The Speed of Light and the Fine‐Structure Constant

Abstract

The fine structure constant α includes the speed of light as given by α = e 2 4πε 0 c . It is shown here that, following a T Hεµ formalism, interpreting the permittivity ǫ0 and permeabiliy µ0 of free space under Lorentz local and position invariance, this is not the case. The result is a new expression as α = e 2 4π in a new system of units for the charge that preserves local and position invariance. Hence, the speed of light does not explicitly enter in the constitution of the fine structure constant. The new expressions for the Maxwell's equations are derived and some cosmological implications discussed.La constant de la structure fine insére aussi la vitesse de la lumière en accord avec la formula α = e 2 4πε 0 c . On démontre avec ce travail que, suivant le formulisme T Hεµ et interprétant la permitivité ε0 et la pérmeabilité µ0 du vide selon l'invariant de Lorentz local et de position, cette formula n'est pas l'adéquate. La nouvelle expression es α = e 2 4π . dans un système d'unités neuf pour la chargeélectrique, système qui préserve l'invariant local et de position. Par conséquent, la vitesse de la lumière ne rentre pas dans la constitution du constant de la structure fine. On deduit les nouvelles expressions deséquations de Maxwell et on débat certaines inplications cosmologiques.

Non-expanding universe: a cosmological system of units

“…This equality ensures that the Einstein-Hilbert field equations can be derived from the action principle, Alfonso-Faus [1]. If we take now as the cosmological unit of length the size of the universe ct ≈ 10 28 cm, the cosmological "quantum" of length, then Planck´s constant for the quantum world is the square of the ratio of ct to the Planck´s unit of length L = ct ≈ 10 28 cm = 1 ђ ≡ (ct) 2 c 3 /Gђ ≈ 1/10 122 (6) and from (1), (2) and (6) we get for the cosmological quantum of electrical charge Q ≈ 3.3 10 61 e = 1 (7) This is the same value as has been obtained elsewhere, Alfonso-Faus [7], where we have found equilibrium in the plasma state of the universe with charge (7) pushing outwards against the inward gravitational force. The Debye length of this plasma is a bit larger than the size L in (6).…”

Entropy in the Universe: A New Approach

“…There is another important interpretation for the meaning of the gravitational cross section. In units of the square of Planck's length l * = (G!/c 3 ) 1/2 one can define a gravitational entropy, S mg /k for any mass m, where k is the Boltzmann constant Alfonso-Faus [1] (note that in this paper A e = σ g here):…”

“…Hence the entropy so defined is about the number of time intervals !/mc 2 contained in the age of the Universe t. It is the number of "tics" the particle has undergone during its age. It can be interpreted as the number of gravity quanta emitted (see Alfonso-Faus [1]) during the age of the Universe. For an elementary particle this entropy today is about 10 41 .…”

“…The definition of entropy for any mass m given in this work is just the number of gravity quanta emitted by this mass during the age of the Universe. The mass m 1 of a gravity quantum is given by Alfonso-Faus [1]…”

Entropy In the Universe: A New Approach

“…Here we have a Machian definition of the gravitational cross section for a mass m. It is given by the product of its gravitational radius Gm/c 2 times the size of the Universe R. Since the size of the Universe R is of the order of its gravitational radius GM u /c 2 , where M u is he mass of the Universe, one has that the square root of the gravitational cross section of m (its "gravitational size" λ g as presented by Alfonso-Faus [1]) is of the order of the geometrical mean of two gravitational radii: the gravitational radius of the mass m and the gravitational radius of he Universe:…”