The temporalist model results from the assumption of the fundamental asymmetry of time.

The temporalist model proposes a modification of the characteristics of the photon, during its propagation, without external interaction. This modification appears by a redshift due to the existence of the temporalist constant To.

The search of constant To (restrictive constant) leads us to bring it closer to c (restrictive constant of speeds) and G (standard of the coupling between the masses - Newton - or the masses and the energy and the curve of the metric field - Einstein). Not unlike these fundamental physical constants which form the borders of our physical universe, the temporalist model conceives the temporalist parameter To like another stop of nature : the stop of time is added to the speeds, actions, electric charges, gravitational interactions stop. This stop of time that we indicated under the term of temporalist constant or constant To, we define it as the border of times, as c is the border speeds, h that of the actions, etc...

If the temporalist assumption is exact, the parameter To, quantum parameter, must appear in the quantum phenomena. It is what we checked in a certain number of quantum phenomena:

3) The factor of proportionality of the potential of braking of the photoelectric effect is equal to 1 / To and one finds in this quantum effect the presence of the temporalist constant.

The redshift of the remote galaxies is interpreted, in the theory 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 temporalist effect, a quantum phenomenon, temporal and noncosmological 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 the temporalist effect, the redshift z and the " escape effect " of the galaxies according to their distance to the observer (or of the time of course of radiation T):

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 worth 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.

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 ).

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

In the temporalist model :

The temporalist shifts at the temporalist durations are identical to the relativistic shifts at the relativistic speeds. The essential difference between the relativistic shift and the temporalist shift wavelengths comes from the origin of the shift. On one side, a factor external with radiation, on the other, the temporalist quantum effect intern 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.It would be nevertheless hazardous to affirm that the limits of the observable universe coincide with those of the universe.

How does the temporalist model interpret the phenomenon of gravitation ?

In the temporalist model, the masses and energy are not any more, as in the classical theories of the gravitation, the sources of the (gravitational or metric) fields. The masses and energy are regarded as disturbing parameters of the universal potential of acceleration. The vectors of this universal potential of acceleration, particles X, can be compared to gravitons. The masses and energy, by shielding effect (diffusion or absorption), disturb the temporalist isotropic and balanced field whose potential, in the absence of masses, must be regarded as a potential of acceleration of value G' (temporalist constant of gravitation). The presence of matter and energy exerts a dissymmetrical action on this potential of acceleration by the shielding effect which it produces on the propagation of particles X or gravitons. It is the modification of the potential of acceleration by the disturbing effect of the masses and energy which appears with the observer like a gravitational phenomenon (newtonian theory) or a curve of four-dimensional space (relativistic gravitation). This modification of the isotropic field of acceleration by the masses and energy thus appears as a dissymmetrical field of force which attracts the masses or a curve of the four-dimensional metric field.

In the classical theories of the gravitation, the gravific interaction has an infinite range. In the temporalist model, it cannot any more be so. The range of disturbance of gravific field of gravitons by the mass is limited by the value of universal field of acceleration be G', the temporalist constant of gravitation (6,582 x 10^-10 m/sec² in the S.I or 6,582 x 10^-8 cm/sec² in the cgs system). In other words, if the intensity of disturbance brought by the shielding effect of mass with universal field of acceleration is lower than G', the disturbing action of those ones will not be felt any more.The temporalist gravitation has thus a limited range.

The temporalist gravitation thus imposes on the concentrations matter in the universe a higher space limit given by the approximate formula r = m½. It is the ray of gravitation of the masses. This restriction is specific to the temporalist gravitation. It does not apply to the other theories of the gravitation since, in those ones, the range of the gravitation is infinite.

For more than 20 years a problem has intrigued the planetary scientists and physicists " a tiny, unexplained sunward acceleration in the motions of the Pioneer 10, Pioneer 11, and Ulysses spacecraft " (www.geocities. com/solarstormmonitor/Pioneer.html).Many other sites on the Web bring information on this subject.

