Physical Constants

Fundamental Physical Constants

Goals:
1. Group, then rank order the constants by fundamentality, importance (use by other constants), and place (use by scholars, i.e. citations),
2. Relate to a notation or set of notations where there is a natural link to the Key Ratio and historic discussion.

Background: On September 18, 2019, the Planck base units needed further definition. We assumed that what was found consistently on the web was not necessarily good enough. We turned to the expert studies of the National Institute of Science and Technology (NIST). Are there in fact 64 notations or doublings the Planck Length and Planck Time ? …from the first moment of time? Does Planck Time encapsulate the first moment? Our analysis had begun with the help of data accrued by John Baez. It was time to come back around to that data and to analyze each judgement and conclusion that was based on the Baez work.

354 NIST Fundamental Physical Constants:

Editor’s note: This list of fundamental physical constants is from the National Institute of Science and Technology (NIST). It is replicated here to provide a one-step access to the Numerical value, the Standard Uncertainty, the Relative standard uncertainty and the Concise form. You can compare it to Wikipedia’s list of dimensionless constants, the Aguirre-Rees-Tegmark-Wilczek list of 31 necessary for the Standard Model for Particle Physics, and the list of 26 by John Baez. At some time the work of Simon Plouffe, who identified over a billion such constants (computer-generated), may also be engaged.

Goals:
1. Emerge with two columns, one of the 354 NIST constants and the other as ranked by fundamentality, importance (use by other constants), and place (use by scholars, i.e. citations),
2. Relate to a notation or set of notations where there is a natural link to the Key Ratio and historic discussion.

