-as of [21 SEPTEMBER 2024]–

*SPEED OF LIGHT*
(in a ‘vacuum’)
(‘length’ over ‘time’)
(‘length’ in ‘meters’)
(‘time’ in ‘seconds’)

-THE ‘CAESIUM STANDARD’-
(the ‘frequency standard’)
(measured in ‘hertz’)
(‘units’ per ‘second’)

-PLANCK CONSTANT-
(‘energy quantum’)
(measured in ‘joule-seconds’)
(multiply a photon’s frequency by the ‘planck constant’ to get its total ‘energy’)
(the ‘joule’ is the amount of ‘energy’ transferred when a force of ‘1 newton’ acts on an object over distance of 1 meter)
(the ‘newton’ is the amount of ‘force’ required to accelerate 1 ‘kilo-gram’ of mass at rate of [1 meter/second] divided by ‘second’ in direction of applied force)
(it measures ‘change in velocity over time’)

*LIST OF ‘PHYSICAL CONSTANTS’*

*46 CONSTANTS*

en.wikipedia.org /wiki/List_of_physical_constants

Key to SI Definition Constants:
Δν = the unperturbed ground state hyperfine transition frequency of the caesium-133 atom ΔνCs is 9,192,631,770 hertz

c = the speed of light in vacuum c is exactly 299,792,458 metres per second

h = the Planck constant h is exactly 6.626 06X x 10^–34 joule seconds

e = the elementary charge e is exactly 1.602 17X x 10^–19 coulombs
k_B = the Boltzmann constant k is exactly 1.380 6X x 10^–23 joules per kelvin
N_A = the Avogadro constant N_A is exactly 6.022 14X x 10²³ reciprocal moles
K_cd = the luminous efficacy K_cd of monochromatic radiation of frequency 540 x 10¹² Hz is exactly 683 lumens per watt
Note: X represents the yet unknown final digit(s).

List of physical constants

Contributors to Wikimedia projects10-13 minutes

Table of physical constants[edit]

Symbol	Quantity	Value^[1]	Relative standard uncertainty	Group
$c$	speed of light in vacuum	299792458 m⋅s⁻¹^[2]	0	ud
$h$	Planck constant	6.62607015×10⁻³⁴ J⋅s^[3]	0	ud f
$\hbar = h/2\pi$	reduced Planck constant	1.054571817…×10⁻³⁴ J⋅s^[4]	0	ud f
$G$	Newtonian constant of gravitation	6.67430(15)×10⁻¹¹ m³⋅kg⁻¹⋅s⁻²^[5]	2.2×10⁻⁵	u f
$\varepsilon _{0}=1/\mu _{0}c^{2}$	vacuum electric permittivity	8.8541878128(13)×10⁻¹² F⋅m⁻¹^[6]	1.5×10⁻¹⁰	u f
$\mu_0$	vacuum magnetic permeability	1.25663706212(19)×10⁻⁶ N⋅A⁻²^[7]	1.5×10⁻¹⁰	u f
$Z_{0}=\mu _{0}c$	characteristic impedance of vacuum	376.730313668(57) Ω^[8]	1.5×10⁻¹⁰	u
$e,q_{\text{e}}$	elementary charge	1.602176634×10⁻¹⁹ C^[9]	0	de f
$\Delta \nu _{\text{Cs}}$	hyperfine transition frequency of ¹³³Cs	9192631770 Hz^[10]	0	d
$N_{\text{A}},L$	Avogadro constant	6.02214076×10²³ mol⁻¹^[11]	0	d pf
$k,k_{\text{B}}$	Boltzmann constant	1.380649×10⁻²³ J⋅K⁻¹^[12]	0	d pf
$G_{0}=2e^{2}/h$	conductance quantum	7.748091729…×10⁻⁵ S^[13]	0	e f
$K_{\mathrm {J} }=2e/h$	Josephson constant	483597.8484…×10⁹ Hz⋅V⁻¹^[14]	0	e f
$R_{\mathrm {K} }=h/e^{2}$	von Klitzing constant	25812.80745… Ω^[15]	0	e f
$\Phi _{0}=h/2e$	magnetic flux quantum	2.067833848…×10⁻¹⁵ Wb^[16]	0	e f
$G_{0}^{-1}=h/2e^{2}$	inverse conductance quantum	12906.40372… Ω^[17]	0	e
$\mu _{\mathrm {B} }=e\hbar /2m_{\mathrm {e} }$	Bohr magneton	9.2740100783(28)×10⁻²⁴ J⋅T⁻¹^[18]	3.0×10⁻¹⁰	e
$\mu _{\mathrm {N} }=e\hbar /2m_{\mathrm {p} }$	nuclear magneton	5.0507837461(15)×10⁻²⁷ J⋅T⁻¹^[19]	3.1×10⁻¹⁰	e
$\alpha =e^{2}/4\pi \varepsilon _{0}\hbar c$	fine-structure constant	7.2973525693(11)×10⁻³^[20]	1.5×10⁻¹⁰	a f
$\alpha ^{-1}$	inverse fine-structure constant	137.035999084(21)^[21]	1.5×10⁻¹⁰	a f
$m_{\mathrm {e} }$	electron mass	9.1093837015(28)×10⁻³¹ kg^[22]	3.0×10⁻¹⁰	a f
$m_{\mathrm {p} }$	proton mass	1.67262192369(51)×10⁻²⁷ kg^[23]	3.1×10⁻¹⁰	a f
$m_{\mathrm {n} }$	neutron mass	1.67492749804(95)×10⁻²⁷ kg^[24]	5.7×10⁻¹⁰	a
$a_{0}=\hbar /\alpha m_{\text{e}}c$	Bohr radius	5.29177210903(80)×10⁻¹¹ m^[25]	1.5×10⁻¹⁰	a
$r_{\mathrm {e} }=e^{2}/4\pi \varepsilon _{0}m_{\mathrm {e} }c^{2}$	classical electron radius	2.8179403262(13)×10⁻¹⁵ m^[26]	4.5×10⁻¹⁰	a
$g_{\mathrm {e} }$	electron g-factor	−2.00231930436256(35)^[27]	1.7×10⁻¹³	a
$G_{\mathrm {F} }/(\hbar c)^{3}$	Fermi coupling constant	1.1663787(6)×10⁻⁵ GeV⁻²^[28]	5.1×10⁻⁷	a
$E_{\mathrm {h} }=2R_{\infty }hc$	Hartree energy	4.3597447222071(85)×10⁻¹⁸ J^[29]	1.9×10⁻¹²	a
$h/2m_{\mathrm {e} }$	quantum of circulation	3.6369475516(11)×10⁻⁴ m²⋅s⁻¹^[30]	3.0×10⁻¹⁰	a
$R_{\infty }=\alpha ^{2}m_{\mathrm {e} }c/2h$	Rydberg constant	10973731.568160(21) m⁻¹^[31]	1.9×10⁻¹²	a
$\sigma _{\text{e}}=(8\pi /3)r_{\mathrm {e} }^{2}$	Thomson cross section	6.6524587321(60)×10⁻²⁹ m²^[32]	9.1×10⁻¹⁰	a
$m_{\mathrm {W} }/m_{\mathrm {Z} }$	W-to-Z mass ratio	0.88153(17)^[33]	1.9×10⁻⁴
$\sin ^{2}\theta _{\mathrm {W} }=1-(m_{\mathrm {W} }/m_{\mathrm {Z} })^{2}$	weak mixing angle	0.22290(30)^[34]	1.3×10⁻³	a
$m_{\text{u}}=1\,{\text{Da}}$	atomic mass constant	1.66053906660(50)×10⁻²⁷ kg^[35]	3.0×10⁻¹⁰	pf
$F=N_{\text{A}}e$	Faraday constant	96485.33212… C⋅mol⁻¹^[36]	0	pf
$R=N_{\text{A}}k_{\text{B}}$	molar gas constant	8.314462618… J⋅mol⁻¹⋅K⁻¹^[37]	0	pf
$M_{\text{u}}=M({}^{12}{\text{C}})/12$	molar mass constant	0.99999999965(30)×10⁻³ kg⋅mol⁻¹^[38]	3.0×10⁻¹⁰	pf
$\sigma =\pi ^{2}k^{4}/60\hbar ^{3}c^{2}$	Stefan–Boltzmann constant	5.670374419…×10⁻⁸ W⋅m⁻²⋅K⁻⁴^[39]	0	pf
$c_{1}=2\pi hc^{2}$	first radiation constant	3.741771852…×10⁻¹⁶ W⋅m²^[40]	0	p
$c_{\text{1L}}=c_{1}/\pi$	first radiation constant for spectral radiance	1.191042972…×10⁻¹⁶ W⋅m²⋅sr⁻¹^[41]	0	p
$M({}^{12}{\text{C}})=N_{\text{A}}m({}^{12}{\text{C}})$	molar mass of carbon-12	11.9999999958(36)×10⁻³ kg⋅mol⁻¹^[42]	3.0×10⁻¹⁰	p
$N_{\text{A}}h$	molar Planck constant	3.990312712…×10⁻¹⁰ J⋅Hz⁻¹⋅mol⁻¹^[43]	0	p
$c_{2}=hc/k$	second radiation constant	1.438776877…×10⁻² m⋅K^[44]	0	p
$b$	Wien wavelength displacement law constant	2.897771955…×10⁻³ m⋅K^[45]	0	p
$b'$	Wien frequency displacement law constant	5.878925757…×10¹⁰ Hz⋅K⁻¹^[46]	0	p
$b_{\text{entropy}}$	Wien entropy displacement law constant	3.002916077…×10⁻³ m⋅K^[47]	0	p

