Into the special theory of relativity, Einstein ( 1905 ) introduced a new concept, that of indissociable space and time, four-dimensional space-time. Accordingly, time seems the fourth space dimension oriented from past towards the future, thus defining a " cone of light ". Time and space, closely mixed, constitute reference frames from which the physical phenomena are calibrated: momentum, energy, speed, etc... The physical laws are invariant by change of reference frame. The quantum physics, which integrated relativity in the quantum electrodynamics, hardly modified the relativistic concept of time. It even radicalized it, in a space direction, in the diagrams of Feynman, where the orientation past > future is not privileged any more compared to the orientation future > past (particles and antiparticles). The relations of uncertainty of Heisenberg, by correlating uncertainty on energy and uncertainty on time also do not give a specific definition of time. If einsteinian relativity emphasizes well (cone of light) the arrow of time past > future, it abolishes the concept of time for the photon. A clock moving slows down. A clock moving at the speed of the light would slow down infinitely. The photon, which moves, in the void, at the constant speed of c is, according to einsteinian relativity, immutable and is located apart from time.

In the theory of superstrings, the universe would be composed of eleven dimensions, including seven space dimensions, twisted in spaces of Calabi-Yau and four dimensions of visible space-time. In the dimension of time, the photon does not age. " At the speed of the light, time ceases passing " (Brian Greene 2000).

In last analysis, time is conceived like the fourth space dimension of the universe. The orientation past > future disappears for the photon. Asymmetry past > future is the only parameter distinguishing space dimensions from temporal dimension. This asymmetry, denied by Stephen W. Hawking is affirmed by Roger Penrose (1996). If asymmetry disappears from the concept of time, nothing distinguishes any more temporal dimension from a space dimension. A recent experiment confirmed the asymmetry of time in the strange elementary particles (PLEAR 1998). The temporalist model results from the assumption of the fundamental asymmetry of time.

Special relativity (Einstein 1905) postulates that the light (photons) moves, in the void, at a constant speed c, without modification of its parameters. The temporalist model postulates, on the contrary, that the luminous vibration diminishes, in the course of time, while being propagated in the void.

The temporalist model proposes, on the contrary, a modification of the characteristics of the photon emitted, during its propagation, without external interaction on the photon. I.e. it integrates the concept of time into the nature even of the photon. The redshift of the remote galaxies is currently interpreted like a Doppler effect due to a recession of the galaxies or a cosmological effect due to the expansion of the universe. The temporalist model notes the fact of the redshift. It does not interpret it like resulting from a well-known physical effect (Doppler, cosmological, Compton, gravitational effect, etc...). It links it to the intrinsic physics of the photon. It regards it as a quantum, structural property of the photon, due to the existence of an ignored parameter, of temporal nature, which it indicates under the term of temporalist constant To. It is this constant which affects the photon and which is the mark of the asymmetry of time. We now will seek this constant To postulated by the temporalist model.

The research of the temporalist constant To can go through various ways. Theoretical considerations on the structure of the universe can help us there, but the dimensional analysis as well. The first observation that we can make is that this parameter does not appear openly in the quantum phenomena since it was not detected up to now. One can thus say that if it exists, it is masked or ignored.

What are the great physical constants which can guide us in the research for this unknown temporalist parameter ? We retained four of them: c, h, e and G.

The searching for this constant To led to consider the ratio c / G. This is the relationship between the speed limit c of the physical phenomena, and Newton's gravitational constant G ( the intensity of the attraction of masses or, in General Relativity, the intensity of the curvature in the metric field by the masses and energy ). The ratio c / G indicates to us the maximum duration during which the attraction of the gravitation ( or the intensity of mass-energy on the metric field) can act to reach the speed limit c.

In newtonian mechanics, one obtains, in the cgs system: To = c / G is 2,99792 x 10^10 cm/sec / 6,67 x 10^-8 cm^3/gm-sec^2 = 4,494 x 10^17 sec gm/cm^2. (1)

The value of To would be of 4,494 x 10^17 sec if the gm/cm^2 ratio was about equal to unity.

Or

To = ( c / G ) ( An / Mn )

Where

c = 2,99792 x 10 ^ 10 cm/sec

G = 6,67 x 10 ^ - 8 cm^3/gm-sec^2

Mn = 1,67 x 10 ^ -24 gm ( mass of neutron or proton )

An = about 1,67 barn = 1,67 x 10 ^ - 24 cm ^ 2 ( Scattering cross section of neutron or proton)

The value of To would be of 4,494 x 10 ^ 17 sec if the ratio An / Mn ( cm^2 / gm ) was about equal to unity.

The gravitational interaction relates to the influence of masses ( and energy ) on the other masses or on the metric field. It occurs at the particle level, and more precisely at the level of atoms and molecules ( protons, neutrons, electrons ). It does not occur at the subatomic level of the strong nuclear forces (quarks and gluons) and thus does not enter with the framework of the QCD.

The gravitation, interaction between the masses (and energy) thus relates to, in last analysis, the nucleons (protons and neutrons) whose the atoms are formed and, beyond, astronomical masses (planets and satellites, stars, galaxies, etc...).

Hydrogen and helium are the most abundant elements in the universe :

In the sun, hydrogen represents approximatively 94 % in number of atoms and 73 % in mass and helium respectively 5,9 % and 25 %.

