3.-NEW LORENTZ TRANSFORMATIONS

Of the thesis exposed in epigraph previous it is deduced that the speed that we observed can be considered like the composition of other three defined speeds each one of them in a temporary coordinate.

A reasoning similar to the employee by Marcello Crotti in its exhibition would allow us to obtain the following expression of the factor of Lorentz transformation:

γ = (1 - v₁² /c² - v₂² /c² - v₃² /c²)^1/2

If we replaced the factors corresponding to coordinate t₁ and t₃ by their values obtained in (2.6) we arrived at the following expression:

γ= [ 1 - v₂² /c² + (r²/ R_h²) (1 - ρ(r) / ρ(R_h) ) ]^1/2      (3.1)

If in the expression (3.1) make ρ(r) = 0, that is to say, we eliminate the gravitational field we obtain the classic Lorentz transformation of the Special Relativity:

γ = ( 1 - v₂² /c² + r²/ R_h² )^1/2    (3.2)

The term r²/ R_h² is clearly worthless in a local environment and only it would be perceived in the cosmological environment.

If we make v₂ = 0 en (3.1), that is to say, we only keep in mind the gravitational field, we obtain:

γ = [ 1 + (r²/ R_h²) (1 - ρ(r) / ρ(R_h) ) ]^1/2     (3.3)

This expression if we consider the values of ρ(R_h) and R_h, that is to say, ρ(R_h) = ( (1/2) N (hbar c/ G)^1/2 ) / ( (4/3) π N³ (G hbar/c³)^3/2) y R_h² = N² (G hbar/c³), we obtain, considering ρ(r) defined in a homogeneous spherical energy distribution, the expression also classic of the General Relativity:

γ = ( 1 - 2 G M/c² r + r² / R_h² )^1/2    (3.4)

The term r² / R_h² in this expression make that γ is worth 0 when r spreads 2GM/c² and R_h it becomes sufficiently big, this justify that an universe cannot generate new black holes until it doesn't arrive to a certain age.

This model therefore would allow to formulate the theory of the Relativity in an unique way with the expression (3.1), being the Special Relativity and the General Relativity the particular cases if they are only considered the coordinate t₂ or t₁ for separate respectively. If we interpret the densities of energy as densities of probability, this expression could provide a nexus of union between the General Theory of Relativity and the Quantum Mechanics.

_{© Jorge Ales, 2002. http://www.livinguniverseweb.com}