‘Group’ reflects categorization on the NIST website:^[48]u: universald: definede: electromagnetica: atomic and nuclearp: physico-chemicalf: frequently usedn: non-SI units

There are some notable omissions in the site’s classification: the speed of light (f), vacuum electric permittivity (e), vacuum magnetic permeability (e), hyperfine transition frequency of ¹³³Cs (p).

References[edit]

^ The values are given in the so-called concise form; the number in parentheses is the standard uncertainty and indicates the amount by which the least significant digits of the value are uncertain.
^ “2018 CODATA Value: speed of light in vacuum”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Planck constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: reduced Planck constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-28.
^ “2018 CODATA Value: Newtonian constant of gravitation”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: vacuum electric permittivity”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: vacuum magnetic permeability”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: characteristic impedance of vacuum”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-10-31.
^ “2018 CODATA Value: elementary charge”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: hyperfine transition frequency of Cs-133”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-18.
^ “2018 CODATA Value: Avogadro constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Boltzmann constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: conductance quantum”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Josephson constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: von Klitzing constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: magnetic flux quantum”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: inverse of conductance quantum”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Bohr magneton”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: nuclear magneton”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: fine-structure constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: inverse fine-structure constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: electron mass in u”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: proton mass”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: neutron mass”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-08-23.
^ “2018 CODATA Value: Bohr radius”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: classical electron radius”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: electron g factor”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2020-03-13.
^ “2018 CODATA Value: Fermi coupling constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Hartree energy”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: quantum of circulation”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Rydberg constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Thomson cross section”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: W to Z mass ratio”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-12-21.
^ “2018 CODATA Value: weak mixing angle”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: atomic mass constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Faraday constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: molar gas constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: molar mass constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Stefan–Boltzmann constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: first radiation constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: first radiation constant for spectral radiance”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: molar mass of carbon-12”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: molar Planck constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: second radiation constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Wien wavelength displacement law constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Wien frequency displacement law constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ Delgado-Bonal A (May 2017). “Entropy of radiation: the unseen side of light”. Scientific Reports. 7 (1): 1642. Bibcode:2017NatSR…7.1642D. doi:10.1038/s41598-017-01622-6. PMC 5432030. PMID 28490790.
^ “Fundamental Physical Constants from NIST”.

A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant value in time.

It is contrasted with a mathematical constant, which has a fixed numerical value, but does not directly involve any physical measurement.

There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε0, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed for any object and its dimension is length divided by time; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless.

The term fundamental physical constant is sometimes used to refer to universal-but-dimensioned physical constants such as those mentioned above.[1]

Increasingly, however, physicists only use fundamental physical constant for dimensionless physical constants, such as the fine-structure constant α.

Physical constant, as discussed here, should not be confused with other quantities called “constants”, which are assumed to be constant in a given context without being fundamental, such as the “time constant” characteristic of a given system, or material constants (e.g., Madelung constant, electrical resistivity, and heat capacity).

Since May 2019, all of the SI base units have been defined in terms of physical constants.

As a result, five constants:

the speed of light in vacuum, c;

the Planck constant, h;

the elementary charge, e;

the Avogadro constant, NA;

and the Boltzmann constant, kB,

have known exact numerical values when expressed in SI units.

The first three of these constants are fundamental constants, whereas NA and kB are of a technical nature only: they do not describe any property of the universe, but instead only give a proportionality factor for defining the units used with large numbers of atomic-scale entities.

Choice of units[edit]
Whereas the physical quantity indicated by a physical constant does not depend on the unit system used to express the quantity, the numerical values of dimensional physical constants do depend on choice of unit system. The term “physical constant” refers to the physical quantity, and not to the numerical value within any given system of units. For example, the speed of light is defined as having the numerical value of 299792458 when expressed in the SI unit metres per second, and as having the numerical value of 1 when expressed in the natural units Planck length per Planck time. While its numerical value can be defined at will by the choice of units, the speed of light itself is a single physical constant.

Any ratio between physical constants of the same dimensions results in a dimensionless physical constant, for example, the proton-to-electron mass ratio. Any relation between physical quantities can be expressed as a relation between dimensionless ratios via a process known as nondimensionalisation.

The term of “fundamental physical constant” is reserved for physical quantities which, according to the current state of knowledge, are regarded as immutable and as non-derivable from more fundamental principles. Notable examples are the speed of light c, and the gravitational constant G.

The fine-structure constant α is the best known dimensionless fundamental physical constant. It is the value of the elementary charge squared expressed in Planck units. This value has become a standard example when discussing the derivability or non-derivability of physical constants. Introduced by Arnold Sommerfeld, its value as determined at the time was consistent with 1/137. This motivated Arthur Eddington (1929) to construct an argument why its value might be 1/137 precisely, which related to the Eddington number, his estimate of the number of protons in the Universe.[2] By the 1940s, it became clear that the value of the fine-structure constant deviates significantly from the precise value of 1/137, refuting Eddington’s argument.[3]

With the development of quantum chemistry in the 20th century, however, a vast number of previously inexplicable dimensionless physical constants were successfully computed from theory. In light of that, some theoretical physicists still hope for continued progress in explaining the values of other dimensionless physical constants.

