Chapter 8
The redshift z - Theoretical
Prediction of the Hubble Constant Ho
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.
When a photon is
emitted by a remote source of light, an optical electron of atom in a star for
example, it is propagated in space. Its energy is characterized by its
frequency of vibration: E = h w (with E energy, h Planck constant, w
frequency). According to the temporalist model, and contrary to
the traditional formulation, the existence of constant To imposes and implies
that this energy is not stable. It evolves just like the parameters which are
linked to it. If the duration of propagation is t, the loss of energy will be
ÅE such as E - E' / E = t / To ( with E emitted energy and E' received energy
). If the photon loses energy (as in the Compton effect), one deduces from them
the modifications of wavelengths: z = y' - y / y = v
/ c = t / To ( with z redshift, y emitted wavelength , y' observed
wavelength, v speed of galaxy in the Doppler effect, c speed of light).
We will examine,
in chapter 9, the parameter of energizing variation of photon E - E' / E = t /
To and its consequences. We study here, more precisely, the redshift of the
wavelength y of the photon, implied by the existence of constant
To and such as it appears in the redshift of the remote galaxies. A photon
emitted in a remote galaxy at the moment Te is propagated in space and reaches
the observer at the Tr moment, in the reference frame related to the observer.
This photon is propagated for one length of time Tr - Te = distance from the
galaxy / c = t. The redshift of the wavelength of photon z is equal to t / To.
We note immediately that this formulation of redshift of wavelengths connect
with formulation of Doppler radial effect z = vr / c (with vr radial speed). In
the temporalist model, the variation in wavelength of a photon be proportional
with ratio between duration of propagation of photon and constant To. In the
Doppler radial effect, the variation in wavelength of photon be proportional
with ratio between the radial speed of luminous source (compared to the
observer) and the speed of light. In both cases, it is a relationship between a
parameter (duration or speed) and the restrictive physical constant of these
parameters To or c. However, in both cases, the physical significance is very
different. In the Doppler or cosmological effect, the luminous source is moving
and the wavelength of the photon, in a reference frame related to the photon
does not vary. The Doppler or cosmological effect is a space effect. In the
temporalist model, the lengthening wavelength of the photon is a temporalist
effect due to the existence of constant To. The luminous source is stationary and,
in a reference frame related to the photon, the wavelength of this one
lengthens. It consists of a temporal or temporalist effect, the lengthening of
the duration of the vibration of the photon which is propagated in space, hence
that of its wavelength.. " Reddening " temporalist, considered as a
Doppler or cosmological effect, of a space nature, is interpreted in recession
of the galaxies, hence a retrograde pseudovelocity or an " escape effect
" of the remote galaxies.
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.
Updated 2008: The value of the temporalist effect or " leak effect " at 1 Mpc 1 = 67.71 km / sec and that of Ho = 1 / 4.5546 10.17 sec (about 14.43 billion years) have been theoretically established by the
author in 1962. The latest data provided by WMAP5 (2006)
(Cosmological Parameters Summary - Chapter VI - WMAP + BAO+ SN) provide the latest values of H °: 70.1 + -1.3
km / sec / Mpc (is 68.8 km / sec / Mpc)
and t ° = 13.73 + -0.12 (is 13.85
billion years). One can see, the
latest experimental data WMAP5 (less accurate) confirm the theoretical
values (more accurate) set by the temporalist model, several decades ago. Chapter 8
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:
y' / y = 1 + v/c / (1 - v²/c²)½ = (c+v /
c-v) ½
or z = (y' - y )) )/ y = (c+v / c-v) ½ - 1
with y the
emitted wavelength and y' the wavelength of the received radiation.
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:
y' / y = 1 + t / To / (1 - t² / To ²)½ =
(To +t / To -t) ½
or z = ( y' - y ))/ y = (To +t / To -t) ½ - 1
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 :
Ho = 1 / To =
1 / 4,55465 x 10^17 sec
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 last data
given by WMAP ( February 2003) made it possible to fix the value of the
constant Ho of Hubble at 68 Km/sec/Mpc
what well confirms the temporalist value of Ho is 67,71 Km/sec/Mpc. (
http://map.gsfc.nasa.gov/m_mm/mr_limits.html ).
The latest data provided by WMAP5
(2006) (Cosmological Parameters Summary - Chapter VI - WMAP + BAO+ SN) provide the latest values of H °: 70.1 + -1.3
km / sec / Mpc (is 68.8 km / sec / Mpc) and t ° = 13.73 + -0.12 (is 13.85
billion years). One can see, the latest
experimental data WMAP5 (less accurate) confirm the theoretical values (more
accurate) set by the temporalist model, several decades ago.
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.
Next : 9 The temporalist gravitation - The anomalous radial
acceleration of Pioneer 10
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Updated 2008: origin and explanation of large structures
of the universe (filaments - supercluster of galaxies - big voids) - Chapter 10