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5.10. Doppler Effect
5.10.1 General
Doppler effect in electromagnetic phenomena has been often used in order
to prove expansion of the Universe [124]. Availability of the model of the
photon and the laws of its motion allows us to check correctness of
interpretation of infrared and ultraviolet biases of the spectral lines formed
by emission of the stars of the Universe.
It is known that the explanation of the bias of the spectral lines in
modern physics is based on Doppler effect, which is manifested and registered
easily during acoustic wave propagation.
An electromagnetic wave (Fig. 4) is formed by the photon flux. The distance
between the pulses of modulated wave is equal to the length 
of the
electromagnetic wave.
It can be easily seen that during electromagnetic wave propagation
Doppler effect (Fig. 4) is similar to acoustic wave propagation. The change of
electromagnetic emission (Fig. 4)
depends of velocities and directions of motion both of the source and the
receiver of such emission. For example, if the directions of motion of the
source or the reflector of such wave coincide with the direction of motion of
the wave itself, its frequency is increased. Each photon, which forms such
wave, acts in a different way.
If the directions of motion of the photon source and the photons
themselves (Fig. 5) coincide (Fig. 5), frequency of the photons being born is
increased as well, and the spectrum is displaced into ultraviolet range. If in
a similar case the photon is not born, but reflected, its wavelength is
increased in accordance with Compton effect, frequency is decreased, and the spectrum
is displaced into infrared range. It remains unclear if the wavelength and
frequency of a separate photon depend on the direction of motion and velocity
of its receiver. It becomes necessary to analyse Doppler effect in detail
during emission of not an electromagnetic wave, but of separate photons (Fig.
5).
It appears from the analysis of motion of the model of the photon (Fig.
5) that the process of its creation is a transient phenomenon. The essence of
Doppler effect is in the fact that the electrons of the source emit the photons
with smaller or larger energy. The change of durability of the transient
phenomenon stipulated by various directions of the photon emission in relation
to the direction of motion of the source is the most probable cause of it.
The longer the photon creation process, which we call the transient
phenomenon, the larger mass (energy) will be given to the electron by the
photon, and the wavelength of such photon will be displaced into infrared
range. That’s why it is necessary to find the answer to a fundamental question:
does emission source velocity in relation to space influence durability of the
transient phenomenon, i.e. the photon creation process? If so, durability of
the transient phenomenon should depend on the direction of the start of the
photon in relation to emission source motion direction. As the transient
phenomenon takes place actually in the electromagnetic field of the electron of
the emission source, there is every reason to believe that the photon mass can
be changed during this transient phenomenon.
It appears from the analysis of kinematics of the photon model motion (Figs 5, 6) that the
increase of its velocity from any initial value to value C always takes place
with acceleration, which is generated by the process of interaction between its
electromagnetic fields. That’s why we should get mathematical models describing
to the first approximation the process
of the start of the photon from a resting source and a moving source, due to
which the spectra are displaced [18], [130], [174]. There are two
interpretations of this effect: the relativistic interpretation and the
classical one [18], [130], [178].
5.10.2. The Relativistic Interpretation of the
Doppler Effect
The relativistic interpretation is based
on the second Einstein’s postulate: Any ray of light moves in the stationary system
of co-ordinates with the determined velocity, whether the ray be emitted by a
stationary or a moving body[161]. The Lorentz transformations originate from this wording of the
postulate (3) and (4).
It is clear from Fig. 2 that 
and 
. If we insert these values in the formula (1) or (2), we’ll
find [18]
(113)
or
,
(114)
where 
and 
are frequencies of
electromagnetic emission in the moving and stationary reference systems, respectively.
If we designate 
, we’ll have
(115)
This is the relativistic mathematical model of the calculation of the
Doppler effect. As 
, it results from the ratios (114) that emission
frequency 
of the moving source
is greater than radiation frequency 
of stationary source,
i.e. the mathematical models (114) and (115) describe only ultraviolet shift of
the spectra.
If we write the ratio (115) in the following form
,
(116)
it will show to what extent frequency 
of the photon emitted
from the stationary source (Fig. 2) is less than frequency 
of the photon emitted
by the moving source, and it will not characterize the infrared shift of the
spectra. As in both formulas (114), (115) and (116) 
, both formulas describe the ultraviolet shift of the
spectra, and we have no right to use the mathematical model (116) for the
calculation of the infrared shift of the spectra.
Let us prescribe several values 
and determine values 
and 
for them (Table 2).
Table 2.