It is known that the Universe would be very different if these constants took values significantly different from those we observe. For example, a few percent change in the value of the fine structure constant would be enough to eliminate stars like our Sun. This has prompted attempts at anthropic explanations of the values of some of the dimensionless fundamental physical constants.

Natural units[edit]
It is possible to combine dimensional universal physical constants to define fixed quantities of any desired dimension, and this property has been used to construct various systems of natural units of measurement. Depending on the choice and arrangement of constants used, the resulting natural units may be convenient to an area of study. For example, Planck units, constructed from c, G, ħ, and kB give conveniently sized measurement units for use in studies of quantum gravity, and Hartree atomic units, constructed from ħ, me, e and 4πε0 give convenient units in atomic physics. The choice of constants used leads to widely varying quantities.

Number of fundamental constants[edit]
The number of fundamental physical constants depends on the physical theory accepted as “fundamental”. Currently, this is the theory of general relativity for gravitation and the Standard Model for electromagnetic, weak and strong nuclear interactions and the matter fields. Between them, these theories account for a total of 19 independent fundamental constants. There is, however, no single “correct” way of enumerating them, as it is a matter of arbitrary choice which quantities are considered “fundamental” and which as “derived”. Uzan (2011) lists 22 “unknown constants” in the fundamental theories, which give rise to 19 “unknown dimensionless parameters”, as follows:

the gravitational constant G,
the speed of light c,
the Planck constant h,
the 9 Yukawa couplings for the quarks and leptons (equivalent to specifying the rest mass of these elementary particles),
2 parameters of the Higgs field potential,
4 parameters for the quark mixing matrix,
3 coupling constants for the gauge groups SU(3) × SU(2) × U(1) (or equivalently, two coupling constants and the Weinberg angle),
a phase for the QCD vacuum.
The number of 19 independent fundamental physical constants is subject to change under possible extensions of the Standard Model, notably by the introduction of neutrino mass (equivalent to seven additional constants, i.e. 3 Yukawa couplings and 4 lepton mixing parameters).[4]

The discovery of variability in any of these constants would be equivalent to the discovery of “new physics”.[5]

The question as to which constants are “fundamental” is neither straightforward nor meaningless, but a question of interpretation of the physical theory regarded as fundamental; as pointed out by Lévy-Leblond 1977, not all physical constants are of the same importance, with some having a deeper role than others. Lévy-Leblond 1977 proposed a classification schemes of three types of constants:

A: physical properties of particular objects
B: characteristic of a class of physical phenomena
C: universal constants
The same physical constant may move from one category to another as the understanding of its role deepens; this has notably happened to the speed of light, which was a class A constant (characteristic of light) when it was first measured, but became a class B constant (characteristic of electromagnetic phenomena) with the development of classical electromagnetism, and finally a class C constant with the discovery of special relativity.[6]

Tests on time-independence[edit]
By definition, fundamental physical constants are subject to measurement, so that their being constant (independent on both the time and position of the performance of the measurement) is necessarily an experimental result and subject to verification.

Paul Dirac in 1937 speculated that physical constants such as the gravitational constant or the fine-structure constant might be subject to change over time in proportion of the age of the universe. Experiments can in principle only put an upper bound on the relative change per year. For the fine-structure constant, this upper bound is comparatively low, at roughly 10−17 per year (as of 2008).[7]

The gravitational constant is much more difficult to measure with precision, and conflicting measurements in the 2000s have inspired the controversial suggestions of a periodic variation of its value in a 2015 paper.[8] However, while its value is not known to great precision, the possibility of observing type Ia supernovae which happened in the universe’s remote past, paired with the assumption that the physics involved in these events is universal, allows for an upper bound of less than 10−10 per year for the gravitational constant over the last nine billion years.[9]

Similarly, an upper bound of the change in the proton-to-electron mass ratio has been placed at 10−7 over a period of 7 billion years (or 10−16 per year) in a 2012 study based on the observation of methanol in a distant galaxy.[10][11]

It is problematic to discuss the proposed rate of change (or lack thereof) of a single dimensional physical constant in isolation. The reason for this is that the choice of units is arbitrary, making the question of whether a constant is undergoing change an artefact of the choice (and definition) of the units.[12][13][14]

For example, in SI units, the speed of light was given a defined value in 1983. Thus, it was meaningful to experimentally measure the speed of light in SI units prior to 1983, but it is not so now. Similarly, with effect from May 2019, the Planck constant has a defined value, such that all SI base units are now defined in terms of fundamental physical constants. With this change, the international prototype of the kilogram is being retired as the last physical object used in the definition of any SI unit.

Tests on the immutability of physical constants look at dimensionless quantities, i.e. ratios between quantities of like dimensions, in order to escape this problem. Changes in physical constants are not meaningful if they result in an observationally indistinguishable universe. For example, a “change” in the speed of light c would be meaningless if accompanied by a corresponding change in the elementary charge e so that the ratio e2/(4πε0ħc) (the fine-structure constant) remained unchanged.[15]

Fine-tuned universe[edit]
Some physicists have explored the notion that if the dimensionless physical constants had sufficiently different values, our Universe would be so radically different that intelligent life would probably not have emerged, and that our Universe therefore seems to be fine-tuned for intelligent life. However, the phase space of the possible constants and their values is unknowable, so any conclusions drawn from such arguments are unsupported. The anthropic principle states a logical truism: the fact of our existence as intelligent beings who can measure physical constants requires those constants to be such that beings like us can exist. There are a variety of interpretations of the constants’ values, including that of a divine creator (the apparent fine-tuning is actual and intentional), or that ours is one universe of many in a multiverse (e.g. the many-worlds interpretation of quantum mechanics), or even that, if information is an innate property of the universe and logically inseparable from consciousness, a universe without the capacity for conscious beings cannot exist.

The fundamental constants and quantities of nature have been discovered to be fine-tuned to such an extraordinarily narrow range that if it were not, the origin and evolution of conscious life in the universe would not be permitted.[16]

Table of physical constants[edit]
The table below lists some frequently used constants and their CODATA recommended values. For a more extended list, refer to List of physical constants.

