Editing Base unit of measurement (section)

== Natural units ==
{{main|Natural units}}
A set of base dimensions of quantity is a minimal set of units such that every physical quantity can be expressed in terms of this set. The traditional base dimensions are [[mass]], [[length]], [[time]], [[electric charge|charge]], and [[temperature]], but in principle, other base quantities could be used.  [[Electric current]] could be used instead of charge or [[speed]] could be used instead of length.  Some physicists have not recognized temperature as a base dimension since it simply expresses the energy per particle per degree of freedom which can be expressed in terms of energy (or mass, length, and time).<ref>{{Cite journal |last=Quincey |first=Paul |last2=Brown |first2=Richard J C |date=2017-08-01 |title=A clearer approach for defining unit systems |url=https://iopscience.iop.org/article/10.1088/1681-7575/aa7160 |journal=Metrologia |volume=54 |issue=4 |pages=454–460 |doi=10.1088/1681-7575/aa7160 |issn=0026-1394|arxiv=1705.03765 }}</ref>  Duff argues that only dimensionless values have physical meaning and all dimensional units are human constructs.<ref name="hep-th1412.2040">{{cite journal|author=Michael Duff|title=How fundamental are fundamental constants?|arxiv=1412.2040|author-link=Michael Duff (physicist)|doi=10.1080/00107514.2014.980093|url=https://www.tandfonline.com/doi/abs/10.1080/00107514.2014.980093|url-access=subscription|journal=Contemporary Physics|volume=56|issue=1|pages=35–47|year=2015|bibcode=2015ConPh..56...35D|hdl=10044/1/68485|s2cid=118347723|access-date=2020-04-03|archive-date=2021-11-22|archive-url=https://web.archive.org/web/20211122065250/https://www.tandfonline.com/doi/abs/10.1080/00107514.2014.980093|url-status=live}}</ref>

There are other relationships between physical quantities that can be expressed by means of fundamental constants, and to some extent it is an arbitrary decision whether to retain the fundamental constant as a quantity with dimensions or simply to define it as unity or a fixed [[dimensionless quantity|dimensionless number]], and reduce the number of explicit base quantities by one.  The [[ontological]] issue is whether these fundamental constants really exist as dimensional or dimensionless quantities.  This is equivalent to treating length as the same as time or understanding electric charge as a combination of quantities of mass, length, and time which may seem less natural than thinking of temperature as measuring the same material as energy (which is expressible in terms of mass, length, and time).

For instance, time and distance are related to each other by the [[speed of light]], ''c'', which is a fundamental constant. It is possible to use this relationship to eliminate either the base unit of time or that of distance. Similar considerations apply to the [[Planck constant]], ''h'', which relates energy (with dimension expressible in terms of mass, length and time) to frequency (with dimension expressible in terms of time). In theoretical physics it is customary to use such units (natural units) in which {{nowrap|1=''c'' = 1}} and {{nowrap|1=''ħ'' = 1}}.  A similar choice can be applied to the [[vacuum permittivity]], ''ε''<sub>0</sub>.
* One could eliminate either the metre or the second by setting ''c'' to unity (or to any other fixed dimensionless number).
* One could then eliminate the kilogram by setting ''ħ'' to a dimensionless number.
* One could eliminate the ampere by setting either the vacuum permittivity ''ε''<sub>0</sub> or the [[elementary charge]] ''e'' to a dimensionless number.
* One could eliminate the mole as a base unit by setting the [[Avogadro constant]] ''N''{{sub|A}} to 1.  This is natural as it is a technical scaling constant.
* One could eliminate the kelvin as it can be argued that temperature simply expresses the energy per particle per [[degree of freedom]], which can be expressed in terms of energy (or mass, length, and time). Another way of saying this is that the [[Boltzmann constant]] ''k''<sub>B</sub> is a technical scaling constant and could be set to a fixed dimensionless number.
* Similarly, one could eliminate the candela, as that is defined in terms of other physical quantities via a technical scaling constant, ''K''{{sub|cd}}.
* That leaves one base dimension and an associated base unit, but there are several fundamental constants left to eliminate that too – for instance, one could use ''G'', the [[gravitational constant]], ''m''<sub>e</sub>, the [[electron rest mass]], or Λ, the [[cosmological constant]].

The preferred choices vary by the field in physics.  Using natural units leaves every physical quantity expressed as a dimensionless number, which is noted by physicists disputing the existence of incompatible base quantities.<ref name="hep-th1412.2040" /><ref>{{cite book|last=Jackson|first=John David|title=Classical Electrodynamics|year=1998|publisher=John Wiley and Sons|pages=775|chapter-url=http://homepages.spa.umn.edu/~kd/Ast8001/em_units.pdf|access-date=13 January 2014|chapter=Appendix on Units and Dimensions|quote=The ''arbitrariness'' in the number of fundamental units and in the dimensions of any physical quantity in terms of those units has been emphasized by Abraham, Plank, Bridgman, Birge, and others.|archive-date=13 January 2014|archive-url=https://web.archive.org/web/20140113162927/http://homepages.spa.umn.edu/~kd/Ast8001/em_units.pdf|url-status=dead}}</ref><ref>{{cite journal|last=Birge|first=Raymond T.|title=On the establishment of fundamental and derived units, with special reference to electric units. Part I.|journal=American Journal of Physics|year=1935|volume=3|issue=3|pages=102–109|url=http://www.brynmawr.edu/physics/DJCross/docs/files/birge2.pdf|access-date=13 January 2014|quote=Because, however, of the arbitrary character of dimensions, as presented so ably by Bridgman, the choice and number of fundamental units are arbitrary.|bibcode=1935AmJPh...3..102B|doi=10.1119/1.1992945|archive-url=https://web.archive.org/web/20150923221228/http://www.brynmawr.edu/physics/DJCross/docs/files/birge2.pdf|archive-date=23 September 2015|url-status=dead}}</ref>