DOPPLER EFFECT AND SPECIAL RELATIVITY Han Erim January 1, 2010 May 25, 2012 (Last Update) Copyright 2009 © Han Erim All Rights Reserved
Here we mention about the Doppler Effect only on electromagnetic waves.
ALICE LAW AND DOPPLER EFFECT
Doppler Effect depends on directly the mathematical rules of (c+v)(c–v) mathematics which belong to Alice Law. Since Alice Law explains how the (c+v)(c–v) mathematics is formed, it also shows the reasons of the Doppler Effect in detail. The existence of Doppler Effect is also an empirical verification of Alice Law.




Figure 1  As seen on the animation, a pencil that is moving up and down, is drawing a line on a moving sheet. If this sheet moves with a stable velocity then pencil will draw a continuous and smooth sine curve. If we change the velocity of the paper then the shape of the sine curves will change. Notice that this graphic animation is very familiar with my publication called as
"The Reason Behind Special Relativity" which tells the machine that puts the bottles on a walking conveyor. 



Figure 2  Figure2 Notice that this sample is also very similar to my publication called as ‘"The Reason Behind Special Relativity" which tells the lantern and the observer. In the mentioned section I used the particle feature of the photons, in here I used the wave feature of the photons.
To provide an accurate harmony with the mathematical equations, let’s assume that the light source beams always in same wavelength and photons are beamed in equal frequencies.
In the animation, the photons (electromagnetic waves) that are put in the field of the observer by the torch are going to the observer. Electromagnetic waves will always go with a speed of c (speed of light constant) according to the field of the observer and through the field of the observer. In case when the observer moves, the field that belongs to the observer moves too. Therefore, while the electromagnetic waves, that have been emitted from the source to the field of the observer, are entering to the field of the observer, their wavelength and frequency change depending to the moving speed of the observer. (You can find detailed information about ‘’Field Concept” in my publications and “Field Concept’ section in Alice Law Version 6”)
As a conclusion, even in case of lamp beams always with the same wavelength and the same frequency, if the observer moves then radiation of the torch will be different for him and the wavelength and frequency of the light that reaches to him changes. 

 
Figure 3 This animation is a slightly improved one compared to the previous one. The codes of the animation are being done according to (c+v)(cv) mathematic rules so the results are considerably realistic. You can download the source codes from
here. (Flash CS3 ActionScript 3.0) download. I principally put a magnet as a source of electromagnetic wave to provide a continuous radiation of the wave. It could also be a light source like above instead of a magnet; almost the same principles will be hold. I did not use a ruler which symbolizes the field of spaceship in this animation. Imagine the field concept in your mind. The electromagnetic waves coming toward to the spaceship will travel in the field of the spaceship. We can observe the changes that happen on the electromagnetic waves when we move the spaceship. Spaceship comes to the source with the speed of light or leaves the source with the speed of light we can see that what kind of an event that will occur on the electromagnetic wave happens. We see that electromagnetic waves stop when the spaceship comes closer to the source with the speed of light. This situation must not surprise you. We watch the event from a different reference system. According to our reference system, electromagnetic waves that move towards to the spaceship can stop. But notice that, speed of the same electromagnetic waves according to the spaceship, the field of the spaceship; does not change and it is always c (speed of light). In the animation, when the wavelength changes the color of the electromagnetic wave changes. But it is clear that color change is symbolic. Because here we have the chance of using visible colors only. You can see in which class the electromagnetic wave will be when the wavelength shortens or extends from the table placed on the right side. You can stop the animation at any time and by moving up the ruler you can check the length of the wavelength. The length of the ruler always indicates the wavelength.


Conclusions: Neither the spaceship moves nor not, the speed of the electromagnetic waves that comes to the spaceship is always c (speed of light) according to the spaceship.
While the spaceship is coming closer to the source or moving away from the source, electromagnetic waves change. This change happens while the electromagnetic wave is being emitted from the source (or rather, while the electromagnetic wave is enters the field of the spaceship).
REDSHIFT, is extension of wavelength and means that the electromagnetic wave loses energy. Redshift is always represented with (c+v).
BLUESHIFT, is shortening of the wavelength and means that the electromagnetic wave gains energy. Blueshift is always be represented with (cv).
Above, the v value is the speed difference between two reference systems (magnet and spaceship) and the c value is the speed of light constant.
In the animation, the spaceship is in motion and the source is stationary. If the spaceship is stationary and the source is in motion Doppler Effect will occur completely in the same way. It is not important which one is moving or both of them are moving. As long as the source and the target have a velocity difference then the Doppler Effect will occur.
In the animation it seems that acceleration, deceleration or changing of movement direction of the spaceship has no effect on the electromagnetic waves that moves in the field. This is because of the codes of the animation is written as so. The experiments will give an answer of that will cause a difference or not.
We clearly see that any kind of differences that occurred on the wavelength does not change the total energy of the electromagnetic wave (the energy that is between two peak points). Only the energy of the electromagnetic wave does take place in a larger (Redshift) or a more narrow distance (Blueshift) on the field of the spaceship. Instead of this, we can say that the frequency of the electromagnetic wave changes. In one respect, Doppler Effect is the law of conservation of energy between electromagnetic wave and its target.
As a result of change of the wavelength, the amount of energy that reaches to the spaceship in unit time, changes. This situation is sensed and measured as frequency change of the electromagnetic wave.
We see that there are minimum and maximum limitations for extending and shortening of the wavelength. This limit values are depend on the velocity difference between the reference systems which is coming closer to the c (speed of light) value and according to the moving directions of the reference systems which are coming closer or moving away from each other. In Doppler Effect, the amounts of the changes on an electromagnetic wave are between the below limitations.
 