Quantity Symbol Value[17] Relative
standard
uncertainty
elementary charge e 1.602176634×10−19 C[18] 0
Newtonian constant of gravitation G 6.67430(15)×10−11 m3⋅kg−1⋅s−2[19] 2.2×10−5
Planck constant h 6.62607015×10−34 J⋅s[20] 0
speed of light in vacuum c 299792458 m⋅s−1[21] 0
vacuum electric permittivity {\displaystyle \varepsilon {0}=1/\mu {0}c^{2}} 8.8541878128(13)×10−12 F⋅m−1[22] 1.5×10−10
vacuum magnetic permeability \mu_0 1.25663706212(19)×10−6 N⋅A−2[23] 1.5×10−10
electron mass {\displaystyle m_{\mathrm {e} }} 9.1093837015(28)×10−31 kg[24] 3.0×10−10
fine-structure constant {\displaystyle \alpha =e^{2}/2\varepsilon {0}hc} 7.2973525693(11)×10−3[25] 1.5×10−10 Josephson constant {\displaystyle K{\mathrm {J} }=2e/h} 483597.8484…×109 Hz⋅V−1[26] 0
Rydberg constant {\displaystyle R_{\infty }=\alpha ^{2}m_{\mathrm {e} }c/2h} 10973731.568160(21) m−1[27] 1.9×10−12
von Klitzing constant {\displaystyle R_{\mathrm {K} }=h/e^{2}} 25812.80745… Ω[28] 0
See also[edit]
List of common physics notations
References[edit]
^ “Archived copy”. Archived from the original on 2016-01-13. Retrieved 2016-01-14.CS1 maint: archived copy as title (link) NIST
^ A.S Eddington (1956). “The Constants of Nature”. In J.R. Newman (ed.). The World of Mathematics. 2. Simon & Schuster. pp. 1074–1093.
^ H. Kragh (2003). “Magic Number: A Partial History of the Fine-Structure Constant”. Archive for History of Exact Sciences. 57 (5): 395–431. doi:10.1007/s00407-002-0065-7. S2CID 118031104.
^ Uzan, Jean-Philippe (2011). “Varying Constants, Gravitation and Cosmology” (PDF). Living Reviews in Relativity. 14 (1): 2. arXiv:1009.5514. Bibcode:2011LRR….14….2U. doi:10.12942/lrr-2011-2. PMC 5256069. PMID 28179829. Any constant varying in space and/or time would reflect the existence of an almost massless field that couples to matter. This will induce a violation of the universality of free fall. Thus, it is of utmost importance for our understanding of gravity and of the domain of validity of general relativity to test for their constancy.
^ Uzan, Jean-Philippe (2011). “Varying Constants, Gravitation and Cosmology” (PDF). Living Reviews in Relativity. 14 (1): 2. Bibcode:2011LRR….14….2U. doi:10.12942/lrr-2011-2. PMC 5256069. PMID 28179829.
^ Lévy-Leblond, J. (1977). “On the conceptual nature of the physical constants”. La Rivista del Nuovo Cimento Series 2. 7 (2): 187–214. Bibcode:1977NCimR…7..187L. doi:10.1007/bf02748049. S2CID 121022139.Lévy-Leblond, J.-M. (1979). “The importance of being (a) Constant”. In Toraldo di Francia, G. (ed.). Problems in the Foundations of Physics, Proceedings of the International School of Physics ‘Enrico Fermi’ Course LXXII, Varenna, Italy, July 25 – August 6, 1977. New York: NorthHolland. pp. 237–263.
^ T. Rosenband; et al. (2008). “Frequency Ratio of Al+ and Hg+ Single-Ion Optical Clocks; Metrology at the 17th Decimal Place”. Science. 319 (5871): 1808–12. Bibcode:2008Sci…319.1808R. doi:10.1126/science.1154622. PMID 18323415. S2CID 206511320.
^ J.D. Anderson; G. Schubert; V. Trimble; M.R. Feldman (April 2015), “Measurements of Newton’s gravitational constant and the length of day”, EPL, 110 (1): 10002, arXiv:1504.06604, Bibcode:2015EL….11010002A, doi:10.1209/0295-5075/110/10002, S2CID 119293843
^ J. Mould; S. A. Uddin (2014-04-10), “Constraining a Possible Variation of G with Type Ia Supernovae”, Publications of the Astronomical Society of Australia, 31: e015, arXiv:1402.1534, Bibcode:2014PASA…31…15M, doi:10.1017/pasa.2014.9, S2CID 119292899
^ Bagdonaite, Julija; Jansen, Paul; Henkel, Christian; Bethlem, Hendrick L.; Menten, Karl M.; Ubachs, Wim (December 13, 2012). “A Stringent Limit on a Drifting Proton-to-Electron Mass Ratio from Alcohol in the Early Universe” (PDF). Science. 339 (6115): 46–48. Bibcode:2013Sci…339…46B. doi:10.1126/science.1224898. hdl:1871/39591. PMID 23239626. S2CID 716087.
^ Moskowitz, Clara (December 13, 2012). “Phew! Universe’s Constant Has Stayed Constant”. Space.com. Archived from the original on December 14, 2012. Retrieved December 14, 2012.
^ Michael Duff (2015). “How fundamental are fundamental constants?”. Contemporary Physics. 56 (1): 35–47. arXiv:1412.2040. Bibcode:2015ConPh..56…35D. doi:10.1080/00107514.2014.980093 (inactive 2020-11-10).CS1 maint: DOI inactive as of November 2020 (link)
^ Duff, M. J. (13 August 2002). “Comment on time-variation of fundamental constants”. arXiv:hep-th/0208093.
^ Duff, M. J.; Okun, L. B.; Veneziano, G. (2002). “Trialogue on the number of fundamental constants”. Journal of High Energy Physics. 2002 (3): 023. arXiv:physics/0110060. Bibcode:2002JHEP…03..023D. doi:10.1088/1126-6708/2002/03/023. S2CID 15806354.
^ Barrow, John D. (2002), The Constants of Nature; From Alpha to Omega – The Numbers that Encode the Deepest Secrets of the Universe, Pantheon Books, ISBN 978-0-375-42221-8 “[An] important lesson we learn from the way that pure numbers like α define the World is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by α is a combination of the electron charge, e, the speed of light, c, and Planck’s constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of α remained the same, this new world would be observationally indistinguishable from our World. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value you cannot tell, because all the pure numbers defined by the ratios of any pair of masses are unchanged.”
^ Leslie, John (1998). Modern Cosmology & Philosophy. University of Michigan: Prometheus Books. ISBN 1573922501.
^ The values are given in the so-called concise form, where the number in parentheses indicates the standard uncertainty referred to the least significant digits of the value.
^ “2018 CODATA Value: elementary charge”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Newtonian constant of gravitation”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Planck constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: speed of light in vacuum”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: vacuum electric permittivity”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: vacuum magnetic permeability”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: electron mass in u”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: fine-structure constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Josephson constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: Rydberg constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
^ “2018 CODATA Value: von Klitzing constant”. The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). “CODATA Recommended Values of the Fundamental Physical Constants: 2006” (PDF). Reviews of Modern Physics. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP…80..633M. doi:10.1103/RevModPhys.80.633. Archived from the original (PDF) on 2017-10-01.
Barrow, John D. (2002), The Constants of Nature; From Alpha to Omega – The Numbers that Encode the Deepest Secrets of the Universe, Pantheon Books, ISBN 978-0-375-42221-8.
External links[edit]
Sixty Symbols, University of Nottingham
IUPAC – Gold Book

en.wikipedia.org /wiki/Physical_constant

Physical constant

Contributors to Wikimedia projects

19-24 minutes

en.wikipedia.org /wiki/2019_redefinition_of_the_SI_base_units
2019 redefinition of the SI base units
Contributors to Wikimedia projects
52-65 minutes

The SI system after the 2019 redefinition: Dependence of base unit definitions on physical constants with fixed numerical values and on other base units. Arrows are shown in the opposite direction compared to typical dependency graphs, i.e. a\rightarrow b in this chart means a is used to define b.

The SI system after 1983, but before the 2019 redefinition: Dependence of base unit definitions on other base units (for example, the metre is defined as the distance travelled by light in a specific fraction of a second), with the constants of nature and artefacts used to define them (such as the mass of the IPK for the kilogram).

Effective 20 May 2019, the 144th anniversary of the Metre Convention, the SI base units were redefined in agreement with the International System of Quantities.[1][2] In the redefinition, four of the seven SI base units – the kilogram, ampere, kelvin, and mole – were redefined by setting exact numerical values for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (kB), and the Avogadro constant (NA), respectively. The second, metre, and candela were already defined by physical constants and were not subject to correction to their definitions. The new definitions aimed to improve the SI without changing the value of any units, ensuring continuity with existing measurements.[3][4] In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes,[5][6] which the International Committee for Weights and Measures (CIPM) had proposed earlier that year after determining that previously agreed conditions for the change had been met.[7]:23 These conditions were satisfied by a series of experiments that measured the constants to high accuracy relative to the old SI definitions, and were the culmination of decades of research.

