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FundamentalPhysicalConstants1.ocd
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<?xml version="1.0" encoding="UTF-8"?>
<CD xmlns="http://www.openmath.org/OpenMathCD">
<CDComment>
This document is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
The copyright holder grants you permission to redistribute this
document freely as a verbatim copy. Furthermore, the copyright
holder permits you to develop any derived work from this document
provided that the following conditions are met.
a) The derived work acknowledges the fact that it is derived from
this document, and maintains a prominent reference in the
work to the original source.
b) The fact that the derived work is not the original OpenMath
document is stated prominently in the derived work. Moreover if
both this document and the derived work are Content Dictionaries
then the derived work must include a different CDName element,
chosen so that it cannot be confused with any works adopted by
the OpenMath Society. In particular, if there is a Content
Dictionary Group whose name is, for example, `math' containing
Content Dictionaries named `math1', `math2' etc., then you should
not name a derived Content Dictionary `mathN' where N is an integer.
However you are free to name it `private_mathN' or some such. This
is because the names `mathN' may be used by the OpenMath Society
for future extensions.
c) The derived work is distributed under terms that allow the
compilation of derived works, but keep paragraphs a) and b)
intact. The simplest way to do this is to distribute the derived
work under the OpenMath license, but this is not a requirement.
If you have questions about this license please contact the OpenMath
society at http://www.openmath.org.
Author: Joseph B. Collins (2009), Naval Research Laboratory, Washington, DC.
Copyright Notice: This is a work of the U.S. Government and is not
subject to copyright protection in the United States. Foreign copyrights
may apply.
</CDComment>
<CDName>FundamentalPhysicalConstants1</CDName>
<CDBase>http://www.openmath.org/cd</CDBase>
<CDURL>http://www.openmath.org/cd/FundamentalPhysicalConstants1.ocd</CDURL>
<CDReviewDate>2017-12-31</CDReviewDate>
<CDStatus>experimental</CDStatus>
<CDDate>2005-05-28</CDDate>
<CDVersion>3</CDVersion>
<CDRevision>3</CDRevision>
<CDComment>
Author: J B Collins
</CDComment>
<Description>
This CD defines symbols which represent five fundamental physical constants
and the Planck units that they define.
</Description>
<CDDefinition>
<Name>speed-of-light</Name>
<Role>constant</Role>
<Description>
This symbol represents the speed of light in a vacuum.
Its value is implied by the definition of the metre
[17th CGPM (1983)]. Consequently, the speed of light is defined to be
exactly 299,792,458 metre per second (in the SI).
It is commonly represented with the short, italic symbol, "c".
</Description>
<CMP> The speed of light is 299,792,458 metre per second </CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMS cd="physical_consts1" name="speed_of_light"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMI> 299792458 </OMI>
<OMA>
<OMS cd="arith1" name="divide"/>
<OMS cd="SI_BaseUnits1" name="metre"/>
<OMS cd="SI_BaseUnits1" name="second"/>
</OMA>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>Planck-constant</Name>
<Role>constant</Role>
<Description>
This symbol represents the fundamental constant equal to the ratio of
the energy of a photon to its frequency.
By measurement it is found to be approximately equal to
6.62606896(33)*10^(-34) J s [CODATA 2006].
It is commonly represented with the short, italic symbol, "h".
</Description>
<CMP>
Planck constant ~ 6.62606896 * 10^–34 J s
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="approx"/>
<OMS cd="FundamentalPhysicalConstants1" name="Planck-constant"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMA>
<OMS cd="bigfloat1" name="bigfloat"/>
<OMF dec="6.62606896"/>
<OMI>10</OMI><OMI>-34</OMI>
</OMA>
<OMS cd="SI_NamedDerivedUnits1" name="joule"/>
<OMS cd="SI_BaseUnits1" name="second"/>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>reduced-Planck-constant</Name>
<Role>constant</Role>
<Description>
This symbol represents the Planck constant divided by 2*pi.
It is commonly represented with the short, italic symbol, h with a
horizontal bar ("h-bar"), Unicode: U+210F , HTML: ℏ.
