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Update August 25, 2023

Physical and cosmological constants

Cosmological and physical constants

Image: Absorption lines of chemical elements.
When a chemical element is crossed by white light, the colored spectrum that reaches us is dotted with black lines.
These lines are the signature of the chemical elements crossed by the light.
Thanks to these lines we can know the chemical composition of the atmosphere of a star.
For the same element, the absorption lines correspond to the emission lines (see the 2 spectra at the bottom of the image). A chemical element absorbs the radiation it is able to emit. Absorption and emission lines have the same wavelength. In other words, the black lines of the absorption spectrum of lithium correspond to the colored lines of its emission spectrum.

Why does physics have constants?

The question of why the universe has physical constants is a deep and complex question that still arouses much thought among scientists and philosophers.
Their existence could be due to the initial conditions of the universe during the Big Bang or to deep properties of fundamental reality that we do not yet understand.
Indeed, the initial conditions of the universe could fix the values of the constants which then influenced the evolution and the structure of the universe such as we know it.
Some theorists evoke the idea of a multiverse, where our universe would be only one among many possible realities. In this context, the constants could vary from one universe to another, and our universe would possess the values that allow the emergence of life and conscious observers.

As far as our material world is concerned, the constants of physics are "fixed" values that determine the fundamental properties of the universe as a whole, from the infinitely small to the infinitely large. These constants are necessary to describe and predict the behavior of physical phenomena as well as the properties of matter and energy at different scales.
These constants make it possible to maintain the consistency of physical laws and to account for the diversity of phenomena observed at different scales. They are also tools that allow us to study and test the limits of our scientific theories (Newtonian Gravitation, Special Relativity, Quantum Mechanics, Quantum Electrodynamics, General Relativity, etc.).
For modern physics to develop, it needs universal laws. These laws make it possible to repeat experiences, here and elsewhere, today and tomorrow, within a framework which is the Universe.
Constants therefore play a central role in physical theories.
Paradoxically the constants can vary over very long periods of time. But this does not prevent structuring the domains of validity of the different physical and astrophysical theories.

NB: The constants use 3 fundamental units of physics, which are the kilogram (symbol kg), the meter (symbol m) and the second (symbol s). Although, the value of a constant is intimately linked to the arbitrary value of the meter, the kilogram and the second, we rather define ratios (mass ratios, force ratios, etc.) to avoid calculation errors.

What are the constants in physics?

(G) Universal gravitational constant: G = ≈ 6.674 × 10^-11 m^3/kg/s^2.
This constant defines the gravitational force between any two masses. It was defined by the English physicist Isaac Newton (1643-1727) in his major publication "Philosophiæ Naturalis Principia Mathematica" simply called "Principia", published in 1687.

(e) Elementary charge: e ≈ 1.602 × 10^-19 C.
This constant is the smallest unit of electric charge carried by an electron or a proton. It was defined between 1777 and 1785 by the French physicist Charles-Augustin de Coulomb (1736-1806) during experiments on electrical interactions between electrical charges.

(kₑ) Electrical constant: kₑ ≈ 8.988 × 10^9 N m²/C².
This constant defines the electric force between charges in vacuum. It was defined in 1785 by the French physicist Charles-Augustin de Coulomb (1736-1806).

(ε₀) Vacuum permittivity constant: ε₀ ≈ 8.854 × 10^-12 F/m.
This constant describes the intensity of the electrical interaction between charges in a vacuum, that is to say the capacity of the vacuum to allow the propagation of electric fields. It was defined by the British physicist James Clerk Maxwell (1831-1879).

(c) Speed of light in vacuum: c ≈ 299,792,458 m/s.
This constant is the maximum speed at which information or energy can travel through the universe. It was defined between 1881 and 1887 with great precision by Albert Abraham Michelson (1852-1931) in his experiments in measuring the speed of light using interferometers.

(h) Planck's constant: h ≈ 6.626 × 10^-34 J s.
This constant relates the energy of a particle to its frequency. It was defined in 1900 by the German physicist Max Planck (1858-1947) as part of his work on black body radiation.

(α) Fine structure constant: α ≈ 1/137.
This constant characterizes the electromagnetic force and measures the intensity of the electromagnetic interactions between charges. It was first introduced in 1916 by English physicist Arnold Sommerfeld (1868-1951) and accurately calculated by physicists such as Richard Feynman (1918-1988) and others.

(mₑ) Rest mass of the electron: mₑ ≈ 9.109 × 10^-31 kg.
This constant is the intrinsic mass of the electron at rest. It was introduced by Albert Abraham Michelson (1852-1931) and Edward Williams Morley (1838-1923), who performed interferometry experiments to measure Planck's constant (h) and the speed of light with great precision. (c), which made it possible to more accurately calculate the rest mass of the electron (mₑ).