The previous major change of the metric system occurred in 1960 when the International System of Units (SI) was formally published. At this time the metre was redefined: the definition was changed from the prototype of the metre to a certain number of wavelengths of a spectral line of a krypton-86 radiation, making it derivable from universal natural phenomena.[Note 1] The kilogram remained defined by a physical prototype, leaving it the only artefact upon which the SI unit definitions depend. At this time the SI, as a coherent system, was constructed around seven base units, powers of which were used to construct all other units. With the 2019 redefinition, the SI is constructed around seven defining constants, allowing all units to be constructed directly from these constants. The designation of base units is retained but is no longer essential to define SI measures.[4]

The metric system was originally conceived as a system of measurement that was derivable from unchanging phenomena,[8] but practical limitations necessitated the use of artefacts – the prototype of the metre and prototype of the kilogram – when the metric system was introduced in France in 1799. Although it was designed for long-term stability, the masses of the prototype kilogram and its secondary copies have shown small variations relative to each other over time; they are not thought to be adequate for the increasing accuracy demanded by science, prompting a search for a suitable replacement. The definitions of some units were defined by measurements that are difficult to precisely realise in a laboratory, such as the kelvin, which was defined in terms of the triple point of water. With the 2019 redefinition, the SI became wholly derivable from natural phenomena with most units being based on fundamental physical constants.

A number of authors have published criticisms of the revised definitions; their criticisms include the premise that the proposal failed to address the impact of breaking the link between the definition of the dalton[Note 2] and the definitions of the kilogram, the mole, and the Avogadro constant.

Background[edit]
The basic structure of SI was developed over about 170 years between 1791 and 1960. Since 1960, technological advances have made it possible to address weaknesses in SI such as the dependence on a physical artefact to define the kilogram.

Development of SI[edit]
During the early years of the French Revolution, the leaders of the French National Constituent Assembly decided to introduce a new system of measurement that was based on the principles of logic and natural phenomena. The metre was defined as one ten-millionth of the distance from the north pole to the equator and the kilogram as the mass of one thousandth of a cubic metre of pure water. Although these definitions were chosen to avoid ownership of the units, they could not be measured with sufficient convenience or precision to be of practical use. Instead, realisations were created in the form of the mètre des Archives and kilogramme des Archives which were a “best attempt” at fulfilling these principles.[9]

By 1875, use of the metric system had become widespread in Europe and in Latin America; that year, twenty industrially developed nations met for the Convention of the Metre, which led to the signing of the Treaty of the Metre, under which three bodies were set up to take custody of the international prototypes of the kilogram and the metre, and to regulate comparisons with national prototypes.[10][11] They were:

CGPM (General Conference on Weights and Measures, Conférence générale des poids et mesures) – The Conference meets every four to six years and consists of delegates of the nations that had signed the convention. It discusses and examines the arrangements required to ensure the propagation and improvement of the International System of Units and it endorses the results of new fundamental metrological determinations.
CIPM (International Committee for Weights and Measures, Comité international des poids et mesures) – The Committee consists of eighteen eminent scientists, each from a different country, nominated by the CGPM. The CIPM meets annually and is tasked with advising the CGPM. The CIPM has set up a number of sub-committees, each charged with a particular area of interest. One of these, the Consultative Committee for Units (CCU), advises the CIPM on matters concerning units of measurement.[12]
BIPM (International Bureau for Weights and Measures, Bureau international des poids et mesures) – The Bureau provides safe keeping of the international prototypes of the kilogram and the metre, provides laboratory facilities for regular comparisons of the national prototypes with the international prototype, and is the secretariat for the CIPM and the CGPM.
The first CGPM (1889) formally approved the use of 40 prototype metres and 40 prototype kilograms made by the British firm Johnson Matthey as the standards mandated by the Convention of the Metre.[13] One of each of these was nominated by lot as the international prototypes, the CGMP retained other copies as working copies, and the rest were distributed to member nations for use as their national prototypes. About once every 40 years, the national prototypes were compared with and recalibrated against the international prototype.[14]

In 1921 the Convention of the Metre was revised and the mandate of the CGPM was extended to provide standards for all units of measure, not just mass and length. In the ensuing years, the CGPM took on responsibility for providing standards of electrical current (1946), luminosity (1946), temperature (1948), time (1956), and molar mass (1971).[15] The 9th CGPM in 1948 instructed the CIPM “to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention”.[16] The recommendations based on this mandate were presented to the 11th CGPM (1960), where they were formally accepted and given the name “Système International d’Unités” and its abbreviation “SI”.[17]

Impetus for change[edit]
There is a precedent for changing the underlying principles behind the definition of the SI base units; the 11th CGPM (1960) defined the SI metre in terms of the wavelength of krypton-86 radiation, replacing the pre-SI metre bar and the 13th CGPM (1967) replaced the original definition of the second, which was based on Earth’s average rotation from 1750 to 1892,[18] with a definition based on the frequency of the radiation emitted or absorbed with a transition between two hyperfine levels of the ground state of the caesium-133 atom. The 17th CGPM (1983) replaced the 1960 definition of the metre with one based on the second by giving an exact definition of the speed of light in units of metres per second.[19]

Since their manufacture, drifts of up to 2×10−8 kilograms per year in the national prototype kilograms relative to the international prototype of the kilogram (IPK) have been detected. There was no way of determining whether the national prototypes were gaining mass or whether the IPK was losing mass.[21] Newcastle University metrologist Peter Cumpson has since identified mercury vapour absorption or carbonaceous contamination as possible causes of this drift.[22][23] At the 21st meeting of the CGPM (1999), national laboratories were urged to investigate ways of breaking the link between the kilogram and a specific artefact.

Metrologists investigated several alternative approaches to redefining the kilogram based on fundamental physical constants. Among others, the Avogadro project and the development of the Kibble balance (known as the “watt balance” before 2016) promised methods of indirectly measuring mass with very high precision. These projects provided tools that enable alternative means of redefining the kilogram.[24]

A report published in 2007 by the Consultative Committee for Thermometry (CCT) to the CIPM noted that their current definition of temperature has proved to be unsatisfactory for temperatures below 20 K and for temperatures above 1300 K. The committee took the view that the Boltzmann constant provided a better basis for temperature measurement than did the triple point of water because it overcame these difficulties.[25]

At its 23rd meeting (2007), the CGPM mandated the CIPM to investigate the use of natural constants as the basis for all units of measure rather than the artefacts that were then in use. The following year this was endorsed by the International Union of Pure and Applied Physics (IUPAP).[26] At a meeting of the CCU held in Reading, United Kingdom, in September 2010, a resolution[27] and draft changes to the SI brochure that were to be presented to the next meeting of the CIPM in October 2010 were agreed to in principle.[28] The CIPM meeting of October 2010 found “the conditions set by the General Conference at its 23rd meeting have not yet been fully met.[Note 4] For this reason the CIPM does not propose a revision of the SI at the present time”.[30] The CIPM, however, presented a resolution for consideration at the 24th CGPM (17–21 October 2011) to agree to the new definitions in principle, but not to implement them until the details had been finalised.[31] This resolution was accepted by the conference,[32] and in addition the CGPM moved the date of the 25th meeting forward from 2015 to 2014.[33][34] At the 25th meeting on 18 to 20 November 2014, it was found that “despite [progress in the necessary requirements] the data do not yet appear to be sufficiently robust for the CGPM to adopt the revised SI at its 25th meeting”,[35] thus postponing the revision to the next meeting in 2018. Measurements accurate enough to meet the conditions were available in 2017 and the redefinition[36] was adopted at the 26th CGPM (13–16 November 2018).