</Description>
<CMP>
reduced Planck constant = h/(2*pi)
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMS cd="FundamentalPhysicalConstants1" name="reduced-Planck-constant"/>
<OMA>
<OMS cd="arith1" name="divide"/>
<OMS cd="FundamentalPhysicalConstants1" name="Planck-constant"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMI>2</OMI>
<OMS name="pi" cd="nums1"/>
</OMA>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>gravitational-constant</Name>
<Role>constant</Role>
<Description>
This symbol represents the constant of proportionality in Newton's law
of universal gravitation.
By measurement it is found to be approximately equal to
6.6742(10)*10^-11 newton metre^2 per kilogram^2.
It is commonly represented with the short, italic symbol, "G".
</Description>
<CMP>
G ~ 6.6742(10)*10^-11 newton metre^2 per kilogram^2
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="approx"/>
<OMS cd="FundamentalPhysicalConstants1" name="gravitational-constant"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMA>
<OMS cd="bigfloat1" name="bigfloat"/>
<OMF dec="6.6742"/>
<OMI>10</OMI><OMI>-11</OMI>
</OMA>
<OMS cd="SI_NamedDerivedUnits1" name="newton"/>
<OMS cd="SI_BaseUnits1" name="metre"/>
<OMA>
<OMS cd="arith1" name="divide"/>
<OMS cd="SI_BaseUnits1" name="metre"/>
<OMA>
<OMS cd="arith1" name="power"/>
<OMS cd="SI_BaseUnits1" name="kilogram"/>
<OMI>2</OMI>
</OMA>
</OMA>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>Boltzmann-constant</Name>
<Role>constant</Role>
<Description>
The Boltzmann constant relates energy at the particle level with temperature observed at the bulk level via the ideal gas law, pV = NkT.
By measurement it is found to be approximately equal to
1.3806504(24)*10^(-23) joule per kelvin.
It is commonly represented with the short, italic symbol, "k".
</Description>
<CMP>
k ~ 1.3806504*10^(-23) joule kelvin^-1
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="approx"/>
<OMS cd="FundamentalPhysicalConstants1" name="Boltzmann-constant"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMA>
<OMS cd="bigfloat1" name="bigfloat"/>
<OMF dec="1.3806504"/>
<OMI>10</OMI><OMI>-23</OMI>
</OMA>
<OMA>
<OMS cd="arith1" name="divide"/>
<OMS cd="SI_NamedDerivedUnits1" name="joule"/>
<OMS cd="SI_BaseUnits1" name="kelvin"/>
</OMA>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>Coulomb-constant</Name>
<Role>constant</Role>
<Description>
The value of the Coulomb constant is implied by international definitions of the
speed of light and the vacuum permeability.
By definition, its exact value is equal to (299,792,458)^2 * 10^-7 N m^2 C^-2.
It is commonly represented with the short, italic symbol, "k" subscripted with the
upright letter "e".
</Description>
<CMP>
k ~ 1.3806504*10^(-23) joule kelvin^-1
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="approx"/>
<OMS cd="FundamentalPhysicalConstants1" name="Coulomb-constant"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMA>
<OMS cd="bigfloat1" name="bigfloat"/>
<OMF dec="1.3806504"/>
<OMI>10</OMI><OMI>-23</OMI>
</OMA>
<OMA>
<OMS cd="arith1" name="divide"/>
<OMS cd="SI_NamedDerivedUnits1" name="joule"/>
<OMS cd="SI_BaseUnits1" name="kelvin"/>
</OMA>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>Planck-length</Name>
<Role>constant</Role>
<Description>
The Planck length is defined to be sqrt(h-bar*G/(c^3)).
Its value derived from measurement is 1.616252(81) * 10^−35 metre.
It is commonly represented with the short, italic symbol, "l", subscripted with an upright capital "P".