alpha particle mass alpha particle mass energy equivalent alpha particle mass energy equivalent (MeV) alpha particle mass in u alpha particle molar mass alpha particle relative atomic mass alpha particle-electron mass ratio alpha particle-proton mass ratio Angstrom star atomic mass constant atomic mass constant energy equivalent atomic mass constant energy equivalent (MeV) atomic mass unit-electron volt relationship atomic mass unit-hartree relationship atomic mass unit-hertz relationship atomic mass unit-inverse meter relationship atomic mass unit-joule relationship atomic mass unit-kelvin relationship atomic mass unit-kilogram relationship atomic unit of 1st hyperpolarizability atomic unit of 2nd hyperpolarizability atomic unit of action atomic unit of charge atomic unit of charge density atomic unit of current atomic unit of electric dipole moment atomic unit of electric field atomic unit of electric field gradient atomic unit of electric polarizability atomic unit of electric potential atomic unit of electric quadrupole moment atomic unit of energy atomic unit of force atomic unit of length atomic unit of magnetic dipole moment atomic unit of magnetic flux density atomic unit of magnetizability atomic unit of mass atomic unit of momentum atomic unit of permittivity atomic unit of time atomic unit of velocity Avogadro constant Bohr magneton Bohr magneton in eV/T Bohr magneton in Hz/T Bohr magneton in inverse meter per tesla Bohr magneton in K/T Bohr radius Boltzmann constant Boltzmann constant in eV/K Boltzmann constant in Hz/K Boltzmann constant in inverse meter per kelvin classical electron radius Compton wavelength conductance quantum conventional value of ampere-90 conventional value of coulomb-90 conventional value of farad-90 conventional value of henry-90 conventional value of Josephson constant conventional value of ohm-90 conventional value of volt-90 conventional value of von Klitzing constant conventional value of watt-90 Cu x unit deuteron g factor deuteron magnetic moment deuteron magnetic moment to Bohr magneton ratio deuteron magnetic moment to nuclear magneton ratio deuteron mass deuteron mass energy equivalent deuteron mass energy equivalent (MeV) deuteron mass in u deuteron molar mass deuteron relative atomic mass deuteron rms charge radius deuteron-electron magnetic moment ratio deuteron-electron mass ratio deuteron-neutron magnetic moment ratio deuteron-proton magnetic moment ratio deuteron-proton mass ratio electron charge to mass quotient electron g factor electron gyromagnetic ratio electron gyromagnetic ratio in MHz/T electron magnetic moment electron magnetic moment anomaly electron magnetic moment to Bohr magneton ratio electron magnetic moment to nuclear magneton ratio electron mass electron mass energy equivalent electron mass energy equivalent in MeV electron mass in u electron molar mass electron relative atomic mass electron to alpha particle mass ratio electron to shielded helion magnetic moment ratio electron to shielded proton magnetic moment ratio electron volt electron volt-atomic mass unit relationship electron volt-hartree relationship electron volt-hertz relationship electron volt-inverse meter relationship electron volt-joule relationship electron volt-kelvin relationship electron volt-kilogram relationship electron-deuteron magnetic moment ratio electron-deuteron mass ratio electron-helion mass ratio electron-muon magnetic moment ratio electron-muon mass ratio electron-neutron magnetic moment ratio electron-neutron mass ratio electron-proton magnetic moment ratio electron-proton mass ratio electron-tau mass ratio electron-triton mass ratio elementary charge elementary charge over h-bar Faraday constant Fermi coupling constant fine-structure constant: first radiation constant first radiation constant for spectral radiance Hartree energy Hartree energy in eV hartree-atomic mass unit relationship hartree-electron volt relationship hartree-hertz relationship hartree-inverse meter relationship hartree-joule relationship hartree-kelvin relationship hartree-kilogram relationship helion g factor helion magnetic moment helion magnetic moment to Bohr magneton ratio helion magnetic moment to nuclear magneton ratio helion mass helion mass energy equivalent helion mass energy equivalent (MeV) helion mass in u helion molar mass helion relative atomic mass helion shielding shift helion-electron mass ratio helion-proton mass ratio hertz-atomic mass unit relationship hertz-electron volt relationship hertz-hartree relationship hertz-inverse meter relationship hertz-joule relationship hertz-kelvin relationship hertz-kilogram relations hyperfine transition frequency of Cs-133 inverse fine-structure constant inverse meter-atomic mass unit relationship inverse meter-electron volt relationship inverse meter-hartree relationship inverse meter-hertz relationship inverse meter-joule relationship inverse meter-kelvin relationship inverse meter-kilogram relationship inverse of conductance quantum Josephson constant joule-atomic mass unit relationship joule-electron volt relationship joule-hartree relationship joule-hertz relationship joule-inverse meter relationship joule-kelvin relationship joule-kilogram relationship kelvin-atomic mass unit relationship kelvin-electron volt relationship kelvin-hartree relationship kelvin-hertz relationship kelvin-inverse meter relationship kelvin-joule relationship kelvin-kilogram relationship kilogram-atomic mass unit relationship kilogram-electron volt relationship kilogram-hartree relationship kilogram-hertz relationship kilogram-inverse meter relationship kilogram-joule relationship kilogram-kelvin relationship lattice parameter of silicon lattice spacing of ideal Si (220) Loschmidt constant (273.15 