Redefinition[edit]
The numerical values adopted by the CGPM[36] are identical to the published CODATA 2017 values.[37]

Following the successful 1983 redefinition of the metre in terms of an exact numerical value for the speed of light, the BIPM’s Consultative Committee for Units (CCU) recommended and the BIPM proposed that four further constants of nature should be defined to have exact values. These are:

The Planck constant h is exactly 6.62607015×10−34 joule-second (J⋅s).
The elementary charge e is exactly 1.602176634×10−19 coulomb (C).
The Boltzmann constant k is exactly 1.380649×10−23 joule per kelvin (J⋅K−1).
The Avogadro constant NA is exactly 6.02214076×1023 reciprocal mole (mol−1).
These constants are described in the 2006 version of the SI manual but in that version, the latter three are defined as “constants to be obtained by experiment” rather than as “defining constants”. The redefinition retains unchanged the numerical values associated with the following constants of nature:

The speed of light c is exactly 299792458 metres per second (m⋅s−1);
The ground state hyperfine structure transition frequency of the caesium-133 atom ΔνCs is exactly 9192631770 hertz (Hz);
The luminous efficacy Kcd of monochromatic radiation of frequency 540×1012 Hz (540 THz) – a frequency of green-colored light at approximately the peak sensitivity of the human eye – is exactly 683 lumens per watt (lm⋅W−1).
The seven definitions above are rewritten below with the derived units (joule, coulomb, hertz, lumen, and watt) expressed in terms of the seven base units: second, metre, kilogram, ampere, kelvin, mole, and candela, according to the 9th SI Brochure.[4] In the list that follows, the symbol sr stands for the dimensionless unit steradian.

ΔνCs = Δν(133Cs)hfs = 9192631770 s−1
c = 299792458 m⋅s−1
h = 6.62607015×10−34 kg⋅m2⋅s−1
e = 1.602176634×10−19 A⋅s
k = 1.380649×10−23 kg⋅m2⋅K−1⋅s−2
NA = 6.02214076×1023 mol−1
Kcd = 683 cd⋅sr⋅s3⋅kg−1⋅m−2
As part of the redefinition, the International Prototype of the Kilogram was retired and definitions of the kilogram, the ampere, and the kelvin were replaced. The definition of the mole was revised. These changes have the effect of redefining the SI base units, though the definitions of the SI derived units in terms of the base units remain the same.

Impact on base unit definitions[edit]
Following the CCU proposal, the texts of the definitions of all of the base units were either refined or rewritten, changing the emphasis from explicit-unit to explicit-constant-type definitions.[38] Explicit-unit-type definitions define a unit in terms of a specific example of that unit; for example, in 1324 Edward II defined the inch as being the length of three barleycorns[39] and since 1889 the kilogram has been defined as being the mass of the international Prototype of the kilogram. In explicit-constant definitions, a constant of nature is given a specified value and the definition of the unit emerges as a consequence; for example, in 1983, the speed of light was defined as exactly 299792458 metres per second. The length of the metre could be derived because the second had been independently defined. The previous[19] and 2019[4][37] definitions are given below.

Second[edit]
The new definition of the second is effectively the same as the previous one, the only difference being that the conditions under which the definition applies are more rigorously defined.

Previous definition: The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
2019 definition: The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the caesium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom,[40] to be 9192631770 when expressed in the unit Hz, which is equal to s−1.
The second may be expressed directly in terms of the defining constants:

1 s = 9192631770/ΔνCs.
Metre[edit]
The new definition of the metre is effectively the same as the previous one, the only difference being that the additional rigour in the definition of the second propagated to the metre.

Previous definition: The metre is the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second.
2019 definition: The metre, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299792458 when expressed in the unit m⋅s−1, where the second is defined in terms of the caesium frequency ΔνCs.
The metre may be expressed directly in terms of the defining constants:

1 m = 9192631770/299792458c/ΔνCs.
Kilogram[edit]

The definition of the kilogram changed fundamentally; the previous definition defined the kilogram as the mass of the international prototype of the kilogram, which is an artifact rather than a constant of nature.[42] The new definition relates the kilogram to, amongst things, the equivalent mass of the energy of a photon given its frequency, via the Planck constant.

Previous definition: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
2019 definition: The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.62607015×10−34 when expressed in the unit J⋅s, which is equal to kg⋅m2⋅s−1, where the metre and the second are defined in terms of c and ΔνCs.
For illustration, an earlier proposed redefinition that is equivalent to this 2019 definition is: “The kilogram is the mass of a body at rest whose equivalent energy equals the energy of a collection of photons whose frequencies sum to [1.356392489652×1050] hertz.”[43]

The kilogram may be expressed directly in terms of the defining constants:

1 kg = (299792458)2/(6.62607015×10−34)(9192631770)hΔνCs/c2.
Leading to

1 J⋅s = h/6.62607015×10−34
1 J = hΔνCs/(6.62607015×10−34)(9192631770)
1 W = h(ΔνCs)2/(6.62607015×10−34)(9192631770)2
1 N = 299792458/(6.62607015×10−34)(9192631770)2h(ΔνCs)2/c
Ampere[edit]
The definition of the ampere underwent a major revision. The previous definition, which is difficult to realise with high precision in practice, was replaced by a definition that is more intuitive and easier to realise.

Previous definition: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10−7 newton per metre of length.
2019 definition: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602176634×10−19 when expressed in the unit C, which is equal to A⋅s, where the second is defined in terms of ΔνCs.
The ampere may be expressed directly in terms of the defining constants as:

1 A = eΔνCs/(1.602176634×10−19)(9192631770).
For illustration, this is equivalent to defining one coulomb to be an exact specified multiple of the elementary charge.

1 C = e/1.602176634×10−19
Because the previous definition contains a reference to force, which has the dimensions MLT−2, it follows that in the previous SI the kilogram, metre, and second – the base units representing these dimensions – had to be defined before the ampere could be defined. Other consequences of the previous definition were that in SI the value of vacuum permeability (μ0) was fixed at exactly 4π×10−7 H⋅m−1.[44] Because the speed of light in vacuum (c) is also fixed, it followed from the relationship

{\displaystyle c^{2}={\frac {1}{\mu {0}\varepsilon {0}}}}

that the vacuum permittivity (ε0) had a fixed value, and from

{\displaystyle Z_{0}={\sqrt {\frac {\mu {0}}{\varepsilon {0}}}},}

that the impedance of free space (Z0) likewise had a fixed value.[45]

A consequence of the revised definition is that the ampere no longer depends on the definitions of the kilogram and the metre; it does, however, still depend on the definition of the second. In addition, the numerical values of the vacuum permeability, vacuum permittivity, and impedance of free space, which were exact before the redefinition, are subject to experimental error after the redefinition.[46] For example, the numerical value of the vacuum permeability has a relative uncertainty equal to that of the experimental value of the fine-structure constant \alpha .[47] The CODATA 2018 value for the relative standard uncertainty of \alpha is 1.5×10−10.[48] [Note 5]

The ampere definition leads to exact values for

1 V = 1.602176634×10−19/(6.62607015×10−34)(9192631770)hΔνCs/e
1 Wb = 1.602176634×10−19/6.62607015×10−34h/e
1 Ω = (1.602176634×10−19)2/6.62607015×10−34h/e2
Kelvin[edit]
The definition of the kelvin underwent a fundamental change. Rather than using the triple point of water to fix the temperature scale, the new definition uses the energy equivalent as given by Boltzmann’s equation.

