The existence, in the physical universe, of constant To involves consequences in the temporalist approach of the gravitational forces or, more precisely, of the gravitational phenomenon. The author does not claim to present here a new model of the gravitation. He simply tried to show how the temporalist model has necessary implications in the interpretation of the gravitational fact.

It is equivalent to speak about redshift or reduction in frequency (or energy) of the wave since they are various aspects of the same quantum phenomenon. The value of this temporalist quantum phenomenon is very low. It is the essential reason for which quantum mechanics neither detected it nor took it into account up to now. It could not appear, in the Hubble-Humason effect, that with minimal distances from 1/2 to 1 megaparsec is minimal durations of 1 million 1/2 to 3 million years. The expansion of the galaxies appears only beyond the local Group, when it differs from local speeds of the galaxies. It is nevertheless right to say that this phenomenon of reduction in the energy of the photons which propagate in space is a continuous phenomenon, which affects all the photons, since their emission.

The existence of constant To implies an evolutionary design of the energy of the photons. Just as the neutrino " was invented " by Pauli to explain the assessments of energy in radioactive disintegrations, it seems to us rational and fertile to suppose that the loss of energy of the photons which propagate in the universe, occurs in the shape of particles emitted by the photons. There does not seem to have any other alternative which makes it possible to preserve the principle of conservation of energy, while authorizing an evolutionary concept of the physics of the photon, in agreement with the existence of constant To. We will see, by confronting this assumption with the facts, that this assumption is justified.

Therefore, stating that the assumption that the reduction in the energy of the photon (or the redshift) appears by the emergence of new particles, those we will name particles X, it results from this that from a field of particles X which we can, by convenience, indicate under the term of temporalist field. It becomes immediately obvious that the existence of this temporalist field has a considerable incidence on the gravitation.

The gravitation knew three significant stages in the history of physics: newtonian gravitation, the relativistic theory of the gravitation and the metric theories which derive from it and quantum attempts at theories of the gravitation. The model of superstrings seems to imply, in a theoretical way, the existence of a gravitational field (Brian Greene 2000).

In these three groups of theories, the gravitation is defined, either like a coupling between the masses (Newton 1687), or like a curve of the metric field by the masses and energy (Einstein 1915), or as a force of exchange between quantum fields whose vector is the graviton (quantum theory of the fields). The joint base of these various interpretations of the gravitation is the existence of a field (attractive, metric or quantum) whose intensity is given by the constant of coupling G or its einsteinian derivative 8µG/c². This constant has a contingent value, which is empirical, and does not rise from the theory. The intensity of the gravitational field is noted. It is not deduced conceptually from the theory.

In these three groups of theories of the gravitation, space, apart from the sources of fields (masses and energy or particles) is regarded as an empty space or quasi-void, apart from the quantum fluctuations. In the temporalist model, it cannot be so since the photons, feed, continuously, the temporalist field whose vector is particle X. Space is equipped with an energy level corresponding to the continual production of particles X by the photons.

How can be determined the state of energy corresponding to the existence in the space of the temporalist field ? It is here that appears the major significance and the justification of the dimension of the parameter G' which we used in chapter 5. We had formulated the assumption of a dimension LT-² (that of an acceleration) of the constant of gravitation G' in the temporalist model whereas newtonian dimension is M-¹L³T-². In newtonian theory, just as in relativistic gravitation, the constant of gravitation G is a parameter attached to the masses and energy. This parameter, as we pointed out, gives the coupling intensity between the masses or the masses (and energy) and the metric field.

The temporalist gravitation interprets differently the parameter G'. The existence of the temporalist field implies that of an energetic field in space, in the absence even of particles of matter or energy. In accordance with the cosmological principle, one can consider, on a large scale, the universe like isotropic and homogeneous. This energetic field of the temporalist field can be regarded as energy associated with the potential with gravitation with a universal gravitational field. This gravitational, homogeneous potential with an acceleration, derives from the temporalist field and either of the present masses. The bringing together of the 2 restrictive constants c and To give us his value: G' (universal constant of acceleration) x To (limit time) = c (speed limit). In the S.I, 6,582 x 10-10 m/sec^2 x 4,5546 10.17 sec = 2,997925 x 10^8 m/sec. In the cgs system, 6,582 x 10^-8 cm/sec^2 x 4,5546 x 10^17 sec = 2,997925 x 10^10 cm/sec. In dimensions, LT-² x T = LT-¹.

