View source for Physical constant

{{short description|Universal and unchanging physical quantity}}

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.

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]] ''ε''<sub>0</sub>, and the [[elementary charge]] ''e''. Physical constants can take many [[dimensional analysis|dimensional]] forms: the speed of light signifies a maximum [[speed]] for any object and its [[Dimensional analysis|dimension]] is [[length]] divided by [[time]]; while the [[proton-to-electron mass ratio]] is [[dimensionless]].

The term "fundamental physical constant" is sometimes used to refer to universal-but-dimensioned physical constants such as those mentioned above.<ref>{{cite web |url=http://physics.nist.gov/cuu/Constants/ |title=Fundamental Physical Constants from NIST |access-date=2016-01-14 |url-status=live |archive-url=https://web.archive.org/web/20160113222630/http://physics.nist.gov/cuu/Constants/ |archive-date=2016-01-13 }} NIST</ref> Increasingly, however, physicists reserve the expression for the narrower case of [[dimensionless physical constant|dimensionless universal physical constant]]s, such as the [[fine-structure constant]] ''α'', which characterizes the strength of the [[electromagnetic interaction]].

Physical constants, as discussed here, should not be confused with [[empirical constant]]s, which are [[coefficient]]s or [[parameter]]s assumed to be constant in a given context without being fundamental.<ref name="ISO80000-1">{{cite web | website=iso.org |title=ISO 80000-1:2022 Quantities and units — Part 1: General | url=https://www.iso.org/obp/ui/#iso:std:iso:80000:-1:ed-2:v1:en | access-date=2023-08-31}}</ref> Examples include the [[characteristic time]], [[characteristic length]], or [[characteristic number (physics)|characteristic number]] (dimensionless) of a given system, or [[material constant]]s (e.g., [[Madelung constant]], [[Electrical resistivity and conductivity|electrical resistivity]], and [[heat capacity]]) of a particular material or substance.<!-- and because even if "in principle" they could be derived from the Standard Model, they cannot be in practice and still have to be measured-->

== Characteristics ==
Physical constants are parameters in a physical theory that cannot be explained by that theory. This may be due to the apparent fundamental nature of the constant or due to limitations in the theory. Consequently, physical constants must be measured experimentally.<ref name=UzanVaryingConstants/>{{rp|9}}

The set of parameters considered physical constants change as physical models change and how fundamental they appear can change. For example, <math>c</math>, the speed of light, was originally considered a property of light, a specific system. The discovery and verification of Maxwell's equations connected the same quantity with an entire system, [[electromagnetism]]. When the theory of [[special relativity]] emerged, the quantity came to be understood as the basis of causality.<ref name=UzanVaryingConstants/> The speed of light is so fundamental it now defines the international [[metre |unit of length]].

== Relationship to units ==
=== Numerical values ===
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 {{val|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 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.
[[File:SI Illustration Base Units and Constants Colour Full.svg|thumb|Illustration of the SI system of units, with base units and defining constants used to define them: '''s''' – the frequency of the caesium transition for the '''[[second]]''', '''kg''' – the mass of the IPK for the '''[[kilogram]]''', '''mol''' – the mass in kilograms of an atom of carbon 12 for the '''[[Mole (unit)|mole]]''', '''cd''' – the sensitivity of the human eye for the '''[[candela]]''', '''K''' – the Boltzmann constant for the '''[[kelvin]]''', '''A''' – the magnetic permeability of vacuum for the '''[[ampere]]''', '''m''' – the speed of light for the '''[[metre]]'''.]]

=== International System of Units ===
{{Main | SI base unit}}

Since [[2019 revision of the SI|2019 revision]], all of the units in the [[International System of Units]] have been defined in terms of fixed natural phenomena, including three fundamental constants: the speed of light in vacuum, ''c''; the Planck constant, ''h''; and the [[elementary charge]], ''e''.<ref name="SI9th">{{SIbrochure9th}}.</ref>{{rp|128}}

As a result of the new definitions, an SI unit like the [[kilogram]] can be written in terms of fundamental constants and one experimentally measured constant, Δ''ν''<sub>Cs</sub>:<ref name=SI9th/>{{rp|131}}
: 1&nbsp;kg = {{math|{{sfrac|({{val|299792458}}){{sup|2}}|({{val|6.62607015|e=-34}})({{val|9192631770}})}}{{sfrac|{{gaps|''h''|Δ''ν''<sub>Cs</sub>}}|''c''{{sup|2}}}}}}.

