ≈
* ≈
* A dash (—) indicates where the system is not sufficient to express the quantity.
Stoney units
The Stoney unit system uses the following defining constants:
: , , , ,
where is the
speed of light, is the
gravitational constant, is the
Coulomb constant, and is the
elementary charge.
George Johnstone Stoney's unit system preceded that of Planck by 30 years. He presented the idea in a lecture entitled "On the Physical Units of Nature" delivered to the
British Association in 1874.
Stoney units did not consider the
Planck constant, which was discovered only after Stoney's proposal.
Planck units
The Planck unit system uses the following defining constants:
: , , , ,
where is the
speed of light, is the
reduced Planck constant, is the
gravitational constant, and is the
Boltzmann constant.
Planck units form a system of natural units that is not defined in terms of properties of any prototype, physical object, or even
elementary particle. They only refer to the basic structure of the laws of physics: and are part of the structure of
spacetime in
general relativity, and is at the foundation of
quantum mechanics
Quantum mechanics is the fundamental physical Scientific theory, theory that describes the behavior of matter and of light; its unusual characteristics typically occur at and below the scale of atoms. Reprinted, Addison-Wesley, 1989, It is ...
. This makes Planck units particularly convenient and common in theories of
quantum gravity, including
string theory.
Planck considered only the units based on the universal constants , , , and
B to arrive at natural units for
length
Length is a measure of distance. In the International System of Quantities, length is a quantity with Dimension (physical quantity), dimension distance. In most systems of measurement a Base unit (measurement), base unit for length is chosen, ...
,
time
Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...
,
mass
Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
, and
temperature
Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
, but no electromagnetic units. The Planck system of units is now understood to use the reduced Planck constant, , in place of the Planck constant, .
[Tomilin, K. A., 1999,]
Natural Systems of Units: To the Centenary Anniversary of the Planck System
", 287–296.
Schrödinger units
The Schrödinger system of units (named after Austrian physicist
Erwin Schrödinger) is seldom mentioned in literature. Its defining constants are:
: , , , .
Geometrized units
Defining constants:
: , .
The geometrized unit system,
[
] used in
general relativity, the base physical units are chosen so that the
speed of light, , and the
gravitational constant, , are set to one.
Atomic units
The atomic unit system uses the following defining constants:
[
: , , , .
The atomic units were first proposed by Douglas Hartree and are designed to simplify atomic and molecular physics and chemistry, especially the hydrogen atom.][
] For example, in atomic units, in the Bohr model
In atomic physics, the Bohr model or Rutherford–Bohr model was a model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear Rutherford model, model, i ...
of the hydrogen atom an electron in the ground state has orbital radius, orbital velocity and so on with particularly simple numeric values.
Natural units (particle and atomic physics)
This natural unit system, used only in the fields of particle and atomic physics, uses the following defining constants:[
]
: , , , ,
where is the speed of light, e is the electron mass, is the reduced Planck constant, and 0 is the vacuum permittivity.
The vacuum permittivity 0 is implicitly used as a nondimensionalization constant, as is evident from the physicists' expression for the fine-structure constant, written , which may be compared to the corresponding expression in SI: .
Strong units
Defining constants:
: , , .
Here, is the proton rest mass. ''Strong units'' are "convenient for work in QCD and nuclear physics, where quantum mechanics and relativity are omnipresent and the proton is an object of central interest".[
. Furthe]
see
See also
* Anthropic units
* Astronomical system of units
* Dimensionless physical constant
* International System of Units
The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official s ...
* ''N''-body units
* Outline of metrology and measurement
* Unit of measurement
A unit of measurement, or unit of measure, is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other qua ...
Notes and references
External links
The NIST website
(National Institute of Standards and Technology
The National Institute of Standards and Technology (NIST) is an agency of the United States Department of Commerce whose mission is to promote American innovation and industrial competitiveness. NIST's activities are organized into Outline of p ...
) 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.
Pedagogic Aides to Quantum Field Theory
Click on the link for Chap. 2 to find an extensive, simplified introduction to natural units.
Natural System Of Units In General Relativity (PDF)
by Alan L. Myers (University of Pennsylvania). Equations for conversions from natural to SI units.
{{DEFAULTSORT:Natural Units
Metrology