PhysicalConstant.jl

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Introduction

PhysicalConstant.jl provides common physical constants. They are defined as Constant objects, which can be turned into Quantity objects (from Unitful.jl package) or Measurement objects (from Measurements.jl package) at request.

Constants are grouped into different submodules, so that the user can choose different datasets as needed. Currently, only 2019 edition based on 26th CGPM and the anticipated CODATA recommended values of the fundamental physical constants is provided.

Installation

Measurements.jl is available for Julia 0.7 and later versions, and can be installed with Julia built-in package manager. In a Julia session run the command

pkg> add https://github.com/laguer/PhysicalConstant.jl

Usage

You can load the package as usual with using PhysicalConstant but this module does not provide anything useful for the end-users. You most probably want to directly load the submodule with the dataset you are interested in. For example, for CODATA 2019 load PhysicalConstants.CODATA2019:

julia> using PhysicalConstant.CODATA2019

julia> C
Gravitational velocity in vacuum (C)
Value                         = 3.6993e44 m s^-1 
Standard uncertainty          = (exact)
Relative standard uncertainty = (exact)
Reference                     = CODATA 2019

julia> Gg
Newtonian constant of gravitation (Gg)
Value                         = 6.67408e-11 m^3 kg^-1 s^-2
Standard uncertainty          = 3.1e-15 m^3 kg^-1 s^-2
Relative standard uncertainty = 4.6e-5
Reference                     = CODATA 2019

C and Gg are two of the new Constants defined in the PhysicalConstant.CODATA2019 module, the full list of available constants is given below.

You can turn a Constant into a Quantity object, with physical units, by using float(x):

julia> float(Float32(inv(big(α))))
137.036f0

You can optionally specify the floating-point precision of the resulting number, this package takes care of keeping the value accurate also with BigFloat:

julia> float(Float32, ε_0)
8.854188f-12 F m^-1

julia> float(BigFloat, ε_0)
8.854187817620389850536563031710750260608370166599449808102417152405395095459979e-12 F m^-1

julia> big(ε_0)
8.854187817620389850536563031710750260608370166599449808102417152405395095459979e-12 F m^-1

julia> big(ε_0) - inv(big(μ_0) * big(c)^2)
0.0 A^2 s^4 kg^-1 m^-3

Note that big(x) is an alias for float(BigFloat, x).

If in addition to units you also want the standard uncertainty associated with the constant, use measurement(x):

julia> using Measurements

julia> measurement(ħ)
1.0545718001391127e-34 ± 1.2891550390443523e-42 J s

julia> measurement(Float32, ħ)
1.0545718e-34 ± 1.289e-42 J s

julia> measurement(BigFloat, ħ)
1.054571800139112651153941068725066773746246506229852090971714108355028066256094e-34 ± 1.289155039044352219727958483317366332479123130497697234856105486877064060837251e-42 J s

julia> measurement(BigFloat, ħ) / (measurement(BigFloat, h) / (2 * big(pi)))
1.0 ± 0.0

Inserting unicode (e.g. Greek letters)

Julia supports the use of unicode characters such as α and β in your code

Unicode characters can be typed quickly in Jupyter using the tab key

Try creating a new code cell and typing \alpha, then hitting the tab key on your keyboard

Shell Commands

You can execute shell commands (system commands) in Jupyter by prepending a semicolon

For example, ; ls will execute the UNIX style shell command ls, which — at least for UNIX style operating systems — lists the contents of the current working directory

These shell commands are handled by your default system shell and hence are platform specific

Package Manager

You can enter the package manager by prepending a ]

For example, ] st will give the status of installed packages in the current environment

Sharing Julia Notebooks

Notebook files are just text files structured in JSON and typically end with .ipynb

A notebook can easily be saved and shared between users — you just need to pass around the ipynb file

To open an existing ipynb file, import it from the dashboard (the first browser page that opens when you start Jupyter notebook) and run the cells or edit as discussed above

The Jupyter organization has a site for sharing notebooks called nbviewer which provides a static HTML representations of notebooks

PhysicalConstant also hosts the PhysicalConstant Notes github repo, where you can upload and share your notebooks with other researchers and the PhysicalConstant community