=== Natural units ===
{{main article |Natural units}}
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 [[speed of light|''c'']], [[gravitational constant|''G'']], [[reduced Planck constant|''ħ'']], and [[Boltzmann constant|''k''<sub>B</sub>]] give conveniently sized measurement units for use in studies of [[quantum gravity]], and [[atomic units]], constructed from [[reduced Planck constant|''ħ'']], [[electron rest mass|''m''<sub>e</sub>]], [[elementary charge|''e'']] and 4''π''[[vacuum permittivity|''ε''<sub>0</sub>]] give convenient units in [[atomic physics]]. The choice of constants used leads to widely varying quantities.

== Number of fundamental constants ==
The number of fundamental physical constants depends on the [[physical theory]] accepted as "fundamental". Currently, <!--"As of the later 20th to 21st century"--> 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<ref name=UzanVaryingConstants/> lists 22 "fundamental constants of our standard model" 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 [[Cabibbo–Kobayashi–Maskawa matrix|quark mixing matrix]], 
* 3 coupling constants for the [[gauge group]]s [[Standard Model (mathematical formulation)|SU(3) × SU(2) × U(1)]] (or equivalently, two coupling constants and the [[Weinberg angle]]),
* a phase for the [[QCD vacuum|quantum chromodynamics vacuum]].
The number of 19 independent fundamental physical constants is subject to change under possible [[Physics beyond the Standard Model|extensions of the Standard Model]], notably by the introduction of [[neutrino mass]] (equivalent to seven additional constants, i.e. 3 Yukawa couplings and 4 [[Pontecorvo–Maki–Nakagawa–Sakata matrix|lepton mixing]] parameters).<ref name=UzanVaryingConstants>{{cite journal | url= | doi=10.12942/lrr-2011-2| title=Varying Constants, Gravitation and Cosmology| journal=Living Reviews in Relativity| volume=14| year=2011| last1=Uzan| first1=Jean-Philippe| issue=1| pages=2| doi-access=free| pmid=28179829| pmc=5256069| arxiv=1009.5514| bibcode=2011LRR....14....2U}}</ref>

The discovery of variability in any of these constants would be equivalent to the discovery of "[[new physics]]".<ref name=UzanVaryingConstants/>

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 {{harvnb|Lévy-Leblond|1977}}, not all physical constants are of the same importance, with some having a deeper role than others.{{harvnb|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 [[electromagnetism|electromagnetic phenomena]]) with the development of [[classical electromagnetism]], and finally a class C constant with the discovery of [[special relativity]].<ref>{{cite journal |last1=Lévy-Leblond |first1=J. |title=On the conceptual nature of the physical constants |journal=La Rivista del Nuovo Cimento |series=Series 2|date=1977 |volume=7 |issue=2 |pages=187–214|doi=10.1007/bf02748049|bibcode=1977NCimR...7..187L |s2cid=121022139 }}{{cite book|last=Lévy-Leblond |first=J.-M. |chapter=The importance of being (a) Constant |editor1-last=Toraldo di Francia |editor1-first=G. |title=Problems in the Foundations of Physics, Proceedings of the International School of Physics 'Enrico Fermi' Course LXXII, Varenna, Italy, July 25 – August 6, 1977 |pages=237–263 |publisher=NorthHolland |location=New York |date=1979}}</ref>

== Tests on time-independence ==
{{main article|Time-variation of fundamental constants}}
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<sup>−17</sup> per year (as of 2008).<ref>
{{cite journal |author=Rosenband |first=T. |display-authors=etal |year=2008 |title=Frequency Ratio of Al<sup>+</sup> and Hg<sup>+</sup> Single-Ion Optical Clocks; Metrology at the 17th Decimal Place |url=https://zenodo.org/record/1230892 |journal=[[Science (journal)|Science]] |volume=319 |issue=5871 |pages=1808–12 |bibcode=2008Sci...319.1808R |doi=10.1126/science.1154622 |pmid=18323415 |s2cid=206511320 |doi-access=free}}</ref>