This anomalous acceleration has several characteristics:

1) Its value, according to authors', would be of 7,59 x 10^-8 cm/sec^2 (http://renshaw.teleinc.com/papers/prl-pi/prl-pi.stm),

8,74 (+or - 1,33) x 10^-8 cm/sec^2 (http://csep10.phys.utk.edu/newsgroups/mond/messages/22.html),

" about 10 billion times smaller than the acceleration we feel from Earth' s gravitational pull " (www.geocities. com/solarstormmonitor/Pioneer.html - http://spaceprojects.arc.nasa.gov/Space_Projects/pioneer/PNStat.html).

2) The order of magnitude of this anomalous acceleration is c x Ho (Hubble constant).

3) This anomalous acceleration, independent of the distance, is constant for a spacecraft velocity.

4) This anomalous acceleration is radial.

This unexplained effect resulted very precisely from the universal temporalist isotropic field of acceleration G' = c / To with G' temporalist constant of gravitation, c speed of the light and To temporalist constant is 6,582 x 10^-8 cm/sec^2 = 2,997925 x 10^10 cm/sec / 4,5546 X 10^17 sec.

The temporalist model proposes:

1) The order of magnitude of this anomalous acceleration c x Ho (Hubble constant) corresponds to the temporalist model with c / To (Ho = 1/To) = G '.

2) When the spacecrafts leave a circular or elliptic trajectory to take a radial trajectory directed out of the solar system, the influence of the universal temporalist field of acceleration appears and slows down the speed of the spacecrafts (Pioneer 10, Pioneer 11, Ulysses, Galileo, etc...).

3) The universal temporalist field of acceleration does not disturb the circular or elliptic orbits of the planets of the solar system but only the radial trajectories.

4) An experimental measurement validates the temporalist model. In September 1998, the slowing of the speed of Pioneer 10 had led to a delay on its envisaged trajectory of approximately 400.000 km. The radial trajectory of Pioneer 10 started between 1973 and 1974 had thus lasted approximately 24,5 years is 7,73 x10^8 sec. The deceleration for this duration with a constant of acceleration of 6,582 x 10^-8 cm/sec^2 is equal to 6,582 x 10^-8 cm/sec^2 x 7,73 x 10^8 sec x 7,73 x 10^8 sec = 3,93293 x 10^10 cm = 393293 km.

We can calculate, for the well-known concentrations of matter, from the earth planet to the greatest structures of the universe, the theoretical ray of gravitation, with finished range, and confront it with the observed dimensions of these various masses (in the cgs system).

One notes that, in accordance with the requirements of the temporalist model, the concentrations of matter, from the earth to the greatest structures, are, in order of magnitude, equal or lower than the rays of gravitation. The dimension of the voids, about 10.26 cm and more, is also explained by the lower ray of gravitation of the superclusters of galaxies of about 10.25 cm.

The classical theories of the gravitation for which the range of the forces is unlimited, just as the Hot Big Bang, can give an account neither of the preceding results nor of their precision. The universe is structured at intervals of distribution in three dimensions as in a chess-board. These structures, which are not to be understood in the preceding models, rise naturally from the finished range of the rays of gravitation specific to the model of temporalist gravitation.

The major arguments of the temporalist model which we propose can be summarized in three groups:

1) The existence of the temporalist quantum constant To and his consequences.

2) Whereas the model of Hot Big Bang spent decades to reach the current value of the constant Ho of Hubble (approximately 72 Km/sec/Mpc) with experimental measurement of more than 153.000 redshifts (data base IPAC of NASA 2001), the temporalist model theoretically established, in 1962, the value of the temporalist effect or "escape effect " of the galaxies with 67,71 Km/sec/Mpc. 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 ).

