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DOPPLER EFFECT
and
SPECIAL RELATIVITY
Han Erim
1 January 2010
25 May 2012 (Last update)
Copyright 2009 © Han Erim All Rights Reserved
Here, only the Doppler Effect taking place on electromagnetic waves is described.
What is the Doppler Effect: The changes in the frequency and wavelength of an electromagnetic wave are
called the Doppler Effect. For the Doppler Effect to occur, there must be a difference in velocity between the
source that emits the electromagnetic wave and the target to which the electromagnetic wave arrives. The Doppler
Effect is observed and measured at the target side.
ALICE LAW AND THE DOPPLER EFFECT
The Doppler Effect directly depends on the rules of the (c+v)(c−v) mathematics belonging to Alice Law. Since
Alice Law explains in detail how the (c+v)(c−v) mathematics arises, it also shows very clearly the reasons for
the Doppler Effect. The very existence of the Doppler Effect is, at the same time, an experimental verification
of Alice Law.
Let us see the reason why the Doppler Effect occurs, starting from the figure below.
flash
Figure 1 – As we see in the animation, a pen that moves up and down in place draws a line on a moving
sheet of paper. If the paper moves at a constant speed, the line drawn will be a continuous and smooth sine
curve. If we change the speed of the paper, the shape of the sine curves changes. Notice that this graphic
animation is very similar to the conveyor-belt machine example that places bottles on the belt in my
publication "The Reason for Special
Relativity".
flash
Figure 2 – Let us note that this animation is almost identical to the "Lamp and Observer" example in my
publication "The Reason for Special
Relativity". In that animation I used the particle nature of photons, whereas here the wave nature of
photons is used.
To achieve exact agreement with the mathematical equations, let us assume that the light source always emits at
the same wavelength, and that photons are emitted at intervals equal to the wavelength.
In the animation, the photons (electromagnetic waves) placed by the lamp into the observer’s field advance
toward the observer. The electromagnetic waves move within the observer’s field, and their speed with respect to
this field is always c (the speed of light). When the observer moves, the field belonging to the observer also
moves. Therefore, at the moment when the electromagnetic waves emitted from the source enter the observer’s
field, their wavelength and frequency change, depending on the velocity of the observer. (You can find detailed
information about the field concept in Alice Law Version 6 and in my publication titled Field Concept.)
As a result, although the lamp always emits with the same wavelength and the same frequency, if the observer is
in motion, the emission of the lamp will be different for the observer, and the wavelength and frequency of the
light reaching the observer will change.
flash
Figure 3 – This animation is a more advanced version of the previous one. Since the code of the
animation is written according to the rules of the (c+v)(c−v) mathematics, the results it gives are quite
realistic. You can download the source code here (Flash CS3 Actionscript 3.0) – download.
Explanation of the graphic animation:
To ensure continuous wave emission, I have deliberately placed a magnet as the electromagnetic wave source in
the animation. Instead of the magnet, a light source similar to the one above could also have been used; almost
the same principles would apply.
You can choose the oscillation speed of the magnet from the control at the bottom left. In the animation, the
electromagnetic waves generated depending on the oscillation speed of the magnet propagate toward the spaceship
with speed c (the speed of light). In this animation I did not use a ruler representing the field of the
spaceship. Please keep the field concept in mind. The electromagnetic waves coming toward the spaceship travel
within the field of the spaceship.
When we move the spaceship, we can observe the changes that occur on the electromagnetic wave. When the
spaceship approaches the source at the speed of light, or when it recedes from the source at the speed of
light, we can see what kind of phenomenon takes place on the electromagnetic wave.
When the spaceship approaches the source at the speed of light, we see that the electromagnetic waves appear to
come to a stop. Do not let this surprise you. We are observing the event from a different reference frame. In
our reference frame, the electromagnetic waves going toward the spaceship may appear stationary. But note
carefully that, with respect to the spaceship itself and to its field, the speed of these same electromagnetic
waves does not change and is always c (the speed of light).
In the animation we see that when the wavelength changes, the color of the electromagnetic wave also changes.
However, the color change here is of course symbolic, because we can only use visible colors. When the
wavelength
becomes shorter or longer, you can see from the table on the right into which class of the electromagnetic
spectrum the wave falls.
You can stop the animation at any moment and move the ruler to check the length of the wavelength. The length
of the ruler always shows the wavelength.
Results:
Whether the spaceship is in motion or at rest, the speed of the electromagnetic waves coming toward the
spaceship is always c (the speed of light) with respect to the spaceship.
While the spaceship is approaching the source or receding from it, the electromagnetic waves undergo changes.
This change takes place at the moment of emission of the electromagnetic wave from the source (more precisely,
at the moment when the electromagnetic wave enters the field of the spaceship).
REDSHIFT is the lengthening of the wavelength and means that the
electromagnetic wave loses energy. Redshift is always represented by (c+v).
BLUESHIFT is the shortening of the wavelength and means that the
electromagnetic wave gains energy. Blueshift is always represented by (c−v).
Here, v is the relative speed between the reference frames (magnet and spaceship), and c is the speed of
light.
In the animation the spaceship is moving and the source is at rest. If the spaceship is at rest and the source
is moving, the Doppler Effect occurs in exactly the same way. It does not matter which one is moving, or if both
are moving. As long as there is a speed difference between the source and the target, the Doppler Effect will
occur.