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.<ref name="anderson2015">{{citation |author1=Anderson |first=J. D. |title=Measurements of Newton's gravitational constant and the length of day |date=April 2015 |journal=EPL |volume=110 |issue=1 |pages=10002 |arxiv=1504.06604 |bibcode=2015EL....11010002A |doi=10.1209/0295-5075/110/10002 |s2cid=119293843 |author2=Schubert |first2=G. |author3=Trimble |first3=V. |author4=Feldman |first4=M. R.}}</ref> 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<sup>−10</sup> per year for the gravitational constant over the last nine billion years.<ref>{{citation |author1=Mould |first=J. |title=Constraining a Possible Variation of G with Type Ia Supernovae |date=2014-04-10 |journal=Publications of the Astronomical Society of Australia |volume=31 |pages=e015 |arxiv=1402.1534 |bibcode=2014PASA...31...15M |doi=10.1017/pasa.2014.9 |s2cid=119292899 |author2=Uddin |first2=S. A.}}.</ref>

Similarly, an upper bound of the change in the [[proton-to-electron mass ratio]] has been placed at 10<sup>−7</sup> over a period of 7 billion years (or 10<sup>−16</sup> per year) in a 2012 study based on the observation of [[methanol]] in a distant galaxy.<ref name="Science-20121213">{{cite journal |last1=Bagdonaite |first1=Julija |last2=Jansen |first2=Paul |last3=Henkel |first3=Christian |last4=Bethlem |first4=Hendrick L. |last5=Menten |first5=Karl M. |last6=Ubachs |first6=Wim |title=A Stringent Limit on a Drifting Proton-to-Electron Mass Ratio from Alcohol in the Early Universe |date=December 13, 2012 |journal=[[Science (journal)|Science]] |doi=10.1126/science.1224898 |bibcode = 2013Sci...339...46B |volume=339 |issue=6115 |pages=46–48 |pmid=23239626|hdl=1871/39591 |s2cid=716087 |url=https://research.vu.nl/ws/files/668474/Science-2013-Bagdonaite-46-8.pdf }}</ref><ref name="Space-20121213">{{cite web |last=Moskowitz |first=Clara |title=Phew! Universe's Constant Has Stayed Constant |url=http://www.space.com/18894-galaxy-alcohol-fundamental-constant.html |date=December 13, 2012 |publisher=[[Space.com]] |access-date=December 14, 2012 |url-status=live |archive-url=https://web.archive.org/web/20121214081926/http://www.space.com/18894-galaxy-alcohol-fundamental-constant.html |archive-date=December 14, 2012 }}</ref>

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.<ref name="hep-th1412.2040">{{cite journal|first=Michael |last=Duff |title=How fundamental are fundamental constants?|arxiv=1412.2040|doi=10.1080/00107514.2014.980093|author-link=Michael Duff (physicist)|url=https://www.tandfonline.com/doi/abs/10.1080/00107514.2014.980093|journal=Contemporary Physics|volume=56|issue=1|pages=35–47|year=2015|bibcode=2015ConPh..56...35D|hdl=10044/1/68485 |s2cid=118347723 }}</ref><ref>{{cite arXiv |eprint=hep-th/0208093 |first1=Michael J. |last1=Duff |title=Comment on time-variation of fundamental constants |date=13 August 2002}}</ref><ref>{{cite journal |last1=Duff |first1=M. J. |last2=Okun |first2=L. B. |last3=Veneziano |first3=G. |title=Trialogue on the number of fundamental constants |journal=Journal of High Energy Physics |date=2002 |volume=2002 |issue= 3|pages=023 |arxiv=physics/0110060 |bibcode=2002JHEP...03..023D |doi=10.1088/1126-6708/2002/03/023|s2cid=15806354 }}</ref>

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 [[variable speed of light|"change" in the speed of light]] ''c'' would be meaningless if accompanied by a corresponding change in the elementary charge ''e'' so that the expression {{math|''e''<sup>2</sup>/(4π''ε''<sub>0</sub>''ħc'')}} (the fine-structure constant) remained unchanged.<ref>{{citation |last=Barrow |first=John D. |title=The Constants of Nature; From Alpha to Omega – The Numbers that Encode the Deepest Secrets of the Universe |year=2002 |url=https://archive.org/details/constantsofnatur0000barr |publisher=Pantheon Books |isbn=978-0-375-42221-8 |author-link=John D. Barrow |url-access=registration}}.</ref>

