OpenMath Content Dictionary: FundamentalPhysicalConstants1

Canonical URL:

http://www.openmath.org/cd/FundamentalPhysicalConstants1.ocd

CD Base:

http://www.openmath.org/cd

CD File:

FundamentalPhysicalConstants1.ocd

CD as XML Encoded OpenMath:

FundamentalPhysicalConstants1.omcd

Defines:

Boltzmann-constant, Coulomb-constant, Planck-charge, Planck-constant, Planck-length, Planck-mass, Planck-temperature, Planck-time, gravitational-constant, reduced-Planck-constant, speed-of-light

Date:

2005-05-28

Version:

3 (Revision 3)

Review Date:

2017-12-31

Status:

experimental

---

     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.

  Author: J B Collins

This CD defines symbols which represent five fundamental physical constants and the Planck units that they define.

---

speed-of-light

Role:

constant

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".

Commented Mathematical property (CMP):

The speed of light is 299,792,458 metre per second

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="physical_consts1">speed_of_light</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <cn type="integer">299792458</cn>
   <apply><csymbol cd="arith1">divide</csymbol>
    <csymbol cd="SI_BaseUnits1">metre</csymbol>
    <csymbol cd="SI_BaseUnits1">second</csymbol>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (speed_of_light, times ( 299792458 , divide (metre, second) ) )

Popcorn

physical_consts1.speed_of_light = 299792458 * SI_BaseUnits1.metre / SI_BaseUnits1.second

Rendered Presentation MathML

$$\mathrm{speed\_of\_light}=299792458\frac{\mathrm{metre}}{\mathrm{second}}$$

Signatures:

sts

---

[Next: Planck-constant] [Last: Planck-temperature] [Top]

---

Planck-constant

Role:

constant

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".

Commented Mathematical property (CMP):

Planck constant ~ 6.62606896 * 10^–34 J s

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">approx</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">Planck-constant</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">6.62606896</cn>
    <cn type="integer">10</cn>
    <cn type="integer">-34</cn>
   </apply>
   <csymbol cd="SI_NamedDerivedUnits1">joule</csymbol>
   <csymbol cd="SI_BaseUnits1">second</csymbol>
  </apply>
 </apply>
</math>

Prefix

approx (Planck-constant, times (bigfloat ( 6.62606896 , 10, -34) , joule, second) )

Popcorn

relation1.approx(FundamentalPhysicalConstants1.Planck-constant, bigfloat1.bigfloat(6.62606896, 10, -34) * SI_NamedDerivedUnits1.joule * SI_BaseUnits1.second)

Rendered Presentation MathML

$$\mathrm{Planck-constant}\approx 6.62606896\times {10}^{-34}\times \mathrm{joule}\times \mathrm{second}$$

Signatures:

sts

---

[Next: reduced-Planck-constant] [Previous: speed-of-light] [Top]

---

reduced-Planck-constant

Role:

constant

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.

Commented Mathematical property (CMP):

reduced Planck constant = h/(2*pi)

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">reduced-Planck-constant</csymbol>
  <apply><csymbol cd="arith1">divide</csymbol>
   <csymbol cd="FundamentalPhysicalConstants1">Planck-constant</csymbol>
   <apply><csymbol cd="arith1">times</csymbol>
    <cn type="integer">2</cn>
    <csymbol cd="nums1">pi</csymbol>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (reduced-Planck-constant, divide (Planck-constant, times (2, pi) ) )

Popcorn

FundamentalPhysicalConstants1.reduced-Planck-constant = FundamentalPhysicalConstants1.Planck-constant / (2 * nums1.pi)

Rendered Presentation MathML

$$\mathrm{reduced-Planck-constant}=\frac{\mathrm{Planck-constant}}{2\pi }$$

Signatures:

sts

---

[Next: gravitational-constant] [Previous: Planck-constant] [Top]

---

gravitational-constant

Role:

constant

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".

