Units of Measurement |

**In General**
> s.a. constants; Measurement [metrology];
Planck Constant [including Planck units].

* __Idea__: Now most of them
are defined using quantum principles.

* __SI__: There are seven base
units of the SI, the second, meter, kilogram, ampere, kelvin, mole and candela;
From the Nov 2018 decision at the General Conference on Weights and Measures
in Versailles, effective 29 May 2019 all seven will be defined in terms of
physical constants.

@ __General__: Szekeres IJTP(78) [dimensional analysis and fundamental units, axiomatization];
Taylor PT(89)aug;
Hebra 03 [history, r pw(04)mar];
Crease pw(09)sep [origin of some unusual units];
Kershaw HSNS(13) [electromagnetic standards of length];
Hehl & Lämmerzahl a1810-proc [general theory].

@ __SI__: Mills PRS(09),
Foster PRS(09)
[conventions for writing values of quantities];
Aubrecht TPT(12) [changes coming];
Jayson AJP(14)jan
[history, telegraphy and the emergence of the SI];
Newell PT(14);
Mohr & Phillips Metr(15)-a1409 [dimensionless (angular and counting) units];
Pavese a1601 [role of fundamental constants];
Mari et al a1604-conf
[the New SI, conceptual roadmap for setting up a system of units];
Knotts et al TPT(17),
Lopac & Hrupec TPT(19) [the New SI];
news pt(18)nov,
Phy(19)mar,
APS(19)may,
Martín-Delgado a2005 [revamped system based on constants];
news sn(20)apr [the US has resisted for more than 50 years].

@ __Systems of fundamental units__:
NIST reference site;
Jancewicz CEJP(04) [geometrical];
Capitaine & Guinot a0812-proc [astronomical units];
Kitano JMP(13) [mathematical structure];
> s.a. constants [suppression and restoration].

@ __And electromagnetism__:
Desloge AJP(94)jul [conversions];
Carron a1506,
Jayson AJP(14)jan-a1512 [historical development of unit systems].

@ __And fundamental physics__:
Bernal et al FP(02) [?];
Buzcyna et al G&C(11)-a1006 [Stoney units and Planck units];
Sheykin & Manida a2005 [fully universal].

@ __Related topics__: news lat(10)jul ["hella" as proposed prefix for 10^{27}];
Crease pw(10)jul
[Joseph Dombey's misfortunes and the US system].

> __Online resources__:
Bureau International des Poids et Mesures site
and possible future changes;
Internet Encyclopedia of Science pages.

Prefixes for Units (see also Wikipedia page) | |||||

symbol |
prefix |
value |
symbol |
prefix |
value |

d | deci- | 10^{–1} |
da | deca- | 10 |

c | centi- | 10^{–2} |
h | hecto- | 10^{2} |

m | milli- | 10^{–3} |
k | kilo- | 10^{3} |

μ | micro- | 10^{–6} |
M | mega- | 10^{6} |

n | nano- | 10^{–9} |
G | giga- | 10^{9} |

p | pico- | 10^{–12} |
T | tera- | 10^{12} |

f | femto- | 10^{–15} |
P | peta- | 10^{15} |

a | atto- | 10^{–18} |
E | exa- | 10^{18} |

z | zepto- | 10^{–21} |
Z | zetta- | 10^{21} |

y | yacto- | 10^{–24} |
Y | yotta- | 10^{24} |

**Length**

* __Meter__: 1791, defined as
one 10 millionth of the distance from the North Pole to the Equator, along
the meridian through Paris; 1889?, the length of a platinum-iridium rod at the
BIPM (Bureau International des Poids et Mesures) at Sèvres; Now defined
using the speed of light as the distance light travels in 1/299,792,458 of a
second [@ Bates].

* __Conversion__: 1 ly
= 9.461 × 10^{15} m (10 trillion km)
= 6.324 × 10^{4} au;
1 pc = 3.262 ly = 3.086 × 10^{16} m;
1 au = 1.496 × 10^{11} m.

@ __General references__:
Agnoli & D'Agostini phy/04 [origin of meter];
Schücker a0810 [1983 farewell to Sèvres meter].

@ __Related units__: in Wheeler & Ford 98, p24 [the barn, term introduced by Fermi];
Zois a1203-conf [towards an alternative definition for the meter].

**Time**

* __Second__: Originally a
definite fraction of the period of the Earth's orbit in 1900; Now defined
as 9,192,631,770 times the period for the transition between the two hyperfine
levels of the ground state of ^{133}Cs.

@ __References__:
Tal PhSc(11) [measurement accuracy];
Middelmann et al PRL(12) [advances in optical strontium clocks,
candidates for a new definition of the second].

**Mass**

* __Kilogram__: 1889, defined
as the mass of a piece of Pt-iridium at Sèvres, "Le Grand K";
2012, The only fundamental unit still defined using a physical artifact, although
new definitions have been advocated, and an agreement appears to be near; 2018,
Agreement on a new definition based on *h*, effective 20 May 2019.

* __Conversion__:
1 eV/*c*^{2} = 1.8 × 10^{−36} kg,
or 1 kg = 5.6 × 10^{35} eV/*c*^{2}.

@ __General references__:
news dm(11)nov [prototype metal cylinder loses 50 micrograms].

@ __Redefinition of kg__: news pw(03)sep;
Robinson pw(04)may;
news pw(05)mar;
news livesci(05)apr;
Robinson SA(06)dec;
news pt(10)nov;
news wired(11)sep;
Becker CP(12)
[proposed kg definition based on counting the atoms in a ^{28}Si crystal];
news nat(15)oct [getting closer];
news pw(18)nov [new definition];
Ketterle & Jamison PT(20)may.

**Other Quantities** > s.a. Mole.

* __Electric potential__: The volt is
defined using the Josephson effect.

* __Electric current__:
The ampere is defined as the current through two parallel conductors 1 m apart
that results in a certain force between the two conductors; 2018, The ampere will
now be set by the elementary electrical charge *e*, given by 1.602 176 634
× 10^{−27} C.

* __Resistance__: The ohm is defined
using the quantum Hall effect.

* __Temperature__:
0 K = −273.16 °C; The kelvin (K) is currently defined as 1/273.16 of the
temperature difference between absolute zero and the triple point of very pure water
(with a specific ratio of hydrogen and oxygen isotopes) held at a certain pressure;
While the triple-point technique can define the K to better than 1 ppm, the problem
with this definition is that it is based on a specific physical situation, which must
be reproduced whenever a highly accurate definition of the kelvin is required, and
does not work well for very low or very high temperatures, far from water's triple
point; The CIPM (International Committee for Weights and Measures – Comité
International des Poids et Mesures) wants to define all SI units in terms of each other
and the fundamental constants; In the case of the K, this involves the second and
Boltzmann's constant, and therefore an accurate value of the kelvin could be obtained
from the second, which is known to an extremely high degree of accuracy of about one
part in 10^{16}; A redefinition is being planned;
2018, The kelvin will now be set by the set value of the Boltzmann constant.

* __Magnetic field__:
1 T = 10^{4} G.

@ __Redefinition of the ampere__:
news pw(13)may [based on transport measurements of a single electron in graphene];
Keller & Aumentado Phy(16).

> __Online resources__:
Good Calculators site [conversion calculators];
Unit Converter site.

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send feedback and suggestions to bombelli at olemiss.edu – modified 21 may 2020