3) The temporalist model implies and proposes a modification of the gravitation. The temporalist model of gravitation proposes a detailed and coherent explanation of dimensions of the structures of the universe, from the field of terrestrial gravitation to the greatest structures of several hundreds of megaparsecs (as well as voids of comparable dimensions). The model of Hot Big Bang notes these structures but is impotent to give any account of it.

The numerous theoretical difficulties of the model of Hot Big Bang disappear in the temporalist model. It is necessary to underline a significant element which changes all in the analysis of the phenomena, the existence of a macroscopic unbounded time and its consequences.

The temporalist model results from a simple postulate, that of the asymmetry of time and its application to the physics of the photon. From there rises, without other assumption, the existence of the temporalist quantum constant To and its quantum consequences (electric charge, photoelectric effect, constant of fine structure, etc...), the redshifts, the quantum constant of gravitation G', the temporalist gravitation and his model of formation of the structures of the universe.

The temporalist model endeavours to avoid any speculation which cannot be checked by the facts (Popper 1934). It thus proposes a certain number of observations and experiments likely to confirm it or to contradict it, the ones founded on space, the others on time. Certain observational facts or tests seem likely to decide between the temporalist model and the model of Hot Big Bang.

The temporalist model proposes a universe very different from the expanding universe of Hot Big Bang :

The universe does not know an expansion and is relatively stationary.

The universe knew neither primordial explosion, neither inflation phase, neither primordial nucleosynthesis, nor emergence of time, space and energy.

The universe does not have critical density.

The universe does not have a cosmological constant.

The universe exists. It did not have a beginning and will not have any end.

The temporalist constant To is a quantum and nonmacroscopic constant.

There are nevertheless a temporalist horizon, a stop, imposed by the existence of constant To and the redshift of radiations.

There is not an age of the universe but macroscopic lifespans (of stars, galaxies, structures on a large scale, etc...) which can possibly exceed the value of constant To: 4,5546 10.17 sec.

The universe, spatially, does not have limits. The visible universe is limited by the temporalist horizon.

The gravitation has a finished range, proportional to the masses. The rays of gravitation determine dimensions and the distances from the structures of the universe (galaxies, clusters, voids, etc...).

The universe is relatively stationary in space but evolutionary in time.

The dark matter (or missing matter) is estimated from 90 to 99 % of the total matter. One as well detects it in the galaxies, the galaxies clusters, as in the greatest structures of the universe. Many candidates were proposed (MACHOs, neutrinos, WIMPs, brown dwarf stars, supermassif black holes, etc...) but, for the moment, its nature remains unknown.

Which are the currently known characters of the dark matter ?

1) the dark matter follows mainly the luminous matter in its localization in the galaxies, the galaxies clusters and even the great structures of a few ten of megaparsecs

2) the dark matter follows the irregularities of density of distribution of luminous matter in all the visible universe

3) the dark matter represents of 10 with 100 times the mass of luminous matter

4) the dark mass does not exist or is not perceptible in the large voids of several ten with several hundred of megaparsecs (Richard Schaeffer 2001)

We propose the identification of temporalist field of acceleration with dark matter. We indicate below the arguments in favour of our proposal:

1) the temporalist field emanating from the photons, therefore sources of light, corresponds well to the space distribution of the dark mass

2) the temporalist field, because of its origin, follows necessarily the irregularities of the density of distribution of luminous matter in all the visible universe

3) the temporalist field, according to the temporalist model, emanates from the damping of the vibrations of the photons and thus of a continual loss of energy (redshift). The fact that the percentage from 90 to 99 % of dark matter is located in the universe near the sources of light is in phase with the assumption of their temporalist origin

4) a contrario, the big cosmic voids which are not containing luminous matter, cannot thus contain dark matter

5) the temporalist field is not a hypothetical field but a field which necessarily rises from the temporalist model

6) the temporalist field, whose vectors are gravitons, is not a luminous field

The temporalist model proposes a physical universe structured by three normative constants which constitute the borders of our world: h, c and To. The relations between these fundamental universal constants generate all the richness of the physical universe.