Relativistic results of calculation of the Doppler effect
|
|
|
|
|
0.000001 0.00001 0.0001 0.001 0.01 0.1 |
1.0000009 1.0000099 1.0000999 1.0010004 1.0100504 1.10554 |
0.9999989 0.9999899 0.9998999 0.9990004 0.9900494 0.904534 |
The results of Table 1 show
unambiguously that frequency 
of the emitted photon
is increased with the increase of velocity 
of movement of the
reference system (for example, of a star). It means that an ultraviolet shift
of the spectral lines is increased. Physical sense being present in mathematical
symbols 
and 
deprives us of the
right to give another interpretation of the mathematical models (114), (115) and (116).
Thus, we have got an unambiguous answer: the relativistic mathematical
models (115) and (116) describe only ultraviolet shift of the spectra, and they
are not connected with their infrared shift.
In science, the Lorentz transformations (3) and (4) have been used for the
calculation of the so called relativistic effects for about a hundred years.
Now we get to know that they give the possibility to calculate the relativistic
effects only for the ultraviolet shift of the spectra and provide no
information concerning the relativistic effects by the infrared shift of the
spectra. It means that the Lorentz transformations misrepresent the reality.
We’ll not repeat Lorentz transformation analysis, which proves
disagreement of these conversion to the space-matter-time unity axiom, but
we’ll note that Doppler effect analysis result being obtained gives us the
right to call Lorentz transformations a theoretical virus.
It results from
the above mentioned facts that within nearly a hundred years the Lorentz transformations
play the role of a theoretical virus in exact sciences, and the scientific
community cannot get rid of it. Now we have a powerful means to struggle
against this virus: the
space-matter-time unity axiom. That’s why there is a hope for convalescence of scientific cognition.
5.10.3. Classical Interpretation of the Doppler Effect
The photon creation process analysis carried out by us [18], [75] has
shown that it is a transient phenomenon, during which the photon (Fig. 5) moves
with acceleration. It appears from this that the transient phenomenon duration
depends on the direction of the emitter and the nascent photon [18], [75]. It
gives us the reason to adjust the wording of the second Einstein’s postulate
and to formulate it in the following way: Velocity of the photons emitted by
a stationary source or a moving one is constant in relation to space and does
not depend on the traffic direction of the source and the value of its velocity
[18].
Thus, velocity
of the photons is constant in relation to space. The photon creation is a
transient phenomenon, during which it moves with acceleration 
and achieves velocity
in relation to space
and moves further with the same velocity [18], [75].
If
the source is stationary (
), the photon creation process will be put down in the
following way (Fig. 9)
.
(117)
From (117), we have
.
(118)
The photon creation process analysis has shown that this process takes
place in the wavelength interval [18], that’s why when the source is
stationary (
), frequency 
of emitted photon
will be equal
.
(119)
Fig. 9. Diagram of addition of velocities of
source 
and photon 
: E is an observer, S
is a source
When the directions of movement of the source and the nascent photon
(Fig. 9, b) coincide, it means that
,
(120)
where 
is time, during which
the photon moves with acceleration.
If we insert acceleration 
from (118), we’ll
find
.
(121)
An important corollary originates from the mathematical model (121): if
the direction of movement of the emitter and the nascent photon coincide (Fig.
9, b), time 
of transient process
is reduced with the increase of traverse velocity 
.
If we proceed to frequencies of the emitted photon, we have
. (122)
As 
, it means that
.
(123)
The mathematical models (122)
shows the increase of frequency of the photon when the directions of its
velocity C and velocity of the source V coincide (Fig. 9, b).
Thus, when the directions of velocities of the source and the nascent photon
coincide, an ultraviolet shift of the spectra is observed.
If
the directions of the source and the nascent photon are opposite (Fig. 9, c),
it means that frequency 
of the photon being
emitted is reduced, and the infrared displacement of the spectra should be
observed.
.
(124)
If we take into consideration
the ratio (118), we’ll have
; (125)
It appears from this that if the direction of movement of the source and
the nascent photon are opposite (Fig.
9, c), time 
of transient process is
increased with the increase of traverse velocity 
. If we proceed to frequencies, we’ll have
(126)
It results from formula (126) that if the directions of movement of the
source and the nascent photon are opposite (Fig. 9, c), frequency 
of the emitted photon is reduced, and the infrared shift of
the spectra can be observed.
The independence of the shift of the spectra from the direction and
velocity of movement of the observer is the main conclusion from the analysis
of the classical mathematical models (122) and (126).
Taking into account that 
we’ll find
.
(127)
Now let us write the results
of the calculation according to the formulas (115), (123) and (127) in Table 3.