Commented Mathematical property (CMP):

G ~ 6.6742(10)*10^-11 newton metre^2 per kilogram^2

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">approx</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">gravitational-constant</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">6.6742</cn>
    <cn type="integer">10</cn>
    <cn type="integer">-11</cn>
   </apply>
   <csymbol cd="SI_NamedDerivedUnits1">newton</csymbol>
   <csymbol cd="SI_BaseUnits1">metre</csymbol>
   <apply><csymbol cd="arith1">divide</csymbol>
    <csymbol cd="SI_BaseUnits1">metre</csymbol>
    <apply><csymbol cd="arith1">power</csymbol>
     <csymbol cd="SI_BaseUnits1">kilogram</csymbol>
     <cn type="integer">2</cn>
    </apply>
   </apply>
  </apply>
 </apply>
</math>

Prefix

approx (gravitational-constant, times (bigfloat ( 6.6742 , 10, -11) , newton, metre, divide (metre, power (kilogram, 2) ) ) )

Popcorn

relation1.approx(FundamentalPhysicalConstants1.gravitational-constant, bigfloat1.bigfloat(6.6742, 10, -11) * SI_NamedDerivedUnits1.newton * SI_BaseUnits1.metre * SI_BaseUnits1.metre / SI_BaseUnits1.kilogram ^ 2)

Rendered Presentation MathML

$$\mathrm{gravitational-constant}\approx 6.6742\times {10}^{-11}\times \mathrm{newton}\times \mathrm{metre}\times \frac{\mathrm{metre}}{{\mathrm{kilogram}}^2}$$

Signatures:

sts

---

[Next: Boltzmann-constant] [Previous: reduced-Planck-constant] [Top]

---

Boltzmann-constant

Role:

constant

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".

Commented Mathematical property (CMP):

k ~ 1.3806504*10^(-23) joule kelvin^-1

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">approx</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">Boltzmann-constant</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">1.3806504</cn>
    <cn type="integer">10</cn>
    <cn type="integer">-23</cn>
   </apply>
   <apply><csymbol cd="arith1">divide</csymbol>
    <csymbol cd="SI_NamedDerivedUnits1">joule</csymbol>
    <csymbol cd="SI_BaseUnits1">kelvin</csymbol>
   </apply>
  </apply>
 </apply>
</math>

Prefix

approx (Boltzmann-constant, times (bigfloat ( 1.3806504 , 10, -23) , divide (joule, kelvin) ) )

Popcorn

relation1.approx(FundamentalPhysicalConstants1.Boltzmann-constant, bigfloat1.bigfloat(1.3806504, 10, -23) * SI_NamedDerivedUnits1.joule / SI_BaseUnits1.kelvin)

Rendered Presentation MathML

$$\mathrm{Boltzmann-constant}\approx 1.3806504\times {10}^{-23}\frac{\mathrm{joule}}{\mathrm{kelvin}}$$

Signatures:

sts

---

[Next: Coulomb-constant] [Previous: gravitational-constant] [Top]

---

Coulomb-constant

Role:

constant

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".

Commented Mathematical property (CMP):

k ~ 1.3806504*10^(-23) joule kelvin^-1

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">approx</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">Coulomb-constant</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">1.3806504</cn>
    <cn type="integer">10</cn>
    <cn type="integer">-23</cn>
   </apply>
   <apply><csymbol cd="arith1">divide</csymbol>
    <csymbol cd="SI_NamedDerivedUnits1">joule</csymbol>
    <csymbol cd="SI_BaseUnits1">kelvin</csymbol>
   </apply>
  </apply>
 </apply>
</math>

Prefix

approx (Coulomb-constant, times (bigfloat ( 1.3806504 , 10, -23) , divide (joule, kelvin) ) )

Popcorn

relation1.approx(FundamentalPhysicalConstants1.Coulomb-constant, bigfloat1.bigfloat(1.3806504, 10, -23) * SI_NamedDerivedUnits1.joule / SI_BaseUnits1.kelvin)

Rendered Presentation MathML

$$\mathrm{Coulomb-constant}\approx 1.3806504\times {10}^{-23}\frac{\mathrm{joule}}{\mathrm{kelvin}}$$

Signatures:

sts

---

[Next: Planck-length] [Previous: Boltzmann-constant] [Top]

---

Planck-length

Role:

constant

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".

Commented Mathematical property (CMP):

l_P ~ 1.616252(81) * 10^−35 metre

Commented Mathematical property (CMP):

l_P = sqrt(h-bar*G/(c^3))

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">Planck-length</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">1.3806504</cn>
    <cn type="integer">10</cn>
    <cn type="integer">-23</cn>
   </apply>
   <csymbol cd="SI_BaseUnits1">metre</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq ( Planck-length, times (bigfloat ( 1.3806504 , 10, -23) , metre) )

Popcorn

FundamentalPhysicalConstants1.Planck-length = bigfloat1.bigfloat(1.3806504, 10, -23) * SI_BaseUnits1.metre

Rendered Presentation MathML

$$\mathrm{Planck-length}=1.3806504\times {10}^{-23}\mathrm{metre}$$

Signatures:

sts

---

[Next: Planck-mass] [Previous: Coulomb-constant] [Top]

---

Planck-mass

Role:

constant

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".