In the universe, hydrogen represents approximatively 85 % in number of atoms and 66 % in mass, helium respectively 13 % and 31 %.

The cross section of the nucleons (protons and neutrons) is thus fundamental in the gravitational phenomenon.

The barn 10^-24 cm^2 has the dimension of a very small surface. It is the order of magnitude of the cross section of a large core of atom. This cross section has nothing to do with the "geometrical properties" of the cores and does not have a particular relationship to their size. It is in connection with the energy of the incidental particles. In general, more energy is weak, more the cross section is large. Let us not forget that, according to quantum mechanics, the diffusion of the particles takes place in consequence of interactions of waves with other waves.

The cross sections of reactions of the proton and the neutron are very similar, once deduced the effects of the electric charge from the proton.

The bound coherent scattering cross section of the neutron by the isotope 1H (of which abundance is 99,985 %) is 1,7583 barn. For the isotope 4He (of which abundance is 99,99986 %), it is 1,34 barn. (NIST Center for Neutron Research - http://www.ncnr.nist.gov/resources/n-lenghts/list.html).

The coherent scattering cross section of the neutron by the isotope 1H, for a wavelength of 1 angstrom of 1,76 barn is confirmed in (http://www.11b.cea.fr/pedagogie/absortrayonsx/absortrayonsx.html) .

An experiment undertaken by a team of the GSI (Darmstadt, Germany) on deuterium and hydrogen targets to incidental energies of 800 Mev to 1 Gev by nucleon of gold, uranium and lead projectiles made it possible to obtain a total cross section of 1765 mb (1,765 barn) with a precision of less than 5 % "what is in connection with measurements of other teams". (http://www.google.fr/search?q=cache:bhNWEprIfqoC:wwwcenbg.in2p3.fr/extra/Noy-ex...)

Another experiment led to the GSI (Darmstadt, Germany) of interaction on a target of a halo of protons of 8Boron gives a cross section of about 1,5 barn with an incidental energy of 20 Mev/nucleon (http://wwwcenbg.in2p3.fr/extra/Noy-exotique/7Be.html).

One can estimate that the average cross section of the nucleons is equal or close of 1,7 barn.The ratio mass /cross section of the proton and of the neutron is thus about the unit: 1,67 x 10^-24 gm/1,7 x 10^-24 cm^2 ~ 1 or gm/cm^2 ~ 1 (2)

In the temporalist model, the equation (1) becomes: c / G = To is 2,99792 x 10^10 cm/sec / 6,67 x 10^-8 cm^3/gm-sec^2 = 4,494 x 10^17 sec gm/cm^2 and with gm/cm^2 ~ 1, c / G = To = 4,494 x 10^17 sec.

The Newton's gravitational constant 6,67 x 10^-8 cm^3/gm-sec^2 is thus interpreted, with gm/cm^2 ~ 1, in the temporalist model in temporalist constant of gravitation G':

G' = 6,67 x 10^-8 cm/sec^2 (3)

The equation (1) becomes, in the temporalist model:

c / G' = To is 2,99792 x 10^10 cm/sec / 6,67 x 10^-8 cm/sec^2 = 4,494 x 10^17 sec is approximately 14,24 billion years. 

It is now advisable to refine the numerical value of the obtained parameter To. It is assumed that constant To is a quantum constant. On the other hand, constant G is a macroscopic constant applying to ponderable masses. The precise measurement of G was derived from considerable masses (compared to atomic masses) with material of average density comparable with iron (Cavendish 1798 torsion balance experiment). However, quantum physics teaches us that the various atomic nuclei have a binding energy (packing-fraction of Aston) that is more or less significant and has a mass defect. The binding energy, by nucleon, for the formed cores from 30 to 120 nucleons is more than 8.5 Mev. It is approximately 9 Mev for the cores having a mass number close to 56 (Fe). The energy of a nucleon being less than one billion electron-volts (that of the proton is 938,1 Mev), the packing-fraction of Aston is thus roughly 1 % of the mass for the atomic masses close to that of iron. It is thus necessary to rectify the " macroscopic " value of G compared to the masses of the quantum particles without binding nuclear energy, electrons, nucleons, etc... As a first approximation, the " quantum " value of G is thus : G = 6,67 x 10 ^-8 cm^3/gm-sec^2 x 99/100 = 6,60 x 10 ^-8 cm^3/gm-sec^2 . We obtain for G' : 6,67 x 10^-8 cm/sec² x 99/100 = 6,60 x 10^-8 cm/sec². This give a more precise value of To : 2,99792 10^10 cm/sec / 6,60 x 10^-8 cm/sec² = 4,5423 x 10^17 sec is approximately 14,4 billion years.

Therefore, we can refine even more this value of To, according to more precise purely quantum constants,. The value of To was established by the author in 1962.

The value of the temporalist constant of gravitation G' leads to a new interpretation of the gravitation with finished range. One of the consequences is the ray of gravitation and the quantitative value of the great structures of the universe (stars, galaxies, galaxies clusters, large voids, etc...). Another consequence is the explanation and the precise value of the anomalous radial acceleration of the spacecrafts Pioneer 10, 11, Ulysses, etc...Chapters 9 and 10 describe these various aspects of the temporalist gravitation..

If the temporalist assumption is exact, the parameter To, quantum parameter, must too appear in the quantum phenomena. It is what we will try to check immediately.