In the animation we see that the acceleration, deceleration, or change of direction of the spaceship does not
cause any change on the electromagnetic waves that have already entered the field. This situation arises from
the way the animation code is written. The answer to whether there will be a change or not must be given by
experiments.
We can clearly see here that, no matter how the wavelength changes, the total energy of the electromagnetic
wave (the energy between two successive peaks) does not change. Only the energy of the electromagnetic wave is
distributed over a wider length (redshift) or a narrower length (blueshift) on the field of the spaceship.
Alternatively, we can say that the frequency of the electromagnetic wave changes. In a sense, the Doppler Effect
is the “Principle of Conservation of Energy” between the electromagnetic wave and its target.
As the wavelength changes, the amount of energy reaching the spaceship per unit time changes. This is perceived
and measured as a change in the frequency of the electromagnetic wave.
We also see here that there are upper and lower limits for the changes in wavelength. These limit values are
determined in cases where the relative speed between the reference frames approaches c (the speed of light),
depending on the direction of motion of the reference frames (whether they are receding from or approaching
each other). In the Doppler Effect, the amount of change in an electromagnetic wave lies within the following
limits.
The way to calculate wavelength and frequency is shown below. Calculations of frequency and wavelength can only
be made on the basis of these equations.
In the animation the source is at rest and the observer is moving. If the observer is at rest and the source
is moving, the equations above remain unchanged.
Because the rules by which Alice Law and thus the (c+v)(c−v) mathematics are formed are not known by
physicists,
you can frequently encounter incorrect interpretations and incorrect mathematical expressions about the Doppler
Effect. The true equations of the Doppler Effect are only those that I have written above. Based on these
equations, different forms of expressing the Doppler Effect can be obtained.
Another important point regarding Doppler is that the concept of frequency used to express the Doppler Effect
is
in fact somewhat forced. This is because electromagnetic waves (photons) are emitted as independent packets of
energy. If the emitted photons are not emitted at intervals equal to their own wavelength, as in our case here,
then the concept of frequency loses its meaning, since in that case the frequency value does not represent the
number of emitted photons. On the other hand, a single photon cannot have a frequency value of its own.
Therefore, the frequency values obtained in measurements do not in reality represent the frequency of the photon
itself, but rather a measure of its energy.
New – The Mechanism of the Doppler Effect
We have seen in the animation above how the electromagnetic wave is emitted. In the graphic below, you can see
in detail how the mechanism of the Doppler Effect works.
We see that the amount of change in wavelength (λΔ) depends on two factors.
1 – In the rest state, the emission time of a portion of the electromagnetic wave equal to one wavelength
(t₀)
2 – The relative speed between the reference frames and the direction of this speed (v)
Note that the emission time t₀ is determined by the electromagnetic wave source. For clarity, speaking in terms
of the animation above, the value t₀ is the time required for the magnet to complete one full oscillation, and
this value is calculated from the equation t = λ / c in the rest state.
The speed of the electromagnetic wave with respect to the field through which it travels is always c. The
motion of the observer does not change the speed c of the electromagnetic wave with respect to the field.
Therefore, the time required for an electromagnetic wave of one wavelength to pass through a point in the field
is always given by t = λ / c. Between time and frequency we have the relation t = 1 / f. That is, t = λ / c and
λ = c / f are the same thing. In physics, λ = c / f is used. However, taking the fundamental relation in the
form t = λ / c, as done here, makes the relationship simple and clear. I would like to note that such a
simplification is made possible by Alice Law.
Using the basic relations above, all other equations related to the Doppler Effect can be obtained.
Doppler Effect and Special Relativity
Physicists have always interpreted the Doppler Effect outside of Special Relativity. However, the Doppler
Effect is entirely within the scope of Special Relativity and is its most natural consequence. Of course, here
one must understand that the true mathematics of Special Relativity is the (c+v)(c−v) mathematics – that is, one
must understand Alice Law. Since Alice Law represents the true mathematics of Special Relativity, the Doppler
Effect is entirely contained within Special Relativity. Within the framework of the Doppler Effect, apart from
the principles and equations I have written here, there is no other Doppler Effect or mathematics. Concepts such
as “relativistic Doppler” have come to an end with Alice Law.
The Doppler Effect is directly related to almost all the results of Special Relativity. Length contraction,
time dilation and simultaneity (speed of perception) can easily be expressed in terms of wavelength and
frequency changes. For in Special Relativity all these observed phenomena occur according to the rules of
the (c+v)(c−v) mathematics, and all these effects take place simultaneously with the changes in wavelength and
frequency. Alice Law shows very clearly the relationship of these effects observed in Special Relativity with
wavelength and frequency changes. See the table below.
The equations above is registered under Notary Public 37 of Beyoglu – Istanbul – Republic of Turkey on
29/December/2009 with no: 35035, by Han Erim.
You can see the mathematical connections of the equations above at the link below.
The relationships between the Doppler Effect and Special Relativity:
http://www.aliceinphysics.com/publications/correlation/en/correlation.html
General Relativity and the Doppler Effect: I would also like to explain the Doppler Effect that occurs
as
a result of the existence of General Relativity. However, I have not included it here because I think the data I
have is insufficient. In my opinion there are significant logical errors and mistakes in the experiment known as
the "Harvard Tower Experiment" (Pound–Rebka experiment 1959), which could have been a serious reference
on this topic. In my view, this important experiment should be repeated.
You can access all information related to Alice Law from my home page.
Alice Law is the foundation of physics.
ANNOUNCEMENT
Alice Law Version 7 has been released (May 7, 2012)
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