In physics, natural unit systems are measurement systems for which selected physical constants have been set to 1 through nondimensionalization of physical units. For example, the speed of light c may be set to 1, and it may then be omitted, equating mass and energy directly E = m rather than using c as a conversion factor in the typical mass–energy equivalence equation E = mc2. 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:
α is the fine-structure constant, e2 / 4πε0ℏc = 0.0072973525643(11) ke is the Coulomb constant, 1 / 4πε0 ≈ 8987551786, so assigning it a value also assigns ε0 a value. ηe = Gme2 / ℏc = 10068233135085418604437102.57πGme2 ≈ 1.7518×10−45 me is the mass of an electron, 9.1093837139(28)×10−31 ηp = Gmp2 / ℏc = 10068233135085418604437102.57πGmp2 ≈ 5.9061×10−39 mp is the mass of a proton, 1.67262192595(52)×10−27 — indicates where the system is not sufficient to express the quantity. kB, the Boltzmann constant, has no interactions with the other constants - it is used only to redefine temperature.
Stoney units
The Stoney unit system uses the following defining constants:
c, G, ke, e, where c is the speed of light, G is the gravitational constant, ke is the Coulomb constant, and e 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:
c, ℏ, G, kB, where c is the speed of light, ℏ is the reduced Planck constant, G is the gravitational constant, and kB 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: c and G are part of the structure of spacetime in general relativity, and ℏ is at the foundation of quantum mechanics. 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 G, h, c, and kB to arrive at natural units for length, time, mass, and temperature, but no electromagnetic units. The Planck system of units is now understood to use the reduced Planck constant, ℏ, in place of the Planck constant, h.
Geometrized units
Defining constants c, G. The geometrized unit system, used in general relativity; the base physical units are chosen so that the speed of light, c, and the gravitational constant, G, are set to one.
Atomic units
The atomic unit system uses the following defining constants:
me, e, ħ, 4πε0 (this is exactly the same as using ke, except in which constant you use when expressing the conversion). 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 of the hydrogen atom an electron in the ground state has orbital radius, orbital velocity and so on with particularly simple numeric values.
Schrödinger units
The Schrödinger system of units (named after Austrian physicist Erwin Schrödinger) were mentioned by Michael Duff (physicist) in his analysis of fundamental constants. Its defining constants are:
e, ħ, G, ke.
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:
c, me, ħ, ε0, where c is the speed of light, me is the electron mass, ħ is the reduced Planck constant, and ε0 is the vacuum permittivity. The vacuum permittivity ε0 is implicitly used as a nondimensionalization constant, as is evident from the physicists' expression for the fine-structure constant, written α = e2/(4π), which may be compared to the corresponding expression in SI: α = e2/(4πε0ħc).
Strong units
Defining constants:
c, mp, ħ. Here, mp 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".
See also
Notes and references
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 Archived 2016-05-12 at the Wayback Machine 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.
