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Physical and Cosmological Constants: Universal Numbers at the Origin of Everything

Why Does Physics Have Constants?

The existence of constants 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 may have set the values of the constants, which then influenced the evolution and structure of the universe as we know it. Some theorists propose the idea of a multiverse, where our universe is just one of many possible realities. In this context, the constants could vary from one universe to another, and our universe possesses the values that allow the emergence of life and conscious observers.

Regarding our material world, the constants of physics are "fixed" values that determine the fundamental properties of the universe as a whole, from the very small to the very 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. They help maintain the coherence of physical laws and 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 allow experiments to be repeated here and elsewhere, today and tomorrow, within the framework of the Universe. Therefore, constants play a central role in physical theories. Paradoxically, constants can vary over very long periods. However, this does not prevent the structuring of the domains of validity of different physical and astrophysical theories.

N. B.: 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, kilogram, and second, we define ratios (mass ratios, force ratios, etc.) to avoid calculation errors.

What Are the Constants of Physics?

1. (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.
2. (e) Elementary Charge: e ≈ 1.602 × 10^-19 C. This constant is the smallest unit of electric charge carried by an electron or proton. It was defined between 1777 and 1785 by the French physicist Charles-Augustin de Coulomb (1736-1806) during experiments on electrical interactions between charges.
3. (kₑ) Electric Constant: kₑ ≈ 8.988 × 10^9 N·m²/C².
   This constant defines the electric force between charges in a vacuum. It was defined in 1785 by the French physicist Charles-Augustin de Coulomb (1736-1806).
4. (ε₀) Vacuum Permittivity: ε₀ ≈ 8.854 × 10^-12 F/m.
   This constant describes the intensity of the electrical interaction between charges in a vacuum, i.e., the capacity of the vacuum to allow the propagation of electric fields. It was defined by the British physicist James Clerk Maxwell (1831-1879).
5. (c) Speed of Light in Vacuum: c ≈ 299 792 458 m/s.
   This constant is the maximum speed at which information or energy can propagate in the universe. It was defined with great precision between 1881 and 1887 by Albert Abraham Michelson (1852-1931) in his experiments measuring the speed of light using interferometers.
6. (h) Planck 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) in the context of his work on blackbody radiation.
7. (α) Fine-Structure Constant: α ≈ 1/137.
   This constant characterizes the electromagnetic force and measures the intensity of electromagnetic interactions between charges. It was first introduced in 1916 by the English physicist Arnold Sommerfeld (1868-1951) and calculated with precision by physicists such as Richard Feynman (1918-1988) and others.
8. (mₑ) Electron Rest Mass: mₑ ≈ 9.109 × 10^-31 kg.
   This constant is the intrinsic mass of an electron at rest. It was introduced by Albert Abraham Michelson (1852-1931) and Edward Williams Morley (1838-1923), who conducted interferometry experiments to measure the Planck constant (h) and the speed of light (c) with great precision, allowing for a more precise calculation of the electron's rest mass (mₑ).
9. (Nₐ) Avogadro Constant: Nₐ ≈ 6.022 × 10^23 mol^-1.
   This constant links the amount of substance to the number of particles. It was proposed and introduced in 1865 by the Italian scientist Amedeo Avogadro (1776-1856).
10. (σ) Stefan-Boltzmann Constant: σ ≈ 5.67 × 10^-8 W/m²K^4.
    This constant describes the energy flux radiated by a black body as a function of its temperature. It was defined in 1879 and 1884 through the joint work of the Austrian physicist Josef Stefan (1835-1893) and the German physicist Ludwig Boltzmann (1844-1906).
11. (k) Boltzmann Constant: k ≈ 1.381 × 10^-23 J/K.
    This constant relates thermal energy to temperature. It was established by the German physicist Ludwig Boltzmann (1844-1906) in the context of his work on entropy.
12. (mₚ) Planck Mass: mₚ ≈ 2.176 × 10^-8 kg. This constant determines how physics operates at extremely high energies and small spatial scales. It was introduced in 1900 by the German physicist Max Planck (1858-1947) in his research on the thermodynamics of black bodies.
13. (Λ) Cosmological Constant: Λ ≈ 2.3 x 10^-18 s^-2.
    This constant is related to dark energy and the accelerated expansion of the universe. It was introduced in 1917 in the equations of general relativity by Albert Einstein (1879-1955).
14. (mₚ) Proton Mass: mₚ ≈ 1.672 × 10^-27 kg.
    This constant defines the mass of a proton, a constituent of atomic nuclei. Precise measurement of the proton mass was made possible by experiments conducted in particle physics and nuclear physics laboratories around the world.
15. (mₙ) Neutron Mass: mₙ ≈ 1.675 × 10^-27 kg.
    This constant defines the mass of a neutron, also a constituent of 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.
16. (αₛ) Strong Coupling Constant: αₛ ≈ 1.
    This is the constant of strong interaction that holds protons and neutrons together (strong interaction between quarks and gluons). It was defined in the early 1970s when quantum chromodynamics was developed by several scientists.
17. (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 has spanned several decades and involved numerous experiments worldwide.
18. (G_F) Fermi Constant: G_F ≈ 1.166 × 10^-5 GeV^-2.
    This constant is used to describe weak interactions between subatomic particles. It was introduced by the Italian physicist Enrico Fermi (1901-1954) in his theory of weak interaction.
19. (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.
20. (u) Atomic Mass Constant: u ≈ 1.660 × 10^-27 kg.
    This constant is used to express atomic masses in atomic mass units (one-twelfth of the mass of a carbon-12 atom). It was defined by the International Union of Pure and Applied Chemistry (IUPAC) in 1961.
21. (λₑ) Compton Wavelength: λₑ ≈ 2.43 × 10^-12 m.
    This constant (lambda e) describes the scattering effect of particles due to electromagnetic forces. The Compton wavelength 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) in his research on the scattering of X-rays and light by charged particles.

What Have the Constants Allowed Us to Verify?

Fundamental constants have played a crucial role in verifying scientific theories and physical models. They have confirmed that the absorption spectrum of different elements has remained unchanged for about 10 billion years.

• The speed of light in vacuum (c) and the Planck constant (h) were essential in validating the predictions of Einstein's theory of special relativity, particularly the effects of time dilation and length contraction at speeds close to the speed of light.
• The universal gravitational constant (G) was used to test the predictions of Einstein's theory of general relativity by observing the bending of light around massive objects and the properties of black holes.
• Constants such as the elementary charge (e), the electron mass (m_e), and the Planck constant (h) have allowed us to validate the predictions of quantum mechanics regarding the behavior of subatomic particles.
• The electric constant (k_e) and the fine-structure constant (α) were used to verify the predictions of quantum electrodynamics, particularly atomic spectra and interactions between charged particles.
• The strong (α_s) and weak (G_F) coupling constants were crucial in confirming the predictions of strong interactions (nuclear force) and weak interactions (responsible for beta decay).
• The mass constants of particles, such as those of the electron, proton, and neutron, have allowed us to verify the models of particle physics, notably the Standard Model.

In summary, physical constants have served as the foundation for validating scientific theories. They have allowed us to build a coherent framework for explaining and predicting a wide range of phenomena observed in the universe, from the very small to the very large.

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