The parameter G' is thus, in temporalist gravitation, a constant attached to the universal and isotropic temporalist field, his dimension being that of an acceleration. G', in the temporalist model, is not attached any more to the matter, hence the disappearance of M in its equation with dimensions. G' is the potential of universal acceleration associated with the existence of the temporalist field. G', relationship between 2 quantum constants, c and To, thus seems also a quantum constant. G', temporalist constant of gravitation, is not any more an empirical parameter, contingent, calculated according to the observations. It rises, theoretically, from the relationship between 2 constants c and To.

How does the temporalist model interpret the phenomenon of the 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'. 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.

Let us compare the formulation of the force of gravitation which is exerted between the masses m and m':

In the temporalist model, one obtains, for the terrestrial field of gravitation, g = G'M / r² is LT-² x L² / L² = LT-².

The comparison between the temporalist formulation and the relativistic formulation is not currently carried out but must be conceived in the same conceptual direction.

It is well-known that the forces of gravitation or the tensors of curve of metric space are proportional to the masses (and with energy). This fact is explained logically in temporalist gravitation since the mass corresponds to the disturbing parameter of the universal isotropic gravific field. We have seen that the disturbing capacity of the mass can be assimilated, at first approximation, with that of his cross section L². The mass acts by deforming the isotropic field of acceleration and this action is all the more considerable since the mass (or its corresponding cross section L²) is significant and space considered nearer to the mass. The constant of proportionality with the distance is given by the well-known factor 1 / r².

In the classical theories of the gravitation, the gravific interaction has an infinite range. In the temporalist model, it cannot any more be thus. The range of the gravific disturbance of the field of the gravitons by the masses is limited by the value of the universal field of acceleration is G' (6,582 x 10^-10 m/sec^2 in the S.I or 6,582 x 10^-8 cm/sec^2 in the cgs system). The disturbance caused by the presence of the masses and energy on the universal field of acceleration will appear by the emergence of a local field of acceleration. This shielding or disturber effect will be perceptible only if it is higher than the universal field of acceleration. In other words, if the intensity of the disturbance brought by the shielding effect of the masses to the universal field of acceleration is lower than G', the disturbing action of those will not felt any more.The temporalist gravitation thus has a limited range.

The temporalist gravitation thus imposes on the matter concentrations 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.

5) Unlike to the traditional forecasts, all the spacecrafts and in particular Pioneer 10, which move away from the sun with a radial trajectory, will stop in galactic space when their speed is reduced to zero by the universal temporalist field of acceleration G ', if they are distant from other stars.

The temporalist model proposes that the mystery of the radial anomalous acceleration is solved, theoretically, by the temporalist model which it validates

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The MOND Theory

http://nedwww.ipac.caltech.edu.level5/Sept01/Milgrom/Milgrom_contents.html

The MOND Theory proposes that when the acceleration deduced from the Newtonian constant of acceleration Gn is lower than a°, is Gn << a°, the Newtonian theory does not apply, the parameter a° being compared to c x Ho. According to the temporalist model where Ho = 1/To, a° ~ c x Ho = c / To is 6,582 x 10^-8 cm/sec^2.

The MOND Theory is proposed like an alternative to the dark mass. The temporalist model does not deny the existence of the dark mass.When the acceleration due to a mass is lower than G', the Newtonian model does not apply any more in the MOND Theory. In the temporalist model, the Newtonian theory does not apply any more for one acceleration lower than G', like in the MOND Theory, but that is due to the finished ray of gravitation of the masses and to the universal temporalist field of acceleration G '. .

We will see, in the following chapter, if the concept of gravitation with finished range of the temporalist model is in agreement with the observations.