Table 3. Results of calculation of the Doppler
Effect
|
|
|
|
|
|
0.000001 0.00001 0.0001 0.001 0.01 0.1 |
1.000001 1.000010 1.000100 1.001000 1.010000 1.100000 |
0.999999 0.999990 0.999900 0.999000 0.990000 0.900000 |
1.0000009 1.0000099 1.0000999 1.0010004 1.0100504 1.1055400 |
The analysis of Table 3 shows that the classical mathematical model
(123) describes ultraviolet shift of the spectra when 
, and the classical mathematical model (127) describes
infrared one (
). The relativistic mathematical model (115) describes only
ultraviolet shift of the spectra (
).
Now we have an opportunity to explain Doppler effect, which is
registered during photon emission, by various durability of transient process
of photon creation.
The process of separation of the photon from the electron is not a
simultaneous one. The bond between them is preserved for some time. Photon
mass, which it takes with it separating from the electron, depends of duration
of preservation of this bond. It is clear from the ratio (120) that if 
, 
. It means that the start of the photon in the direction of
motion of a source, which moves in relation to space with velocity 
, is impossible. In this case, no photon will be emitted by
the electron.
When the direction of motion of the emitted photon coincides with the
direction of motion of the source (Fig. 9, b), duration (121) of the transient
process is reduced as compared with the duration of the transient process at
the start from the resting source. Wavelength and frequency of such photon are
shifted to the ultraviolet range of the spectrum.
When the photon starts in the direction opposite to the motion of the
source (s. Fig. 9, c), duration of the transient process is increased as it is
clear from ratio (125), and we have every reason to suppose that in this case
in the process of loss of the bond with the electron the photon will give more
electromagnetic mass and will arrive to receiver E with the wavelength and
frequency shifted to the infrared range.
The same phenomenon takes place when space rockets are launched. When a
rocket starts to the east, its velocity coincides with the Earth rotation
direction, and it will require less time and less fuel for insertion as
compared with the start with the direction to the west.
When the direction of velocities of the source and the photon coincide,
duration of the transient process (121) is smaller; if there is no coincidence,
duration is larger (125) when the photon emission source is at rest . In the
first case (Fig. 9, b), the photon loses less energy (mass) at its creation,
and it will arrive to us with energy shifted into the ultraviolet range; in the
second case (Fig. 9, c) it loses more mass, and it will arrive to the receiver
with smaller energy (mass) shifted into the infrared range.
A question arises: how does the photon give a part of its
electromagnetic mass to the electromagnetic field of the electron of the
source? The north poles and the south ones of the fields of the photon alternate
on its external contour. If the photon in the moment of its creation or
reflection by one of its magnetic fields interacts with similar field of the
electron emitting it, a bond will be established via the magnetic lines of
force at the opposite polarities between these fields.
Thus, the electron of the atom of the emission source with its field
will try to hold the photon with the help of magnetic lines of force, via which
mass of electromagnetic field (to be more exact, the field itself) of the photon
will flow to the electron of the atom of the emission source. The slower the
photon withdraws, the greater mass will be lost by it. It seems that other
particles are characterized by this process of energy transfer as well. As
during this process “mass” is pumped quasi from one particle into another
having no opportunity to become a photon of energy (s. Fig. 5), this part of
energy is not registered in the experiment [75].
The revealed corpuscular nature of the photon gives every reason to
return to a ballistic hypothesis based on Newton’s concepts concerning light as
a flow of material corpuscles [146], [172]. But this hypothesis acquires a
considerable limitation. Here is its essence.
If a stationary reference system is connected with space vacuum and if
motion of the source emitting the photons is considered in this system,
velocity of emitted photons in relation to the reference system chosen in such
a way will be one and the same all the time and equal to 
despite of the direction of motion and emission source
velocity. This result is stipulated by the fact that persistence of photon
motion velocity is generated by the electromagnetic processes, which take place
in its electromagnetic structure.
Figuratively, the essence of the
photon emission process can be compared with the shots from a gun of such
shells that despite of initial velocity, with which they leave the barrel,
could gain one and the same velocity in relation to the stationary reference
system connected with space. The peculiarity of the photon ballistic hypothesis
originates from this fact: the lack of the phenomenon of the Galilean addition
of velocities of the source and the photon being emitted. When the photon is
emitted, it always gains one and the same velocity itself in relation to space,
which is equal to 
. But the Galilean addition of velocities is preserved
completely when the photon meets the receiver, but it exerts no influence on
energy state of the photon itself.
