In the document: “Is the value of the constants G and c imposed by the universe? Update 12/10/21 ″, we have defined the Planck force fp from the equation of dynamics f = m. g using Planck dimensions (Planck constant, Planck length, Planck mass and Planck time). The value found is fp = c4 / G = 1044 newtons.
Coherence between rationalism and realism
We have shown that it is this Planck force, which appears in Einstein’s equation, which ensures dimensional consistency between the left side of the equation, which is geometric in nature, and the right side, which is physical in nature.
In other words, as relativity is a geometric theory of gravitation, a theory which is a product of the mind of the physicist (rationalism), Planck’s force ensures consistency between the mind of the physicist and the physical world (realism), which gives it the status of a key paradigm for opening up access to the physical world.
We have shown that since it is independent of the value of Planck’s constant, we are entitled to consider this force as a constant of gravitation at any scale other than that of Planck (the smallest in physics ), in particular at the scale of the universe (the largest in physics) where by simple dimensional analysis we can deduce parameters of the laws.
Due to its presence in Einstein’s equation, we will find it in its solutions, in particular in the propagation of gravitational waves, reaction to a disturbance of the solution resulting from the Einstein equation, which will allow us to define an inertia of the universe
Some mysteries explained by this paradigm
At the scale of the universe, we have seen that it could explain the factor of 10122 difference between the energy of the vacuum as predicted by quantum mechanics and the cosmological constant measured by observations (SN1A, CMB, ..) supposed to govern the acceleration of the expansion.
Moreover, by considering this Planck force and the parameters of the universe (mass of the universe, age of the universe), we could deduce the values of G (gravitational constant) and c (velocity of light ) and vice versa of course!
Which would tend to prove that these constants G and c are not “arbitrary” but depend on the universe, a rather comforting idea.
Moreover, its use could clarify the problem of the incompatibility between the measurements of the Hubble constant at z <1 (SN1A for example) and those at z >> 1 by studying the CMB, because if we consider it as a paradigm then the cosmological constant is no longer constant but depends on time.
This paradigm , which provides interesting answers that are compatible with what nature reveals to us through observations, deserves to be explored even if its basis can undoubtedly be improved. See: Is the value of the constants G and c imposed by the universe? Update 12/10/21 ″ for more details.