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FundamentalPhysicalConstants1.omcd
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<OMOBJ xmlns:om="http://www.openmath.org/OpenMath"
xmlns="http://www.openmath.org/OpenMath">
<OMA>
<OMS cd="meta" name="CD"/>
<OMA>
<OMS cd="meta" name="CDComment"/>
<OMSTR>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.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDName"/>
<OMSTR>FundamentalPhysicalConstants1</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDBase"/>
<OMSTR>http://www.openmath.org/cd</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDURL"/>
<OMSTR>http://www.openmath.org/cd/FundamentalPhysicalConstants1.ocd</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDReviewDate"/>
<OMSTR>2017-12-31</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDStatus"/>
<OMSTR>experimental</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDDate"/>
<OMSTR>2005-05-28</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDVersion"/>
<OMSTR>3</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDRevision"/>
<OMSTR>3</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDComment"/>
<OMSTR>Author: J B Collins</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>This CD defines symbols which represent five fundamental physical constants and the Planck units that they define.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>speed-of-light</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>The speed of light is 299,792,458 metre per second</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Planck-constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>Planck constant ~ 6.62606896 * 10^–34 J s</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>reduced-Planck-constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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.</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>reduced Planck constant = h/(2*pi)</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>gravitational-constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>G ~ 6.6742(10)*10^-11 newton metre^2 per kilogram^2</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Boltzmann-constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>k ~ 1.3806504*10^(-23) joule kelvin^-1</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Coulomb-constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>k ~ 1.3806504*10^(-23) joule kelvin^-1</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Planck-length</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>l_P ~ 1.616252(81) * 10^−35 metre</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>l_P = sqrt(h-bar*G/(c^3))</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Planck-mass</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>m_P ~ 2.17644(11) * 10^−8 kilogram</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>m_P = sqrt(h-bar*c/G)</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Planck-time</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>t_P ~ 5.39124(27) * 10^−44 second</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>t_P = sqrt(h-bar*G/(c^5))</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Planck-charge</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>q_P ~ 1.875545870(47) * 10^−18 coulomb</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>q_P = sqrt(h-bar*c*4*pi*eps0)</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
<OMA>
<OMS cd="meta" name="CDDefinition"/>
<OMA>
<OMS cd="meta" name="Name"/>
<OMSTR>Planck-temperature</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Role"/>
<OMSTR>constant</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="Description"/>
<OMSTR>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".</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>l_P ~ 1.416785(71) × 10^32 kelvin</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="CMP"/>
<OMSTR>l_P = sqrt(h-bar*c^5/(G*k^3))</OMSTR>
</OMA>
<OMA>
<OMS cd="meta" name="FMP"/>
<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>
</OMA>
</OMA>
</OMA>
</OMOBJ>