In physics, natural units are physical units of measurement in which only universal physical constants are used as defining constants, such that each of these constants acts as a coherent unit of a quantity. For example, the elementary charge e may be used as a natural unit of electric charge, and the speed of light c may be used as a natural unit of speed. A purely natural system of units has all of its units defined such that each of these can be expressed as a product of powers of defining physical constants.
Through nondimensionalization, physical quantities may then be redefined so that the defining constants can be omitted from mathematical expressions of physical laws, and while this has the apparent advantage of simplicity, it may entail a loss of clarity due to the loss of information for dimensional analysis. It precludes the interpretation of an expression in terms of constants, such as e and c, unless it is known which units (in dimensionful units)[ clarification needed ] the expression is supposed to have. In this case, the reinsertion of the correct powers of e, c, etc., can be uniquely determined.
Quantity | Expression | Approx. metric value |
---|---|---|
Length | 1.380×10−36 m [1] | |
Mass | 1.859×10−9 kg [1] | |
Time | 4.605×10−45 s [1] | |
Electric charge | 1.602×10−19 C | |
The Stoney unit system uses the following defining constants:
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. [2] Stoney units did not consider the Planck constant, which was discovered only after Stoney's proposal.
Quantity | Expression | Approx. metric value |
---|---|---|
Length | 1.616×10−35 m [3] | |
Mass | 2.176×10−8 kg [4] | |
Time | 5.391×10−44 s [5] | |
Temperature | 1.417×1032 K [6] | |
The Planck unit system uses the following defining constants:
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.[ citation needed ]
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. [7] The Planck system of units is now understood to use the reduced Planck constant, ħ, in place of the Planck constant, h. [8]
Quantity | Expression | Approx. metric value |
---|---|---|
Length | 2.593×10−32 m | |
Mass | 1.859×10−9 kg | |
Time | 1.185×10−38 s | |
Electric charge | 1.602×10−19 C [9] | |
The Schrödinger system of units (named after Austrian physicist Erwin Schrödinger) is seldom mentioned in literature. Its defining constants are: [10] [11]
Defining constants:
The geometrized unit system, [12] : 36 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.
Quantity | Expression | Metric value |
---|---|---|
Length | 5.292×10−11 m [13] | |
Mass | 9.109×10−31 kg [14] | |
Time | 2.419×10−17 s [15] | |
Electric charge | 1.602×10−19 C [16] | |
The atomic unit system [17] uses the following defining constants: [18] : 349 [19]
The atomic units were first proposed by Douglas Hartree and are designed to simplify atomic and molecular physics and chemistry, especially the hydrogen atom. [18] : 349 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.
Quantity | Expression | Metric value |
---|---|---|
Length | 3.862×10−13 m [20] | |
Mass | 9.109×10−31 kg [21] | |
Time | 1.288×10−21 s [22] | |
Electric charge | 5.291×10−19 C | |
This natural unit system, used only in the fields of particle and atomic physics, uses the following defining constants: [23] : 509
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), [24] [25] which may be compared to the correspoding expression in SI: α = e2/(4πε0ħc). [26] : 128
Quantity | Expression | Metric value |
---|---|---|
Length | 2.103×10−16 m | |
Mass | 1.673×10−27 kg | |
Time | 7.015×10−25 s | |
Defining constants:
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". [27]
In this system of units the speed of light changes in inverse proportion to the fine-structure constant, therefore it has gained some interest recent years in the niche hypothesis of time-variation of fundamental constants. [28]
Quantity | Planck | Stoney | Atomic | Particle and atomic physics | Strong | Schrödinger |
---|---|---|---|---|---|---|
Defining constants | , , , | , , , | , , , | , , , | , , | , , , |
Speed of light | ||||||
Reduced Planck constant | ||||||
Elementary charge | — | — | ||||
Vacuum permittivity | — | — | ||||
Gravitational constant | ||||||
where:
In this set of units the speed of light changes in inverse proportion to the fine structure constant. From this we can conclude that if c changes but e and ℏ remain constant then the speed of light in Schrödinger units, cψ changes in proportion to c but the speed of light in Planck units, cP stays the same. Whether or not the "speed of light" changes depends on our measuring system (three possible definitions of the "speed of light" are c, cP and cψ). Whether or not c changes is unambiguous because the measuring system has been defined.
A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.