Previous definition: The kelvin, unit of thermodynamic temperature, is 1/273.16 of the thermodynamic temperature of the triple point of water.
2019 definition: The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380649×10−23 when expressed in the unit J⋅K−1, which is equal to kg⋅m2⋅s−2⋅K−1, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.
The kelvin may be expressed directly in terms of the defining constants as:

1 K = 1.380649×10−23/(6.62607015×10−34)(9192631770)hΔνCs/k.
Mole[edit]

The previous definition of the mole linked it to the kilogram. The revised definition breaks that link by making a mole a specific number of entities of the substance in question.

Previous definition: The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
2019 definition:[7]:22 The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214076×1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1 and is called the Avogadro number.[7][49] The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particle or specified group of particles.
The mole may be expressed directly in terms of the defining constants as:

1 mol = 6.02214076×1023/NA.
One consequence of this change is that the previously defined relationship between the mass of the 12C atom, the dalton, the kilogram, and the Avogadro number is no longer valid. One of the following had to change:

The mass of a 12C atom is exactly 12 dalton.
The number of dalton in a gram is exactly the numerical value of the Avogadro number: (i.e., 1 g/Da = 1 mol ⋅ NA).
The wording of the 9th SI Brochure[4][Note 6] implies that the first statement remains valid, which means the second is no longer true. The molar mass constant, while still with great accuracy remaining 1 g/mol, is no longer exactly equal to that. Appendix 2 to the 9th SI Brochure states that “the molar mass of carbon 12, M(12C), is equal to 0.012 kg⋅mol−1 within a relative standard uncertainty equal to that of the recommended value of NAh at the time this Resolution was adopted, namely 4.5×10−10, and that in the future its value will be determined experimentally”,[50][51] which makes no reference to the dalton and is consistent with either statement.

Candela[edit]
The new definition of the candela is effectively the same as the previous definition as dependent on other base units, with the result that the redefinition of the kilogram and the additional rigour in the definitions of the second and metre propagate to the candela.

Previous definition: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 Hz and that has a radiant intensity in that direction of 1/683 watt per steradian.
2019 definition: The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540×1012 Hz, Kcd, to be 683 when expressed in the unit lm⋅W−1, which is equal to cd⋅sr⋅W−1, or cd⋅sr⋅kg−1⋅m−2⋅s3, where the kilogram, metre and second are defined in terms of h, c and ΔνCs.
1 cd = 1/683(6.62607015×10−34)(9192631770)2Kcdh(ΔνCs)2
Impact on reproducibility[edit]
All seven of the SI base units will be defined in terms of defined constants[Note 7] and universal physical constants.[Note 8][52] Seven constants are needed to define the seven base units but there is not a direct correspondence between each specific base unit and a specific constant; except the second and the mole, more than one of the seven constants contributes to the definition of any given base unit.

When the New SI was first designed, there were more than six suitable physical constants from which the designers could choose. For example, once length and time had been established, the universal gravitational constant G could, from a dimensional point of view, be used to define mass.[Note 9] In practice, G can only be measured with a relative uncertainty of the order of 10−5,[Note 10] which would have resulted in the upper limit of the kilogram’s reproducibility being around 10−5 whereas the current international prototype of the kilogram can be measured with a reproducibility of 1.2 × 10−8.[46] The physical constants were chosen on the basis of minimal uncertainty associated with measuring the constant and the degree of independence of the constant in respect of other constants that were being used. Although the BIPM has developed a standard mise en pratique (practical technique)[53] for each type of measurement, the mise en pratique used to make the measurement is not part of the measurement’s definition – it is merely an assurance that the measurement can be done without exceeding the specified maximum uncertainty.

Acceptance[edit]
Much of the work done by the CIPM is delegated to consultative committees. The CIPM Consultative Committee for Units (CCU) has made the proposed changes while other committees have examined the proposal in detail and have made recommendations regarding their acceptance by the CGPM in 2014. The consultative committees have laid down a number of criteria that must be met before they will support the CCU’s proposal, including:

For the redefinition of the kilogram, at least three separate experiments yielding values for the Planck constant having a relative expanded (95%) uncertainty of no more than 5×10−8 must be carried out and at least one of these values should be better than 2×10−8. Both the Kibble balance and the Avogadro project should be included in the experiments and any differences between these must be reconciled.[54][55]
For the redefinition of the kelvin, the relative uncertainty of the Boltzmann constant derived from two fundamentally different methods such as acoustic gas thermometry and dielectric constant gas thermometry must be better than 10−6, and these values must be corroborated by other measurements.[56]
As of March 2011, the International Avogadro Coordination (IAC) group had obtained an uncertainty of 3.0×10−8 and NIST had obtained an uncertainty of 3.6×10−8 in their measurements.[24] On 1 September 2012 the European Association of National Metrology Institutes (EURAMET) launched a formal project to reduce the relative difference between the Kibble balance and the silicon sphere approach to measuring the kilogram from (17±5)×10−8 to within 2×10−8.[57] As of March 2013 the proposed redefinition is known as the “New SI”[3] but Mohr, in a paper following the CGPM proposal but predating the formal CCU proposal, suggested that because the proposed system makes use of atomic scale phenomena rather than macroscopic phenomena, it should be called the “Quantum SI System”.[58]

As of the 2014 CODATA-recommended values of the fundamental physical constants published in 2016 using data collected until the end of 2014, all measurements met the CGPM’s requirements, and the redefinition and the next CGPM quadrennial meeting in late 2018 could now proceed.[59][60]

On 20 October 2017, the 106th meeting of the International Committee for Weights and Measures (CIPM) formally accepted a revised Draft Resolution A, calling for the redefinition of the SI, to be voted on at the 26th CGPM,[7]:17–23 The same day, in response to the CIPM’s endorsement of the final values,[7]:22 the CODATA Task Group on Fundamental Constants published its 2017 recommended values for the four constants with uncertainties and proposed numerical values for the redefinition without uncertainty.[37] The vote, which was held on 16 November 2018 at the 26th GCPM, was unanimous; all attending national representatives voted in favour of the revised proposal.