Commented Mathematical property (CMP):

m_P ~ 2.17644(11) * 10^−8 kilogram

Commented Mathematical property (CMP):

m_P = sqrt(h-bar*c/G)

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">Planck-mass</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">2.17644</cn>
    <cn type="integer">10</cn>
    <cn type="integer">-8</cn>
   </apply>
   <csymbol cd="SI_BaseUnits1">kilogram</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (Planck-mass, times (bigfloat ( 2.17644 , 10, -8) , kilogram) )

Popcorn

FundamentalPhysicalConstants1.Planck-mass = bigfloat1.bigfloat(2.17644, 10, -8) * SI_BaseUnits1.kilogram

Rendered Presentation MathML

$$\mathrm{Planck-mass}=2.17644\times {10}^{-8}\mathrm{kilogram}$$

Signatures:

sts

---

[Next: Planck-time] [Previous: Planck-length] [Top]

---

Planck-time

Role:

constant

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".

Commented Mathematical property (CMP):

t_P ~ 5.39124(27) * 10^−44 second

Commented Mathematical property (CMP):

t_P = sqrt(h-bar*G/(c^5))

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">Planck-time</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">5.39124</cn>
    <cn type="integer">10</cn>
    <cn type="integer">-44</cn>
   </apply>
   <csymbol cd="SI_BaseUnits1">second</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (Planck-time, times (bigfloat ( 5.39124 , 10, -44) , second) )

Popcorn

FundamentalPhysicalConstants1.Planck-time = bigfloat1.bigfloat(5.39124, 10, -44) * SI_BaseUnits1.second

Rendered Presentation MathML

$$\mathrm{Planck-time}=5.39124\times {10}^{-44}\mathrm{second}$$

Signatures:

sts

---

[Next: Planck-charge] [Previous: Planck-mass] [Top]

---

Planck-charge

Role:

constant

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".

Commented Mathematical property (CMP):

q_P ~ 1.875545870(47) * 10^−18 coulomb

Commented Mathematical property (CMP):

q_P = sqrt(h-bar*c*4*pi*eps0)

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">Planck-charge</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">1.875545870</cn>
    <cn type="integer">10</cn>
    <cn type="integer">-18</cn>
   </apply>
   <csymbol cd="SI_NamedDerivedUnits1">coulomb</csymbol>
  </apply>
 </apply>
</math>

Prefix

eq (Planck-charge, times (bigfloat ( 1.875545870 , 10, -18) , coulomb) )

Popcorn

FundamentalPhysicalConstants1.Planck-charge = bigfloat1.bigfloat(1.875545870, 10, -18) * SI_NamedDerivedUnits1.coulomb

Rendered Presentation MathML

$$\mathrm{Planck-charge}=1.875545870\times {10}^{-18}\mathrm{coulomb}$$

Signatures:

sts

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Planck-temperature

Role:

constant

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".

Commented Mathematical property (CMP):

l_P ~ 1.416785(71) × 10^32 kelvin

Commented Mathematical property (CMP):

l_P = sqrt(h-bar*c^5/(G*k^3))

Formal Mathematical property (FMP):

OpenMath XML (source)

<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>

Strict Content MathML

<math xmlns="http://www.w3.org/1998/Math/MathML">
 <apply><csymbol cd="relation1">eq</csymbol>
  <csymbol cd="FundamentalPhysicalConstants1">Boltzmann-constant</csymbol>
  <apply><csymbol cd="arith1">times</csymbol>
   <apply><csymbol cd="bigfloat1">bigfloat</csymbol>
    <cn type="real">1.3806504</cn>
    <cn type="integer">10</cn>
    <cn type="integer">-23</cn>
   </apply>
   <apply><csymbol cd="arith1">divide</csymbol>
    <csymbol cd="SI_NamedDerivedUnits1">joule</csymbol>
    <csymbol cd="SI_BaseUnits1">kelvin</csymbol>
   </apply>
  </apply>
 </apply>
</math>

Prefix

eq (Boltzmann-constant, times (bigfloat ( 1.3806504 , 10, -23) , divide (joule, kelvin) ) )

Popcorn

FundamentalPhysicalConstants1.Boltzmann-constant = bigfloat1.bigfloat(1.3806504, 10, -23) * SI_NamedDerivedUnits1.joule / SI_BaseUnits1.kelvin

Rendered Presentation MathML

$$\mathrm{Boltzmann-constant}=1.3806504\times {10}^{-23}\frac{\mathrm{joule}}{\mathrm{kelvin}}$$

Signatures:

sts

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