Units
of Measurement |

**In General** > s.a. Planck Constant [including
Planck units].

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

@ __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].

@ __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].

@ __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].

@ __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; 2012, The only fundamental
unit still defined using a physical artifact, although new definitions have
been advocated, and an agreement appears to be near.

* __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].

**Other Quantities**

* __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.

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

* __Temperature__:
0 K = –273.16ºC; 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.

* __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).

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send feedback and suggestions to bombelli at olemiss.edu – modified 3
jan 2017