</Description>
<CMP>
l_P ~ 1.616252(81) * 10^−35 metre
</CMP>
<CMP>
l_P = sqrt(h-bar*G/(c^3))
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMS cd="FundamentalPhysicalConstants1" name=" Planck-length"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMA>
<OMS cd="bigfloat1" name="bigfloat"/>
<OMF dec="1.3806504"/>
<OMI>10</OMI><OMI>-23</OMI>
</OMA>
<OMS cd="SI_BaseUnits1" name="metre"/>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>Planck-mass</Name>
<Role>constant</Role>
<Description>
The Planck mass is defined to be sqrt(h-bar*c/G).
Its value derived from measurement is 2.17644(11) * 10^−8 kilogram.
It is commonly represented with the short, italic symbol, "m", subscripted with an upright capital "P".
</Description>
<CMP>
m_P ~ 2.17644(11) * 10^−8 kilogram
</CMP>
<CMP>
m_P = sqrt(h-bar*c/G)
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMS cd="FundamentalPhysicalConstants1" name="Planck-mass"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMA>
<OMS cd="bigfloat1" name="bigfloat"/>
<OMF dec="2.17644"/>
<OMI>10</OMI><OMI>-8</OMI>
</OMA>
<OMS cd="SI_BaseUnits1" name="kilogram"/>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>Planck-time</Name>
<Role>constant</Role>
<Description>
The Planck time is defined to be sqrt(h-bar*G/(c^5)).
Its value derived from measurement is 5.39124(27) * 10^−44 second.
It is commonly represented with the short, italic symbol, "t", subscripted with an upright capital "P".
</Description>
<CMP>
t_P ~ 5.39124(27) * 10^−44 second
</CMP>
<CMP>
t_P = sqrt(h-bar*G/(c^5))
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMS cd="FundamentalPhysicalConstants1" name="Planck-time"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMA>
<OMS cd="bigfloat1" name="bigfloat"/>
<OMF dec="5.39124"/>
<OMI>10</OMI><OMI>-44</OMI>
</OMA>
<OMS cd="SI_BaseUnits1" name="second"/>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>Planck-charge</Name>
<Role>constant</Role>
<Description>
The Planck charge is defined to be sqrt(h-bar*c*4*pi*eps0).
Its value derived from measurement is 1.875545870(47) * 10^−18 coulomb.
It is commonly represented with the short, italic symbol, "q", subscripted with an upright capital "P".
</Description>
<CMP>
q_P ~ 1.875545870(47) * 10^−18 coulomb
</CMP>
<CMP>
q_P = sqrt(h-bar*c*4*pi*eps0)
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMS cd="FundamentalPhysicalConstants1" name="Planck-charge"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMA>
<OMS cd="bigfloat1" name="bigfloat"/>
<OMF dec="1.875545870"/>
<OMI>10</OMI><OMI>-18</OMI>
</OMA>
<OMS cd="SI_NamedDerivedUnits1" name="coulomb"/>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
<CDDefinition>
<Name>Planck-temperature</Name>
<Role>constant</Role>
<Description>
The Planck temperature is defined to be sqrt(h-bar*c^5/(G*k^3)).
Its value derived from measurement is 1.416785(71) × 10^32 kelvin.
It is commonly represented with the short, italic symbol, "T", subscripted with an upright capital "P".
</Description>
<CMP>
l_P ~ 1.416785(71) × 10^32 kelvin
</CMP>
<CMP>
l_P = sqrt(h-bar*c^5/(G*k^3))
</CMP>
<FMP><OMOBJ xmlns="http://www.openmath.org/OpenMath" version="2.0" cdbase="http://www.openmath.org/cd">
<OMA>
<OMS cd="relation1" name="eq"/>
<OMS cd="FundamentalPhysicalConstants1" name="Boltzmann-constant"/>
<OMA>
<OMS cd="arith1" name="times"/>
<OMA>
<OMS cd="bigfloat1" name="bigfloat"/>
<OMF dec="1.3806504"/>
<OMI>10</OMI><OMI>-23</OMI>
</OMA>
<OMA>
<OMS cd="arith1" name="divide"/>
<OMS cd="SI_NamedDerivedUnits1" name="joule"/>
<OMS cd="SI_BaseUnits1" name="kelvin"/>
</OMA>
</OMA>
</OMA>
</OMOBJ></FMP>
</CDDefinition>
</CD>