10.-COSMOLOGICAL REDSHIFT

The light that is received of the distant galaxies suffers a displacement to the red one of cosmological origin. The mechanism that produces this displacement to the red one, according to the classic Cosmology, he remains explained by means of the application of the theory of the General Relativity to the Universe. In the section of interesting link, there can consult the web site "Cosmologia", in it is possible to read an extensive description of the above-mentioned mechanism. Since summary it is possible to say here that this stretching of the waves lengths of the photons that are received owes to the expansion of the space - time suffered by the whole universe during the trip of the above mentioned photons.

The model Living Universe provides another alternative explanation that, since one will see, is more than agreement, curiously, with the Einstein's original idea on the universe.

In the epigraph 5, we were obtaining an expression (6.4) that applied to the photons it was making clear the diversion that they suffer on having crossed a gravitational field. This expression we prune to apply to any particle in same circumstance. In these cases the speed of the particle already will not be c but v, the expression 6.4 will stay like:

v² = v₂² + 2 G M / r - c² r²/ R_h²     (10.1)

The speed that we observe is v₂, for example, in the surface of the Earth a particle in rest would have v₂ =0, and if we despise the cosmological term we obtain:

v² = 2 G M / r      (10.2)

The expression of γ for this particle would be γ = (1 - 2 G M / c² r)^1/2, in complete agreement with the experience. The speed v that is indicated in 10.2 applied to a light source will do that this one suffers the effect Doppler, in this case it would be an effect gravitational Doppler, if it is observed from a system in rest, that is to say, with v = 0, one geostationary satellite, for example.

We apply now (10.1) to the case of the observation of a distant galaxy. In this case, the gravitational term is despicable, we would obtain:

v² = v₂² - c² r²/ R_h²     (10.3)

In this point it is necessary to discuss that can represent the speed v; in case of an immersed particle in a gravitational field, we might assign v = 0 to his condition of movement in free fall, a speed would be observed v₂² = -2 G M / r, that is to say, the escape velocity. We prune to suppose that in case of the distant galaxy, the speed v of any body in free fall in the gravitational field of the universe is the speed with regard to the uniform background of microwaves. In case of the Earth, according to measurements, it is of 600 Km/sg approximately, we prune to suppose that the rest of object of the universe they have a speed of the same order. This speed is also despicable with regard to the cosmological term, it will stay therefore:

v₂² = c² r²/ R_h²     (10.4)

This it is the same speed that they contemplate the models of classic universes, nevertheless, in this case is justified to use the expression of the relativity Doppler shift to calculate the cosmological redshift:

γ = (1 - r²/ R_h² + r²/ R_h²)^1/2 = 1

λ_o / λ_e = γ / ( 1 - r/ R_h ) = 1 / ( 1 - r/ R_h )    (10.5)

z = r / (R_h - r)     (10.5)

This expression of z is the same that is obtained from the application of the General Relativity, nevertheless, in this case arises from the application of the relativity Doppler effect to a light source that moves away with speed v₂ on the electromagnetic time t₂.

This speed v₂, from a quantum point of view, gives information of De Broglie's wavelength of the particle, in the limit when r tends to R_h we see that this length of wave makes to itself equal to the Compton wavelength. Does it imply a real movement? If we calculate the total energy of the particle, we prune to see that is equal to his energy in rest (γ =1), that is to say, his kinetic energy is a zero and we prune to say that a "real" movement does not exist, his of De Broglie's wavelength coincides with the Compton wavelength. This apparent expansion is analogous to the apparent contraction that is observed on the gravitational time t₁. The real expansion produces to itself on the time t₃ and, if all the particles share the same coordinate, cannot be observed directly. The Living Universe model describes, therefore, a static universe just as Einstein proposed initially. The duality of descriptions that this model provides arises in natural way of the quantum nature of the postulate proposed in the epigraph 1.

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