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


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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):
speed_of_light = 299792458 metre 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):
Planck-constant 6.62606896 × 10 -34 × joule × 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):
reduced-Planck-constant = Planck-constant 2 π
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):
gravitational-constant 6.6742 × 10 -11 × newton × metre × metre 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):
Boltzmann-constant 1.3806504 × 10 -23 joule 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):
Coulomb-constant 1.3806504 × 10 -23 joule 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):
Planck-length = 1.3806504 × 10 -23 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):
Planck-mass = 2.17644 × 10 -8 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):
Planck-time = 5.39124 × 10 -44 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):
Planck-charge = 1.875545870 × 10 -18 coulomb
Signatures:
sts


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

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):
Boltzmann-constant = 1.3806504 × 10 -23 joule kelvin
Signatures:
sts


[First: speed-of-light] [Previous: Planck-charge] [Top]