Below you can see how to do the wavelength and frequency calculations. Frequency and wavelength calculations can be done only according to these equations.
In the animation above, the source was stationary and the observer was in motion. If the observer is in stationary and the source is in motion then the equations doesn’t change.
Alice Law and becoming rules of (c+v)(cv) mathematics are not known by the physicists, so you can face frequently wrong comments and wrong mathematical expressions about the Doppler Effect. Real Doppler Effect equations are written by me above. Basing on the above equations some other Doppler Effect formulas can be obtained.
Another important point about the Doppler Effect is to see the frequency notion which is used to express the Doppler Effect is a little compulsory notion. Because the electromagnetic waves (photons) are emitted as independent energy packs from each other. Apart from here, if the emitted photons are not emitted with same distance which is equal to their own wavelengths then frequency notion is meaningless, because in this case, the frequency value does not show the amount of the photons that is emitted. On the other hand, it is not possible for a single photon to have a frequency value which belongs to it. So, a frequency value that is obtained by measurements does not indicate the frequency of the photon but indicates its energy.


New  The Mechanism of Doppler Effect.
We have seen at the above animation, how an electromagnetic wave has been set off. You can see in detail how is works the mechanism of Doppler Effect at the below figure.
We can see that the alteration on the wavelength depends of two factors. 1 In Rest, the duration of setting off a part of electromagnetic wave which is equal to one wavelength. (t0). 2 The speed difference and its direction between reference systems (v).
Let's care attention that, t0 duration time determinates by the source of electromagnetic wave. If we talk about the above animation, t0 value is the duration of one period of the magnet oscillation and this value can be obtained from the t=λ/c equation in Rest position.
The relative speed of an electromagnetic wave will be c which propagates through the field. The movement of the observer does not change the relative speed of electromagnetic wave. Consequently, on a point in the field the necessary passing time of an electromagnetic wave which is equal to one wavelength always determinates by t= λ/c equation. There is t=1/f correlation between time and frequency. In physics λ= c/f equation is used. However, when the basic equation is expressed as t= λ/c it shows the correlations simple and clean. I have to say that, this simplifications is being possible with Alice Law.
By utilizing from the above major equations we can obtain other minor equations of Doppler Effect. 

Doppler Effect and Special Relativity
Physicists always commented on Doppler Effect out of Special Relativity. But the Doppler Effect is in the scope of Special Relativity and a normal result of it. Of course, here we should understand that the math of the Special Relativity is (c+v)(cv) mathematics that is to say we must understand Alice Law. Because of that Alice Law represents the true mathematics of the Special Relativity; Doppler Effect totally takes place inside the Special Relativity. In the scope of Doppler Effect, there is no any other Doppler Effect or mathematics except the equations and the principals that I wrote here. Such concepts like “Relativistic Doppler Effect” have been ended up with the Alice Law.
Doppler Effect is almost related directly with all results of the Special Relativity. Wavelength and frequency changes can be stated easily with space contraction, time dilation and simultaneousness (Speed of Perception) . Because all the situations that is observed in Special Relativity is occur according to the rules of (c+v)(cv) mathematics and all these influences happens at the same time while wavelength and frequency changes occur. Alice Law obviously shows all the relations between these events that is observed in Special Relativity and wavelength and frequency changes. Look at 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.
From the link here , you can see the mathematical connections of the equations above. The Mathematical Relations Between Doppler Effect And Special Relativity: http://www.aliceinphysics.com/publications/correlation/en/correlation.html
General Relativity and Doppler Effect: I would like to mention about the Doppler Effect which occur by the General Relativity influence. But because I considered that data I reached is insufficient I did not add this subject here. I think that in ‘’Harvard Tower Experiment’’ (Pound  Rebka experiment in 1959) test, which can be an important source for his subject, has got big and important logical mistakes. In my opinion this important experiment must be repeated.
You can reach all information about Alice Law from my main page.


ANOUNCE
Alice Law Version 7 has been published (May 7, 2012)


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