Certainly, the formulas (123) and (127) are purely kinematics ones,
that’s why they express the kinematics process of photon emission
approximately. As the electrodynamics of the photon emission process has not
been worked out yet, let us use the mathematical models, which describe energy
indices of the photons. In this case, the details of the process of their
emission remain concealed, but the main index (frequency of the emitted photon)
is calculated more precisely than during the use of the
Kinematics mathematical models (123) and
(127).
As
it is clear, in Table 3 the contradictions between the calculations according
to a classical formula (123) and a relativistic formula (115) are increased
with the increase of 
. There exist the experimental evidences that within the
increase 
the relativistic
formula (115) expresses reality more exactly [178]. As the relativists think, it
serves as a solid argument of authenticity of the Special Theory of Relativity.
Let us give a classical formula, which gives the same result, but it calculates
not only the ultra-violet shift of the spectra, but the infrared one as well.
We have already shown that total energy of the photon is equal to the
sum of energies of its translational motion 
and rotational motion
and that this amount
depends on the value of speed 
and direction of
radiation source motion 
. If the angle between the direction of velocity vector of
source motion 
and the direction of
velocity vector of the photon being emitted (Fig. 10) is equal 
, total energy of the
emitted photon will be written in the following way [194].
Fig. 10. Diagram of
addition of velocities of the source 
and the photon 
(128)
If we take into account that 
and designate 
, we’ll find after
conversion of the equation (128)
(129)
If the directions of the motion of the
source and the photon being emitted coincide, it means that 
and
(130)
When the directions of the motion of
the source and the photon being emitted are counter, it means that 
and
(131)
In Table 2, the calculation results are given according to the classical
formulas (130) and (131) and relativistic formulas (115) and (116). Analysis of
this table shows that the classical formula (130) gives the result, which is
close to the result of the relativistic formula (115), and classical formula
(131) gives the result, for which there is no relativistic formula.
Relativists use the formula (116)
for the calculation of the infrared shift of the spectra having no mathematical
right for it. Such right and such accuracy are given by the classical
mathematical formula (131) (Table 4).
Table 4. Calculation results of Doppler Effect
|
|
(130) |
(131) |
|
|
|
0.000001 0.00001 0.0001 0.001 0.01 0.1 |
1.0000010 1.0000100 1.0001000 1.0010000 1.0100500 1.1050000 |
0.9999990 0.9999900 0.9999000 0.9990005 0.9900500 0.9050000 |
1.0000009 1.0000099 1.0000999 1.0010004 1.0100504 1.1055400 |
0.9999989 0.9999899 0.9998999 0.9990004 0.9900494 0.9045340 |
The results of the simultaneous registration of the usual spectral lines
of the hydrogen atom received from the space object SS433 and the spectral lines
shifted to the ultraviolet and infrared field of the spectrum can serve as a
classical experimental fact, which confirms equity of mathematical models (130)
and (131). It proves the fact that the main part of the space object SS433 is
stationary in relation to space, and two other parts move in relation to space.
The part, which generates the ultraviolet shift, moves to the Earth, and the
part, which generates the infrared shift at that time, moves from the Earth.
Periodicity of the change of values of these shifts is registered [90], [166],
[179].
5.11. Is the
Universe Expanded?
At present, the infrared shift of the spectral lines formed by the
starts of the galaxies is the main evidence of expansion of the Universe. The
question concerning the influence of direction and velocity of the emission
receiver on the value of this shift remains undetermined.
Thus, the photon start process does not influence on its final velocity in
relation to space, and its duration (117), (120) depends on the direction of
motion of the emission source and the photon in relation to space.
The given analysis of Doppler Effect taking into consideration the
photon model (Fig. 5) shows independence of any shift of the spectral lines
from the direction of motion and velocity of emission receiver. The value and
the direction of the shift (into infrared or ultraviolet range of the spectrum)
depend on the direction of motion of the emission source and the emission
itself. If these directions coincide, only the ultraviolet shift of the
spectral lines should be observed; if these directions are opposite, only the
infrared shift is observed. This regularity shows that availability of the
infrared shift of the spectral lines is not enough for unambiguous conclusion
concerning the expansion of the Universe.
As the Earth moves in relation to space, it should be taken into account
during the analysis of the connection of the shift of the spectral lines with
the expansion of the Universe.
For example, if the vectors of
velocities of the Earth and the star are directed along one line in one
and the same side, the value of the shift of a spectral line will point to the
fact of motion of the star in relation to space, but not in relation to the
Earth. In this case if the Earth follows the star with velocity in relation to
space greater than velocity of the star, these celestial bodies will approach
each other. But due to the fact that the time of the start of the photon from
the star in direction to the Earth is increased (125) (as compared with 
), we’ll register the infrared shift of the spectral lines
(126). It means that the distance between the star and the Earth is reduced at
the infrared shift of the spectra.
