phytorch.constants

Constants are just regular Units with a memorable name and a description.

The primary set of constants comes from the CODATA recommended values. Since they change every few years, φtorch organises the values into submodules: codata2014, codata2018, and the special default, which points to the latest release. Constants can be accessed either from any of the CODATA modules, or from phytorch.constants directly (which will fetch them from default):

>>> from phytorch import constants as const
>>> const.default is const.codata2018
True
>>> const.c is const.default.c is const.codata2018.c
True
>>> const.codata2014.G, const.codata2018.G
(<Newtonian constant of gravitation: G = 6.67408e-11 (N m^(2) kg^(2)^(-1))>,
 <Newtonian constant of gravitation: G = 6.6743e-11 (N m^(2) kg^(2)^(-1))>)

CODATA constants

CODATA constants fall in several categories (here we list values from default):

• fundamental defined constants with values set by defining the measurement system itself:

  name(s)	description	symbol	definition
  c	speed of light in vacuum	\(c\)	\(299\,792\,458\ \mathrm{m} / \mathrm{s}\)
  h	Planck constant	\(h\)	\(6.626\,070\,15 \times 10^{-34}\ \mathrm{J}\,\mathrm{s}\)
  k	Boltzman constant	\(k\)	\(1.380\,649 \times 10^{-23}\ \mathrm{J} / \mathrm{K}\)
  e	elementary charge	\(e\)	\(1.602\,176\,634 \times 10^{-19}\ \mathrm{A}\,\mathrm{s}\)
  N_A	Avogadro constant	\(N_A\)	\(6.022\,140\,76 \times 10^{23}\)

• conventional Earth-related “constants” (these are also “exact”):

  name(s)	description	symbol	value
  atm	standard atmosphere	\(\mathrm{atm}\)	\(101\,325\ \mathrm{Pa}\)
  g	standard acceleration of gravity	\(g\)	\(9.80665\ \mathrm{m} / \mathrm{s}^{2}\)

• other fundamental constants, whose values are derived from measurements:

  name(s)	description	symbol	measured value
  α alpha	fine-structure constant	\(\alpha\)	\(7.297\,352\,5693(11) \times 10^{-3}\)
  G	Newtonian constant of gravitation	\(G\)	\(6.674\,30(15) \times 10^{-11}\ \mathrm{kg}^{-1}\,\mathrm{m}^{3}\,\mathrm{s}^{-2}\)
  m_p	proton mass	\(m_p\)	\(1.672\,621\,923\,69(51) \times 10^{-27}\ \mathrm{kg}\)
  m_n	neutron mass	\(m_n\)	\(1.674\,927\,498\,04(95) \times 10^{-27}\ \mathrm{kg}\)
  m_e	electron mass	\(m_e\)	\(9.109\,383\,7015(28) \times 10^{-31}\ \mathrm{kg}\)
  u	atomic mass constant	\(m_u\)	\(1.660\,539\,066\,60(50) \times 10^{-27}\ \mathrm{kg}\)

• derived constants, which are just convenient shorthand combinations of other constants (these are calculated dynamically and so are consistent within the CODATA set):

  name(s)	description	symbol	definition
  ħ hbar	reduced Planck constant	\(\hbar\)	\(h / (2\pi)\)
  μ_0 mu_0	vacuum magnetic permeability	\(\mu_0\)	\(4\pi \, \alpha \hbar / (c e^2)\)
  ε_0 eps_0	vacuum electric permittivity	\(\varepsilon_0\)	\(1 / (\mu_0 c^2)\)
  μ_B mu_B	Bohr magneton	\(\mu_B\)	\(e \hbar / (2 m_e)\)
  μ_N mu_N	nuclear magneton	\(\mu_N\)	\(e \hbar / (2 m_p)\)
  Ryd	Rydberg constant	\(R_{\infty}\)	\(\alpha^2 m_e c / (2 h)\)
  a_0	Bohr radius	\(a_0\)	\(\hbar / (\alpha m_e c)\)
  σ_e sigma_e	Thomson cross section	\(\sigma_e\)	\((8\pi/3) \, \alpha^4 a_0^2\)
  σ sigma	Stefan-Boltzmann constant	\(\sigma\)	\((\pi^2/60) \, k^4 / (\hbar^3 c^2)\)
  b	Wien wavelength displacement law constant	\(b\)	\((h c / k) \,/\, 4.965\!\ldots\)
  b_prime	Wien frequency displacement law constant	\(b^\prime\)	\(2.821\!\ldots \, (k / h)\)

Astronomical constants

• Additionally, phytorch.constants[*] defines a limited set of “astronomical” constants:[†]

  name(s)	description	symbol	valuea, b
  M_earth earthMass	Earth mass	\(M_⊕\)	\(5.972 \times 10^{24}\ \mathrm{kg}\)
  R_earth earthRad earthRadius	Earth equatorial radius	\(R_⊕\)	\(6.378 \times 10^{6}\ \mathrm{m}\)
  M_jupiter jupiterMass	Jupiter mass	\(M_♃\)	\(1.898 \times 10^{27}\ \mathrm{kg}\)
  R_jupiter jupiterRad jupiterRadius	Jupiter equatorial radius	\(R_♃\)	\(7.149 \times 10^{7}\ \mathrm{m}\)
  M_sun solMass solarMass	solar mass	\(M_☉\)	\(1.988 \times 10^{30}\ \mathrm{kg}\)
  R_sun solRad solarRadius	solar radius	\(R_☉\)	\(6.957 \times 10^{8}\ \mathrm{m}\)
  L_sun solLum solarLuminosity	solar luminosity	\(L_☉\)	\(3.828 \times 10^{26}\ \mathrm{W}\)

Footnotes

[*]

In fact, these are defined in phytorch.constants.astro but exported in the same way as constants from default.

[†]

Note that constants are quantities in the sense that they refer to concrete properties of the real Universe. See also phytorch.units.astro for astro(nomical|physical) units that are used for measuring the Universe.

API

Classes

phytorch.constants.constant.Constant

A Unit that represents a universal constant.

class phytorch.constants.constant.Constant

A Unit that represents a universal constant.

A Constant is simply a Unit with a human-friendly name and optionally a description.

description: str

Free-text description of the constant.

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Modules

phytorch.constants.astro
phytorch.constants.default
phytorch.constants.codata2014
phytorch.constants.codata2018

phytorch.constants.astro: module

A module that defines some astronomical constants, which are exported to phytorch.constants in the same way as those from default.

phytorch.constants.codata2014: CODATA = <module 'codata2014'>

CODATA 2014 release: https://pml.nist.gov/cuu/pdf/wall_2014.pdf.

phytorch.constants.codata2018: CODATA = <module 'codata2018'>

CODATA 2018 release: https://pml.nist.gov/cuu/pdf/wall_2018.pdf.

phytorch.constants.default: CODATA = <module 'codata2018'>

The default set of CODATA constants. Currently points to codata2018.

Attempting to access a variable on the top-level constants module will attempt to look the variable up on default, which allows accessing the default constants directly from phytorch.constants.

---

Helper classes

phytorch.constants.codata.CODATA	A module that represents a set of CODATA constants.
phytorch.constants.codata.CODATA_vals	A collection of values for the defined constants of a CODATA set.

class phytorch.constants.codata.CODATA

A module that represents a set of CODATA constants.

It is instantiated with a set of CODATA_vals for the defined constants. It can then automatically calculates derived constants (on demand) and caches them.

class phytorch.constants.codata.CODATA_vals

A collection of values for the defined constants of a CODATA set.