(Nₐ) Avogadro's constant: Nₐ ≈ 6.022 × 10^23 mol^-1.
This constant relates the amount of matter to the number of particles. It was proposed and introduced in 1865 by the Italian scientist Amedeo Avogadro (1776-1856).

(σ) Stefan-Boltzmann constant: σ ≈ 5.67 × 10^-8 W/m²K^4.
This constant describes the flow of energy radiated by a black body as a function of its temperature. It was defined in 1879 and 1884 thanks to the joint work of Austrian physicist Josef Stefan (1835-1893) and German physicist Ludwig Boltzmann (1844-1906).

(k) Boltzmann constant: k ≈ 1.381 × 10^-23 J/K.
This constant relates thermal energy to temperature. It was established by German physicist Ludwig Boltzmann (1844-1906) in the context of his work on entropy.

(mₚ) Planck mass: mₚ ≈ 2.176 × 10^-8 kg.
This constant determines how physics works at extremely high and small energies and spatial scales. It was introduced in 1900 by the German physicist Max Planck (1858-1947) in his research on the thermodynamics of black bodies.

(Λ) Cosmological constant: Λ ≈ 2.3 x 10^-18 s^-2.
This constant is related to dark energy and the accelerating expansion of the universe. It was introduced in 1917 in the equations of general relativity by Albert Einstein (1879-1955).

(mₚ) Mass of the proton: mₚ ≈ 1.672 × 10^-27 kg.
This constant defines the mass of a proton, constituting atomic nuclei. The precise measurement of the mass of the proton has been made possible thanks to experiments performed in particle physics and nuclear physics laboratories around the world.

(mₙ) Mass of the neutron: mₙ ≈ 1.675 × 10^-27 kg.
This constant defines the mass of a neutron, also constituting atomic nuclei. One of the most precise and influential measurements was made in 1969 by a team of physicists led by Richard Edward Taylor (1929-2018) at the University of Toronto.

(αₛ) Strong coupling constant: αₛ ≈ 1.
It is the strong interaction constant that keeps protons and neutrons together (strong interaction between quarks and gluons). It was defined in the early 1970s when quantum chromodynamics was developed by a number of scientists.

(mᵧ) Neutrino mass: (mᵧ) ≈ 1 eV/c² (very small).
This constant defines the mass of neutrinos in particle physics. The search for the neutrino mass took place over several decades and involved several experiments around the world.

(GF) Fermi constant: GF ≈ 1.166 × 10^-5 GeV^-2.
This constant is used to describe the weak interactions between subatomic particles. It was introduced by the Italian physicist Enrico Fermi (1901-1954) during his weak interaction theory.

(a₀) Bohr radius: a₀ ≈ 5.292 × 10^-11 m.
This constant defines the average size of an electron's orbit around a nucleus in hydrogen. It was defined in 1913 by the Danish physicist Niels Bohr (1885-1962) in his atomic model.

(u) Atomic mass constant: u ≈ 1.660 × 10^-27 kg.
This constant is used to express atomic masses in atomic mass units (one-twelfth the mass of a carbon-12 atom). It was defined by the International Union of Pure and Applied Chemistry (IUPAC) in 1961.

(λₑ) Compton length: λₑ ≈ 2.43 × 10^-12 m.
This constant (lambda e) describes the scattering effect of particles due to electromagnetic forces. The Compton length is a characteristic distance associated with the deflection of a particle, such as an electron, by an incident particle, such as a photon. It was defined by the American physicist Arthur Holly Compton (1892-1962) during research in the field of the scattering of X-rays and light by charged particles.

What did the constants verify?

The constants made it possible to check whether the absorption spectrum of the different elements is the same as it was 10 billion years ago.
Constants such as the speed of light in vacuum (c) and Planck's constant (h) helped confirm Einstein's special relativity predictions, including the effects of time dilation and space contraction at speeds close to that of light.
The universal gravitational constant (G) has been used to verify Einstein's predictions of general relativity, including observing the deflection of light around massive objects and the properties of black holes.
Constants such as the elementary charge (e), the mass of the electron (mₑ), and Planck's constant (h) have validated the predictions of quantum mechanics in relation to the behavior of subatomic particles.
The electrical constant (kₑ) and fine structure constant (α) have been used to verify predictions of quantum electromagnetism, including atomic spectra and charged particle interactions.
The strong (αₛ) and weak (G_F) coupling constants were crucial in confirming the predictions of the strong interaction (nuclear force) and the weak interaction (responsible for beta decay).
Mass constants of particles such as the electron, proton and neutron have been used to verify models of particle physics, including the Standard Model.

In summary, physical constants have served as the foundation for validating scientific theories and building a consistent framework to explain and predict a wide range of observed phenomena in the universe, from the infinitely small to the infinitely large.

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