The gravitational constant, denoted by the capital letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity.
The dalton or unified atomic mass unit is a non-SI unit of mass defined as 1/12 of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest. The atomic mass constant, denoted mu, is defined identically, giving mu = 1/12m(12C) = 1 Da.
In physics, the fine-structure constant, also known as the Sommerfeld constant, commonly denoted by α, is a fundamental physical constant which quantifies the strength of the electromagnetic interaction between elementary charged particles.
The Boltzmann constant is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann.
The Bohr radius is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.29177210903(80)×10−11 m.
The hartree, also known as the Hartree energy, is the unit of energy in the atomic units system, named after the British physicist Douglas Hartree. Its CODATA recommended value is Eh = 4.3597447222071(85)×10−18 J = 27.211386245988(53) eV.
The atomic units are a system of natural units of measurement that is especially convenient for calculations in atomic physics and related scientific fields, such as computational chemistry and atomic spectroscopy. They were originally suggested and named by the physicist Douglas Hartree. Atomic units are often abbreviated "a.u." or "au", not to be confused with similar abbreviations used for astronomical units, arbitrary units, and absorbance units in other contexts.
The elementary charge, usually denoted by e, is a fundamental physical constant, defined as the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 e.
In atomic physics, the Bohr magneton is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by its orbital or spin angular momentum. In SI units, the Bohr magneton is defined as
In spectroscopy, the Rydberg constant, symbol for heavy atoms or for hydrogen, named after the Swedish physicist Johannes Rydberg, is a physical constant relating to the electromagnetic spectra of an atom. The constant first arose as an empirical fitting parameter in the Rydberg formula for the hydrogen spectral series, but Niels Bohr later showed that its value could be calculated from more fundamental constants according to his model of the atom.
The magnetic flux, represented by the symbol Φ, threading some contour or loop is defined as the magnetic field B multiplied by the loop area S, i.e. Φ = B ⋅ S. Both B and S can be arbitrary, meaning Φ can be as well. However, if one deals with the superconducting loop or a hole in a bulk superconductor, the magnetic flux threading such a hole/loop is quantized. The (superconducting) magnetic flux quantumΦ0 = h/(2e) ≈ 2.067833848...×10−15 Wb is a combination of fundamental physical constants: the Planck constant h and the electron charge e. Its value is, therefore, the same for any superconductor. The phenomenon of flux quantization was discovered experimentally by B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Näbauer, in 1961. The quantization of magnetic flux is closely related to the Little–Parks effect, but was predicted earlier by Fritz London in 1948 using a phenomenological model.
Vacuum permittivity, commonly denoted ε0, is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is:
The vacuum magnetic permeability, also known as the magnetic constant, is the magnetic permeability in a classical vacuum. It is a physical constant, conventionally written as μ0. Its purpose is to quantify the strength of the magnetic field emitted by an electric current. Expressed in terms of SI base units, it has the unit kg⋅m⋅s−2·A−2. It can be also expressed in terms of SI derived units, N·A−2.
A conventional electrical unit is a unit of measurement in the field of electricity which is based on the so-called "conventional values" of the Josephson constant, the von Klitzing constant agreed by the International Committee for Weights and Measures (CIPM) in 1988, as well as ΔνCs used to define the second. These units are very similar in scale to their corresponding SI units, but are not identical because of the different values used for the constants. They are distinguished from the corresponding SI units by setting the symbol in italic typeface and adding a subscript "90" – e.g., the conventional volt has the symbol V90 – as they came into international use on 1 January 1990.
The Planck constant, or Planck's constant, denoted by , is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a matter wave equals the Planck constant divided by the associated particle momentum.
In particle physics, the electron mass is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about 9.109×10−31 kilograms or about 5.486×10−4 daltons, which has an energy-equivalent of about 8.187×10−14 joules or about 0.511 MeV.
cGh physics refers to the historical attempts in physics to unify relativity, gravitation and quantum mechanics, in particular following the ideas of Matvei Petrovich Bronstein and George Gamow. The letters are the standard symbols for the speed of light (c), the gravitational constant (G), and Planck's constant (h).
In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: c, G, ħ, and kB. Expressing one of these physical constants in terms of Planck units yields a numerical value of 1. They are a system of natural units, defined using fundamental properties of nature rather than properties of a chosen prototype object. Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity.