The redshift of the remote galaxies is interpreted, in the model of Hot Big Bang, like a Doppler effect or a cosmological effect due to the expansion of the universe. In accordance with its working hypothesis, the temporalist model interprets it like a quantum phenomenon, temporal and non-cosmological and spatial. According to the temporalist model, redshift z of the photons which travel in space is the result (apart from any external interaction) of the influence of the asymmetry of time, or of the temporalist constant To, on the parameters of the photons.

One can illustrate redshift z or temporalist effect or " escape effect " of the galaxies according to their distance to the observer (or of the time of course of radiation):

z = vr/c (in the Doppler or cosmological effect) = t/To (in the temporalist effect).

In the Doppler or cosmological effect, the speed of recession is vr = z x c. For a redshift of 200 angströms of a radiation of 4000 angströms, one obtains: 200 / 4000 x 2,997925 10.8 m/sec = 1,4989 10.7 m/sec = 14.989 Km/sec.

In the temporalist model, t = z x To = 200 / 4000 x 4,5546 10.17 sec = 2,2773 10.16 sec and the escape effect vr = c x t/To = 2,997925 10.8 m/sec x 2,2773 10.16 sec / 4,5546 10.17 sec = 1,4989 10.7 m/sec = 14.989 Km/sec.

One can calculate the " escape effect " for a few significant durations:

For 1 second: 2,997925 10.8 m/sec x 1 sec / 4,5546 10.17 sec = 6,582 10-10 m/sec = 6,582 10-8 cm/sec.

For one year: 2,997925 10.8 m/sec x 3,155 10.7 sec / 4,5546 10.17 sec = 2,077 10-2 m/sec = 2,077 cm/sec.  

For a duration corresponding to a distance from 1 Mpc: 2,997925 10.8 m/sec x 10,287 10.13 sec / 4,5546 10.17 sec = 6,771 10.4 m/sec = 67,71 Km/sec.

According to the temporalist assumption, the existence of the quantum temporalist constant To appears, as of the emission of a photon, by a redshift of its wavelength, without external intervention. The temporalist model challenges the need thus, to explain the redshifts of the remote galaxies, of the various cosmological models of expansion of universe (FLRW).

The redshift of the remote galaxies, interpreted in Doppler effect, are also challenged by the temporalist model. The Doppler effect z = vr / c is interpreted in the temporalist model by z = t / To with z redshift, vr radial speed, c speed of the light, t duration of translation of the photon ( or distance / c ) and To is the temporalist constant.

Whereas in the model of Hot Big Bang, the expansion starts only beyond the local system of galaxies, in the temporalist model, the redshift (or escape effect) occurs as of the emission of a photon.

If one applies to the law of Hubble v (speed in Km/sec) = Ho (in Km/sec/Mpc) x d (distance in Mpc) the escape effect for 1 Mpc, we obtain Ho = v / d = 67,71 Km/sec / 3,084 10.19 km (10,287 10.13 sec x 2,997925 10.5 Km/sec) = 2,195 10-18 sec is 1 / 4,5546 10.17 sec.

The value of the " escape effect " to 1 Mpc = 67,71 Km/sec and that of Ho = 1 / 4,5546 10.17 sec were established theoretically by the author in 1962. The last data given by WMAP ( February 2003) made it possible to fix the value of the constant Ho of Hubble at 71 Km/sec/Mpc ( with a margin of error of 5 % ) what well confirms the temporalist value of Ho is 67,71 Km/sec/Mpc. ( http://map.gsfc.nasa.gov/m_mm/mr_limits.html ).

We did not take into account, in the calculation of the redshift and the " escape effect ", of the relativistic correction. However, at the high speeds, or more precisely relativistic, i.e. close to those of the light, the redshift and the "escape effect " are different, as one notes it in the spectrum of the distant quasars. The redshift wavelength can be about several times the original value and the "escape effect " of several times c.

The relativistic correction of the redshift wavelengths and the speed of recession of the remote galaxies applies in the expanding universe. That is due to the limiting speed of the light, a postulate accepted in the model of the expanding universe just as in the temporalist model, and of the deceleration of the clocks which results from it. However, the relativistic correction could not exist in the temporalist universe because it relates to sources of light moving at relativistic speeds. In the temporalist model, in fact radiations vary and the galaxies are stationary. The " escape effect " is an apparent effect here and does not correspond to a Doppler effect at the relativistic speeds. The relativistic redshift, at the long distances, or the great durations, remains nevertheless an experimental fact. Which cannot be explained in the temporalist model by a relativistic effect since the sources of light are stationary. How can one consequently interpret it in the temporalist model ?

In the model of expansion, the redshift of wavelength z at not-relativist speeds by Doppler radial effect be give by the formula z = vr / c. c be a speed in the void that can exceed no physical speed. It is a restrictive constant. In the temporalist model, constant To is, in parallel, a restrictive constant of the durations. The redshift wavelength at the weak durations is given by the formula z = t / To .

At the relativistic speeds, the relativistic relation of the radial Doppler effect is given by the formula:

The constant To corresponding to one limiting duration like c at a speed limit, at long durations, the redshift must be given by a different formula of z = t / To. The temporalist constant playing with respect to time the same limiting role of stop as constant c with respect to speed, the redshift wavelength at temporalist durations (approaching 4,55456 x 10 ^ 17 sec) must be given by a formula similar to that of relativity, speeds being replaced by times:

Interpreted as a Doppler effect, the redshift is regarded as a recession of the galaxies whose value depends on that of the constant of Hubble Ho according to the equation :

v = Ho D (4)

With v speed of recession, Ho Hubble constant and D distance of the galaxy.

We saw, a little earlier, than the redshift by Doppler effect z = v / c is interpreted in the temporalist model by z = t / To with z redshift, v radial speed, c speed of the light, t duration of translation of the photon (or distance / c) and To temporalist constant from where one draws :

z = v / c = t / To and v = ct / To (5)

If one applies this equation (5) to the equation (4), one obtains :

v = Ho x D = ct / To and like D = ct, one obtains v = Ho x ct = ct / To

From where one draws :

According to the temporalist model, the redshift is thus due to the existence and the influence of the quantum constant temporalist To = 4,55465 x 10^17 sec. The "pseudo-velocity of recession" of the galaxies is only one "escape effect" interpreted like a Doppler effect. The quantum temporalist constant To gives of it the theoretical value which is precisely that wich is measured in the observations of the redshifts of the remote galaxies.

One can thus calculate the "pseudo-velocity of recession" of the galaxies at a distance of 1 Mpc, according to the equation (4) :

v = Ho D = 2,997925 x 10 ^ 10 cm/sec x 10,287 x 10 ^ 13 sec / 4,55465 x 10 ^ 17 sec. = 6,771 x 10 ^ 6 cm/sec = 67,71 Km/sec/Mpc.

In 1929, estimated by Hubble at 500 Km/sec/Mpc, the "pseudo-velocity of recession" of the galaxies converges today (after decades and more than 153.000 observations of redshifts by NASA) towards the value of 67,71 Km/sec/Mpc established theoretically in 1962 by the author. This theoretical value was obtained by purely physical considerations, independently of all given astronomical data, wich consolidates its validity.

The temporalist redshifts at the temporalist durations are identical to the relativistic redshifts at the relativistic speeds. The essential difference between the relativistic redshifts and the temporalist redshifts wavelengths comes from the origin of the redshifts. On one side, a factor external with radiation, on the other, the temporalist quantum effect interns with radiation.

The new explanation of redshift z of the remote galaxies proposed by the temporalist model has naturally considerable cosmological implications.

With the distance of 14,43 billion light-years, after temporalist correction, the wavelength and the "escape effect " become infinite, which implies a cut in observable space. Beyond this limit, the universe which, physically, continues in space, is not accessible any more for us. It is the temporalist horizon. In the model of expansion of the universe, one leads to a cosmic horizon of the same order of magnitude but this horizon is space kind whereas the temporalist horizon is time kind. The universe has no limits, for the observer, only those imposed to him by the redshift wavelengths of the electromagnetic waves induced by the temporalist constant that is to say 4,55456 10.17 sec in time and approximately 13,65 10.25 m in space. It would be nevertheless hazardous to affirm that the limits of the observable universe coincide with those of the universe.

In short, the redshifts of the remote galaxies is a quantum phenomen which rises from the temporalist parameter To and not a cosmological macroscopic phenomenon leading to a model of expansion and Big Bang.

The temporalist model ends naturally, without another assumption, to the proposal for a gravitation with finished range ( chapter 9 ).

The chapter 10 validates, for masses going from that of the earth to those of the greatest structures of the universe (superclusters of galaxies, larges voids, etc...) to the relation between the masses and their ray of gravitation.

The temporalist model proposes an universe without beginning or end with many consequences. It makes it possible to solve many problems arising from the model of the Big Bang. It proposes a series of precise tests likely to confirm it or invalidate it (chapter 11).

We will see in the conclusions that the paradox of Olbers as well as of many difficulties of the model of Hot Big Bang find their natural solution in the optics of a temporalist universe. This one is presented, cosmologically, like a space universe relatively static but temporally, dynamics and evolutionary.