If the star follows the Earth with greater velocity than the Earth, in
this case the celestial bodies will approach each other, but the time of the
start (121) of the photon in the direction to the Earth will be less than at 
, and we’ll register the ultraviolet shift (122). Thus, in
both cases the star and the Earth approached each other, but the shift of the
spectral lines were opposite.
Can the motion of the star in relation to the Earth influence on the
shift of the spectral lines? Certainly, not. This process is governed by
velocity of the star not in relation to the planets or galaxies, but in
relation to one thing, which is common for all stars, planets and galaxies: in
relation to space.
Fig. 11. Diagram to the analysis of expansion
of the Universe: AB is a radial direction of the expansion of the Universe; D,
E and S are the galaxies situated on the radial direction of expansion of the
Universe; E is our galaxy.
The important result of the analysis of the spectra of the source SS433
is the fact that the ultraviolet shift of the spectral lines is 20fold less
than the infrared one by equal velocities of motion [179][1].
Obviously, due to this fact the astrophysicists register mainly the infrared
shift of the spectral lines of the majority of stars, and on this basis they
make a conclusion concerning expansion of the Universe. Availability of
ultraviolet shift of the spectra with some stars denotes that the infrared
shift of the spectral lines is an insufficient condition for an unambiguous
conclusion concerning expansion of the Universe. This conclusion will be
unambiguous only in case when both infrared and ultraviolet shifts of the
spectra are taken into consideration.
In order to make an unambiguous conclusion concerning expansion of the
Universe, it is necessary to register a shift of the spectra from the opposite
points of the surface of the Earth (Fig. 11).
If the infrared shift is registered in one direction (for example, from
source S) and the ultraviolet shift is registered in the opposite direction
(from source D), the conclusion concerning expansion of the Universe can be
accepted as the unambiguous one. If this regularity is not confirmed, the
infrared shift of the spectra is not connected with the expansion of the
Universe; a cause of this shift is different, and we should find it.
5.12. Brief Conclusion
Lorentz
transformation analysis carried out with the help of the space-matter-time
unity axiom shows clearly and conclusively that in exact sciences they play the
role of a theoretical virus.
The relativistic mathematical model (114), which originates from the
Lorentz transformations, has nothing to do with the Doppler effect.
The classical wording of the second Einstein’s postulate opens the new
possibilities in the solution of the fundamental tasks of physics [18].
The ultraviolet and infrared shifts of the spectra describe the
classical mathematical models (122) and (126), which originate from the
classical wording of the second Einstein’s postulate. They will give more exact
results when their connection with the mathematical model of the formation of
the spectra of the atoms and the ions is established.
The Doppler Effect of electromagnetic wave (Fig. 4) depends on the
direction of the motion of the receiver and its velocity.
The Doppler Effect of the separate photon (Fig. 5) does not depend on the
direction of the motion of the receiver and its velocity.
The modern conclusion concerning expansion of the Universe made only on
the basis of the analysis of the infrared shift of the spectra cannot be
accepted as an unambiguous one.
We have considered the simplest cases of
Doppler Effect when the emission source of the electromagnetic wave or single
photon moves to the receiver or from it. The electromagnetic wave (Fig. 4) and
single photons (Fig. 5) behave similarly in both cases.
The cases of interaction of electromagnetic wave and the single photons
with the receiver remain unconsidered. But the structure of the electromagnetic
wave (Fig. 4) gives the reason to suppose that velocity and direction of motion
of the receiver of such a wave will generate Doppler Effect as well. The photon
model structure (Fig. 5) points to the fact that is parameters do not depend on
velocity and direction of motion of the receiver of the single photons.
If we consider the process of reflection of the electromagnetic wave,
velocity and direction of motion of the reflector will generate the same
Doppler Effect as velocity and direction of motion of the source.
Single photons forming the electromagnetic wave will behave
differently when they meet the
reflector, because the reflector performs two functions: the function of the
receiver of single photons and the function of their reflection. In this case,
Compton Effect will govern the shift of the spectral lines of the photons.
That’s why the process of the change of the parameters of the single photons in
interaction with the moving reflector should be carried out taking Compton
Effect into consideration.
The
main result of Doppler Effect is Galilean addition of velocities of the photons
and their receivers.
The
Foundations of Physchemistry of Microworld
Copyright Ó2003 Kanarev Ph.
M.
Internet Version - http://book.physchemistry.innoplaza.net
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