== Dimensionless physical constants ==
Any [[ratio]] between physical constants of the same dimensions results in a [[dimensionless physical constant]], for example, the [[proton-to-electron mass ratio]]. 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 and uncertainty 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.<ref>
{{cite book |author=Eddington |first=A. S. |title=The World of Mathematics |publisher=[[Simon & Schuster]] |year=1956 |editor=J.R. Newman |volume=2 |pages=1074–1093 |chapter=The Constants of Nature}}</ref> 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.<ref>
{{cite journal |author=Kragh |first=H. |year=2003 |title=Magic Number: A Partial History of the Fine-Structure Constant |journal=[[Archive for History of Exact Sciences]] |volume=57 |issue=5 |pages=395–431 |doi=10.1007/s00407-002-0065-7 |s2cid=118031104}}</ref>

== Fine-tuned universe ==
{{Main article|Fine-tuned universe|Anthropic principle}}
Some physicists have explored the notion that if the [[dimensionless physical constant]]s 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 universe|fine-tuned]] for intelligent life.<ref>{{cite book |last= Leslie|first= John|date= 1998|title= Modern Cosmology & Philosophy|location= University of Michigan|publisher= Prometheus Books|isbn= 1573922501}}</ref> 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 [[intelligent design|divine creator]] (the apparent fine-tuning is actual and intentional), or that the universe is one universe of many in a [[multiverse]] (e.g. the [[many-worlds interpretation]] of [[quantum mechanics]]), or even that, [[It from bit|if information is an innate property of the universe]] and logically inseparable from consciousness, a universe without the capacity for conscious beings cannot exist.

== Table of physical constants ==
{{main|List of physical constants}}

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

{| class="wikitable sortable"
|-
! Quantity
! Symbol
! Value<ref name="concise">The values are given in the so-called ''concise form'', where the number in parentheses indicates the ''[[standard uncertainty]]'' referred to the [[least significant digit]]s of the value.</ref>
! <small>Relative<br>standard<br>uncertainty</small>
|-
| [[elementary charge]]
| <math>e</math>
| {{physconst|e}}
| {{physconst|e|runc=yes|ref=no}}
|-
| [[gravitational constant|Newtonian constant of gravitation]]
| <math>G</math>
| {{physconst|G}}
| {{physconst|G|runc=yes|ref=no}}
|-
| [[Planck constant]]
| <math>h</math>
| {{physconst|h}}
| {{physconst|h|runc=yes|ref=no}}
|-
| [[speed of light|speed of light in vacuum]]
| <math>c</math>
| {{physconst|c}}
| {{physconst|c|runc=yes|ref=no}}
|- 
| [[vacuum permittivity|vacuum electric permittivity]]
| <math> \varepsilon_0</math>
| {{physconst|eps0}}
| {{physconst|eps0|runc=yes|ref=no}}
|-
| [[vacuum permeability|vacuum magnetic permeability]]
| <math> \mu_0 </math>
| {{physconst|mu0}}
| {{physconst|mu0|runc=yes|ref=no}}
|-
| [[electron|electron mass]]
| <math>m_{\mathrm{e}} </math>
| {{physconst|me}}
| {{physconst|me|runc=yes|ref=no}}
|-
| [[fine-structure constant]]
| <math>\alpha = e^2 / 2 \varepsilon_0 h c </math>
| {{physconst|alpha}}
| {{physconst|alpha|runc=yes|ref=no}}
|-
| [[Josephson constant]]
| <math>K_{\mathrm{J}} = 2 e / h </math>
| {{physconst|KJ}}
| {{physconst|KJ|runc=yes|ref=no}}
|-
| [[Rydberg constant]]
| <math>R_\infin = \alpha^2 m_{\mathrm{e}} c / 2 h </math>
| {{physconst|Rinf}}
| {{physconst|Rinf|runc=yes|ref=no}}
|-
| [[von Klitzing constant]]
| <math>R_{\mathrm{K}} = h / e^2 </math>
| {{physconst|RK}}
| {{physconst|RK|runc=yes|ref=no}}
|-
|}

== See also ==
* [[List of common physics notations]]
* [[List of mathematical constants]]
* [[List of physical constants]]
* [[Mathematical constant]]

== References ==
{{reflist}}

== External links ==
{{Commons category|Physical constants}}
* [http://www.sixtysymbols.com/# Sixty Symbols], University of Nottingham
* [http://goldbook.iupac.org/list_goldbook_phys_constants_defs.html IUPAC – Gold Book]

{{Authority control}}

[[Category:Physical constants| ]]