List of Constants

CODATA CGPM BIPM 2019

Symbol	Name	Value	Unit
ΔνC_s	unperturbed ground state hyperfine	9 192 631 770	Hz
--	transition frequency of the cesium 133	-----	----
-----	-----	-----	----
Gg	Newtonian constant of gravitation	6.67408e-11	m^3 kg^-1 s^-2
G	Sanchez constant of gravitation	6.675453818e-11	m^3 kg^-1 s^-2
N_A	Avogadro constant	6.022140857e23	mol^-1
R	Molar gas constant	8.3144598	J K^-1 mol^-1
R_∞	Rydberg constant	1.0973731568508e7	m^-1
Z_0	Characteristic impedance of vacuum	376.73031346177066	Ω
a_0	Bohr radius	5.2917721067e-11	m
atm	Standard atmosphere	101325.0	Pa
b	Wien wavelength displacement law constant	0.0028977729	K m
c	Speed of light in vacuum	2.99792458e8	m s^-1
C	Gravitational Velocity	3.6993e44	m s^-1
e	Elementary charge	1.602176634e-19	C
g_n	Standard acceleration of gravitation	9.80665	m s^-2
h	Planck constant	6.62607015e-34	J s
k_B	Boltzman Energy-temperature Convers°	1.3806488e-23	J K^-1
k_B'	Boltzmann constant	1.38064852e-23	J K^-1
m_e	Electron mass	9.10938356e-31	kg
m_n	Neutron mass	1.674927471e-27	kg
m_p	Proton mass	1.672621898e-27	kg
m_u	Atomic mass constant	1.66053904e-27	kg
m_H	Hydrogen mass constant	1.6737236e-27	kg
m_m	Muon mass constant μ-	1.83615267e-28	kg
m_t	Tau mass constant τ-	3.16773502e-27	kg
ħ	Planck constant over 2pi	1.0545718001391127e-34	J s
α	Fine-structure constant	0.0072973525664
a	Sanchez Electric constant	137.035999139
ε_0	Electric constant	8.854187817620389e-12	F m^-1
μ_0	Magnetic constant	1.2566370614359173e-6	N A^-2
μ_B	Bohr magneton	9.274009994e-24	J T^-1
σ	Stefan-Boltzmann constant	5.670367e-8	m^2
σ_e	Thomson cross section	6.6524587158e-29	m^2
t_cc	Kotov Cosmic Periodicity	9600.061(2)	s
r_0	Bare Hydrogen radius	5.291772103e-11	m
θ'	CMB Temperature in K CODATA2014	2.7255(6)	K
θ	CMB Temperature in K SANCHEZ	2.725820831	K
a_G	Sanchez Gravitational Coupling Constant	1.691936465e38	-
f	Strong Nuclear Coupling Constant C.Bizouard	8.434502892	-

Updated universal constants and particle properties ( thanks to Jean Maruani / Francis Sanchez)

• The_Dirac_Electron_From_Quantum_Chemistry_to_Holistic_Cosmology @ researchgate
• Dirac_Electron_From_Quantum_Chemistry_to_Holistic_Cosmology @ Wiley

Symbol	Name	Formula	Dimension	Value	Unit
G	Sz constant of gravitation	F_gr=Gmm'/d^2	M^-1L^3T^-2	6.675453818e-11	m^3 kg^-1 s^-2
k_e	Electrostatic constant	k_e.e^2 / ħc	dimensionless	8.98e-9	F^-1.m
α	Fine structure constant	a=α^-1 F_el=ħc/αd^2	dimensionless	(137.0359991)^-1	pure number
δ_e	Electron grav invariant		dimensionless	1.7517e-45	pure number
δ_n	Nucleon grav invariant		dimensionless	5.9138e-39	pure number
δ_X	Cross grav invariant		dimensionless	1.6917e-38	pure number
C	Gravitational velocity		L.T^-1	3.6993e44	m s^-1
R_U	Universe Hubble radius	R_U=2G.M_U/c)^2	L	1.3065e26	m
G_F	Fermi Constant	G_F=ħ^3/cm_F^2	ML^5T^-2	8.7936e52	J.m^3
a_G	Gravitation Sanchez Constant	a_G=ħc/Gm_pm_H	dimensionless	1.6919335e38	pure number
M_U	Universe Sanchez Mass	M_U=(ħc/G)^2/m_e.m_p.m_n	M	8.7936e52	kg
r_0	Bare Hydrogen Bohr radius	aħ/m_ec	L	5.291772103e-11	m
H	Hydrogen-electron mass ratio	m_H/m_e	dimensionless	1837.152645	m_e
p	Proton-electron mass ratio	m_p/m_e	dimensionless	1836.152672	m_e
n	Neutron-electron mass ratio	m_n/m_e	dimensionless	1838.683659	m_e
μ-	Muon-electron mass ratio	m_m/m_e	dimensionless	206.7682869	m_e
τ-	Tau-electron mass ratio	m_t/m_e	dimensionless	3477.441701	m_e

License

The PhysicalConstants.jl package is licensed under the MIT "Expat" License. The original author is Mosè Giordano in arxiv.

New physical constants CODATA2019 added by LaGuer LaGuer for experimental purposes as proposed by Dr Francis M. Sanchez.

Addendum

New physical constants CODATA2019 introduce independent correlated results between T.Quinn experiments at BIPM and C.Bizouard at OBSPM. Data aligned with 26th CGPM/BIPM in anticipation of NIST 2019 release.