K, 100 kPa) Loschmidt constant (273.15 K, 101.325 kPa) luminous efficacy magnetic flux quantum Mo x unit molar gas constant molar mass constant molar mass of carbon-12 molar Planck constant molar volume of ideal gas (273.15 K, 100 kPa) molar volume of ideal gas (273.15 K, 101.325 kPa) molar volume of silicon muon Compton wavelength muon g factor muon magnetic moment muon magnetic moment anomaly muon magnetic moment anomaly muon magnetic moment to Bohr magneton ratio muon magnetic moment to nuclear magneton ratio muon mass muon mass energy equivalent muon mass energy equivalent in MeV muon mass in u muon molar mass muon-electron mass ratio muon-neutron mass ratio muon-proton magnetic moment ratio muon-proton mass ratio muon-tau mass ratio natural unit of action natural unit of action in eV s natural unit of energy natural unit of energy in MeV natural unit of length natural unit of mass natural unit of momentum natural unit of momentum in MeV/c natural unit of time natural unit of velocity neutron Compton wavelength neutron g factor neutron gyromagnetic ratio neutron gyromagnetic ratio in MHz/T neutron magnetic moment neutron magnetic moment to Bohr magneton ratio neutron magnetic moment to nuclear magneton ratio neutron mass neutron mass energy equivalent neutron mass energy equivalent in MeV neutron mass in u neutron molar mass neutron relative atomic mass neutron to shielded proton magnetic moment ratio neutron-electron magnetic moment ratio neutron-electron mass ratio neutron-muon mass ratio neutron-proton magnetic moment ratio neutron-proton mass difference neutron-proton mass difference energy equivalent neutron-proton mass difference energy equivalent (MeV) neutron-proton mass difference in u neutron-proton mass ratio neutron-tau mass ratio Newtonian constant of gravitation Newtonian constant of gravitation over h-bar c nuclear magneton nuclear magneton in eV/T nuclear magneton in inverse meter per tesla nuclear magneton in K/T nuclear magneton in MHz/T Planck constant Planck constant in eV/Hz Planck length Planck mass Planck mass energy equivalent in GeV Planck temperature Planck time proton charge to mass quotient proton Compton wavelength proton g factor proton gyromagnetic ratio proton gyromagnetic ratio in MHz/T proton magnetic moment proton magnetic moment to Bohr magneton ratio proton magnetic moment to nuclear magneton ratio proton magnetic shielding correction proton mass proton mass energy equivalent proton mass energy equivalent in MeV proton mass in u proton molar mass proton relative atomic mass proton rms charge radius proton-electron mass ratio proton-muon mass ratio proton-neutron magnetic moment ratio proton-neutron mass ratio proton-tau mass ratio quantum of circulation quantum of circulation times 2 reduced Compton wavelength reduced muon Compton wavelength reduced neutron Compton wavelength reduced Planck constant reduced Planck constant in eV s reduced Planck constant times c in MeV fm reduced proton Compton wavelength reduced tau Compton wavelength Rydberg constant Rydberg constant times c in Hz Rydberg constant times hc in eV Rydberg constant times hc in J Sackur-Tetrode constant (1 K, 100 kPa) Sackur-Tetrode constant (1 K, 101.325 kPa) second radiation constant shielded helion gyromagnetic ratio shielded helion gyromagnetic ratio in MHz/T shielded helion magnetic moment shielded helion magnetic moment to Bohr magneton ratio shielded helion magnetic moment to nuclear magneton ratio shielded helion to proton magnetic moment ratio shielded helion to shielded proton magnetic moment ratio shielded proton gyromagnetic ratio shielded proton gyromagnetic ratio in MHz/T shielded proton magnetic moment shielded proton magnetic moment to Bohr magneton ratio shielded proton magnetic moment to nuclear magneton ratio shielding difference of d and p in HD shielding difference of t and p in HT speed of light in vacuum standard acceleration of gravity standard atmosphere standard-state pressure Stefan-Boltzmann constant tau Compton wavelength tau energy equivalent tau mass tau mass energy equivalent tau mass in u tau molar mass tau-electron mass ratio tau-muon mass ratio tau-neutron mass ratio tau-proton mass ratio Thomson cross section triton g factor triton magnetic moment triton magnetic moment to Bohr magneton ratio triton magnetic moment to nuclear magneton ratio triton mass triton mass energy equivalent triton mass energy equivalent in MeV triton mass in u triton molar mass triton relative atomic mass triton to proton magnetic moment ratio triton-electron mass ratio triton-proton mass ratio unified atomic mass unit vacuum electric permittivity vacuum magnetic permeability von Klitzing constant W to Z mass ratio weak mixing angle Wien frequency displacement law constant Wien wavelength displacement law constant

81018: 1. Planck length: 1-202 2. Planck Time: 1-202 3. Planck Mass: 1-202 4. Planck temperature: 1-202 5. Speed of light in vacuum: 1-202 6. Josephson constant 7. Fine-structure constant 8. …we have a long way to go. .. Yes, all the way to 354! _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________

What is the path from a dimensionless physical constant to a fundamental physical constant? What is dimensional analysis? See the Buckingham π theorem and nondimensionalization and natural units and system of measurement.

What are the dimensionless physical constants?

What is the hierarchy problem?

Planck units use the gravitational constant G  (a constant of proportionality) measured in a laboratory to just four digits. The modern notation of Newton’s law involving G was introduced in the 1890s by C. V. Boys. The first implicit measurement with an accuracy within about 1% is attributed to Henry Cavendish in a 1798 experiment