Chapter 9
The temporalist
gravitation
The anomalous radial acceleration of
Pioneer 10
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.
We saw that the existence of constant To led,
without other assumption, to the phenomenon of the redshift
of the galaxies (chapter 8). This redshift of the
electromagnetic wave corresponds to a reduction in the frequency v or w
(angular frequency) of the photon and thus of its energy. Correlatively with redshift, one can consider, at first approximation, that
the reduction in the frequency of the photon is proportional to the duration t
which was passed between the moment of its emission Te and that of its
reception Tr is Åw = E - E'
/ E = t / To ( with E emitted energy and E' received energy ). The energy of
the photon E = hw thus varies in the
course of time and its reduction is proportional, also at first approximation, at
the duration of propagation of the photon ÅE = hwe - hwo / hwe = t / To (with hwe emitted energy and hwo observed energy).
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/
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 (
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, at first approximation, 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.
The temporalist field of acceleration can be
compared to a field of pressure whose equation with dimensions is given by p (pression) = F (force) / S (surface) is
MLT-² / L² = ML-¹T-².
Disturbing parameters, or the sources of the gravitational or metric
field, are proportional to the masses. However, the scattering cross sections
of the masses are also proportional to the masses. The barn (10-24 cm²) is the
cross section of a large core (of approximate mass 10^-24 g). We have seen in
the chapter 5 that the gm/cm^2 ratio was about equal to unity. One can thus
state a nuclear principle of equivalence between cross section
in cm² and masses in g. The nuclear density being roughly identical for all
the cores of atoms, the cross section of the atoms is, at first approximation,
proportional to their mass: M ~ L². One must nevertheless state, that the
shielding effect of the disturbing parameter of the masses depends on their
nuclear composition, the nuclear density of the cores varying slightly
according to their nuclear composition. The shielding effect of the disturbing
parameter of the masses is also proportional to the contrary square of the
distances from masses 1 / r².
One can thus assimilate, in last analysis, the disturbing effect of the temporalist field of acceleration by the masses with that
of their cross section according to M~L². By applying this value to the
equation with dimensions of the pressure, we obtain ML-¹T-² = L²L-¹T-² = LT-²
(an acceleration).
Let us compare the formulation of the force of gravitation which is
exerted between the masses m and m':
In newtonian theory, F = Gmm'
/ r² and the equation with dimensions gives F = M-¹L³T-² x M² / L² = MLT-².
In the temporalist model, F = G'mm'
/ r² and the equation with dimensions gives F = LT-² x L² x L² / L² = L³T-² and, by
applying M ~ L², L³T-² = MLT-².
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.
We can calculate it while using, at first approximation, the temporalist equation of the force of newtonian gravitation: F = G'mm' / r² is F = LT-² x L² x L² / L² = L³T-² and, by applying M ~ L², L³T-² = MLT-². For the local field of acceleration, mG' / r², we obtain L² x LT-² / L² = LT-².
The local field of acceleration, to be perceptible, must be higher than
the universal field of acceleration G'. We thus pose mG'
/ r² > G' from where mG' / G' > r² or m > r²
is r < m ½ and with equivalence M ~ L², we obtain r < L.
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.
The anomalous
radial acceleration of Pioneer 10
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 (+ - 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
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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.
Next : 10 Masses and ray of gravitation
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