The new definitions became effective on 20 May 2019.[61]

Concerns[edit]
In 2010, Marcus Foster of the Commonwealth Scientific and Industrial Research Organisation (CSIRO) published a wide-ranging critique of SI; he raised numerous issues ranging from basic issues such as the absence of the symbol “Ω” (Omega, for the ohm) from most Western computer keyboards to abstract issues such as inadequate formalism in the metrological concepts on which SI is based. The changes proposed in the New SI only addressed problems with the definition of the base units, including new definitions of the candela and the mole – units Foster argued are not true base units. Other issues raised by Foster fell outside the scope of the proposal.[62]

Explicit-unit and explicit-constant definitions[edit]
Concerns have been expressed that the use of explicit-constant definitions of the unit being defined that are not related to an example of its quantity will have many adverse effects.[63] Although this criticism applies to the linking of the kilogram to the Planck constant h via a route that requires a knowledge of both special relativity and quantum mechanics,[64] it does not apply to the definition of the ampere, which is closer to an example of its quantity than is the previous definition.[65] Some observers have welcomed the change to base the definition of electric current on the charge of the electron rather than the previous definition of a force between two parallel, current-carrying wires; because the nature of the electromagnetic interaction between two bodies is somewhat different at the quantum electrodynamics level than at classical electrodynamic levels, it is considered inappropriate to use classical electrodynamics to define quantities that exist at quantum electrodynamic levels.[46]

Mass and the Avogadro constant[edit]
When the scale of the divergence between the IPK and national kilogram prototypes was reported in 2005, a debate began about whether the kilogram should be defined in terms of the mass of the silicon-28 atom or by using the Kibble balance. The mass of a silicon atom could be determined using the Avogadro project and using the Avogadro number, it could be linked directly to the kilogram.[66] Concerns that the authors of the proposal had failed to address the impact of breaking the link between the mole, kilogram, dalton, and the Avogadro constant (NA) have also been expressed.[Note 11] This direct link has caused many to argue that the mole is not a true physical unit but, according to the Swedish philosopher Johansson, a “scaling factor”.[62][67]

The 8th edition of the SI Brochure defines the dalton in terms of the mass of an atom of 12C.[68] It defines the Avogadro constant in terms of this mass and the kilogram, making it determined by experiment. The proposal fixes the Avogadro constant and the 9th SI Brochure[4] retains the definition of dalton in terms of 12C, with the effect that the link between the dalton and the kilogram will be broken.[69][70]

In 1993, the International Union of Pure and Applied Chemistry (IUPAC) approved the use of the dalton as an alternative to the unified atomic mass unit with the qualification that the CGPM had not given its approval.[71] This approval has since been given.[72] Following the proposal to redefine the mole by fixing the value of the Avogadro constant, Brian Leonard of the University of Akron, writing in Metrologia, proposed that the dalton (Da) be redefined such that NA = (g/Da) mol−1, but that the unified atomic mass unit (mu) retain its current definition based on the mass of 12C, ceasing to exactly equal the dalton. This would result in the dalton and the atomic mass unit potentially differing from each other with a relative uncertainty of the order of 10−10.[73] The 9th SI Brochure, however, defines both the dalton (Da) and the unified atomic mass unit (u) as exactly 1/12 of the mass of a free carbon-12 atom and not in relation to the kilogram,[4] with the effect that the above equation will be inexact.

Temperature[edit]
Different temperature ranges need different measurement methods. Room temperature can be measured by means of expansion and contraction of a liquid in a thermometer but high temperatures are often associated with colour of blackbody radiation. Wojciech T. Chyla, approaching the structure of SI from a philosophical point of view in the Journal of the Polish Physical Society, argued that temperature is not a real base unit but is an average of the thermal energies of the individual particles that comprise the body concerned.[46] He noted that in many theoretical papers, temperature is represented by the quantities Θ or β where

{\displaystyle \Theta =kT;\ \ \ \beta ={1 \over kT}}

and k is the Boltzmann constant. Chyla acknowledged, however, that in the macroscopic world, temperature plays the role of a base unit because much of the theory of thermodynamics is based on temperature.[46]

The Consultative Committee for Thermometry, part of the International Committee for Weights and Measures, publishes a mise en pratique (practical technique), last updated in 1990, for measuring temperature. At very low and at very high temperatures it often links energy to temperature via the Boltzmann constant.[74][75]

Luminous intensity[edit]
Foster argued that “luminous intensity [the candela] is not a physical quantity, but a photobiological quantity that exists in human perception”, questioning whether the candela should be a base unit.[62] Before the 1979 decision to define photometric units in terms of luminous flux (power) rather than luminous intensities of standard light sources, there was already doubt whether there should be still a separate base unit for photometry. Furthermore, there was unanimous agreement that the lumen was now more fundamental than the candela. However, for the sake of continuity the candela was kept as base unit.[76]

See also[edit]

International System of Units – Modern form of the metric system

International Vocabulary of Metrology

Physical constant – Universal and unchanging physical quantity

SI base unit – One of the seven units of measurement that define the Metric System

2005–2019 definitions of the SI base units

Non-SI units mentioned in the SI – Unit accepted for use in the International System of Units – changes associated with the 2019 redefinition

Notes[edit]

^ The metre was redefined again in 1983 by fixing the value of the speed of light in vacuum. That definition went unaltered in 2019 and remains in effect today.

^ The dalton is not defined in the formal proposal to be voted upon by the CGPM, only in the 9th edition of the SI Brochure.

^ Prototype No. 8(41) was accidentally stamped with the number 41, but its accessories carry the proper number 8. Since there is no prototype marked 8, this prototype is referred to as 8(41).

^ In particular the CIPM was to prepare a detailed mise en pratique for each of the new definitions of the kilogram, ampere, kelvin and mole set by the 23rd CGPM.[29]

^ A note should be added on the definition of magnetic field unit (tesla). When the ampere was defined as the current that when flows in two long parallel wires separated by 1 m causes a force of 2×10−7 N/m on each other, there was also another definition: the magnetic field at the location of each of the wires in this configuration was defined to be 2×10−7 T. Namely 1 T is the intensity of the magnetic field B that causes a force of 1 N/m on a wire carrying a current of 1 A. The number 2×10−7 was written also as μ0/2π. This arbitrary definition is what made the value of μ0 to be exactly 4π×10−7. Accordingly, the magnetic field near a wire carrying current is given by B = μ0I/2πr. Now, with the new definition of the ampere, the definition of the tesla is also affected. More specifically, the definition relying on the force of a magnetic field on a wire carrying current is maintained (F = I⋅B⋅l) while, as mentioned above, μ0 can no longer be exactly 4π×10−7 and has to be measured experimentally. The value of the vacuum permittivity ε0 = 1/(μ0c2) is also affected accordingly. The Maxwell equations will ‘see to it’ that the electrostatic force between two point charges will be F = 1/(4πε0)(q1q2)/r2.

^ A footnote in Table 8 on non-SI units states: “The dalton (Da) and the unified atomic mass unit (u) are alternative names (and symbols) for the same unit, equal to 1/12 of the mass of a free carbon 12 atom, at rest and in its ground state.”

^ Though the three quantities temperature, luminous intensity and amount of substance may be regarded from a fundamental physical perspective as derived quantities, these are perceptually independent quantities and have conversion constants defined that relate the historically defined units to the underlying physics.

^ The definition of the candela is atypical within the base units; translating physical measurements of spectral intensity into units of candela also requires a model of the response of the human eye to different wavelengths of light known as the luminosity function and denoted by V(λ), a function that is determined by the International Commission on Illumination (CIE).

^ The dimensions of G are L3M−1T−2 so once standards have been established for length and for time, mass can, in theory, be deduced from G. When fundamental constants as relations between these three units are set, the units can be deduced from a combination of these constants; for example, as a linear combination of Planck units.

^ The following terms are defined in International vocabulary of metrology – Basic and general concepts and associated terms Archived 17 March 2017 at the Wayback Machine:

measurement reproducibility – definition 2.25

standard measurement uncertainty – definition 2.30

relative standard measurement uncertainty – definition 2.32

^ The two quantities of the Avogadro constant NA and the Avogadro number NN are numerically identical but while NA has the unit mol−1, NN is a pure number.

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