Alice Law Version 7

Doppler Effect

Han Erim

May 7, 2012

THE DOPPLER EFFECT

You may think that (c+v)(c-v) mathematics is not used in physics at all and that it is peculiar to the Alice Law; however, this is not the case. (c+v)(c-v) mathematics shows the mark of its presence in a crucial subtopic of physics. This subtopic is the Doppler Effect.

The Doppler Effect is seen on the electromagnetic waves coming from moving objects and is described as the change in the wavelength of light.

The Doppler Effect is not completely dealt with in the Electromagnetic Theory. The reason is that, as I said before, there has been a mistake made in the establishment of the Electromagnetic Theory and that the mathematics has been insufficient ever since. The Electromagnetic Theory have not used (c+v)(c-v) mathematics although it should have been based on it. Due to this deficiency, a critical subject, the Doppler Effect, have not been able to be understood exactly. Besides, while the Doppler Effect was being formulated, (c+v)(c-v) mathematics were used compulsorily because the Doppler Effect is directly related to the
(c+v)(c-v) mathematics and cannot be explained with any other mathematics. In other words, the Electromagnetic Theory, even if it was incompatible with its own mathematics, had to use (c+v)(c-v) mathematics.

The Alice Law describes the Doppler Effect starting from its cause of formation. In fact, it can be said that the presence of the Doppler Effect is an experimental proof of (c+v)(c-v) mathematics. We will see the Doppler Effect from the point of view of the Alice Law here.

 What is the Doppler Effect? The Doppler Effect is seen on sound and electromagnetic waves; however, its formation mechanism is different in sound and electromagnetic waves. I will mention only the Doppler Effect which is seen on electromagnetic waves here. It is certain in which wavelengths an element radiates. Especially in astronomy, while examining the stars, the question in which wavelengths the star radiates is studied. As a result of this study various information like the elements that constitute the star and the intensity of these elements are obtained. When the wavelengths obtained from stars are compared to the ones that belong to elements with wavelength ruler, a difference is generally found out. If the star observed is a receding one, the wavelengths of the element extend (REDSHIFT); the star is approaching, the wavelengths diminish (BLUESHIFT). This change in wavelengths was named the Doppler Effect in memory of Christian Doppler, who established this effect and adapted it to physics.  Today, we know that the Doppler Effect occurs among all frames that are mobile to each other and it includes all wavelengths.    Electromagnetic Spectrum The spectrum of electromagnetic waves is enormously wide. Theoretically, the wavelengths may vary between zero and infinite. We see the classification of electromagnetic waves according to their wavelengths and frequencies in the table.  Our eyes are sensitive to a very small wavelength gap in this large spectrum distance. We name this gap as visible light. As you know, we use some wavelengths that we cannot see in communication, medicine, heating and many other application fields. The general equation below is the equation between wavelength and frequency for electromagnetic waves. We will cover the reason of this equation in the following pages. Figure 1, The Doppler Effect occurs very similarly to the animation here.

There is a rolled moving paper in the animation. We can control the speed of the paper. The pencil swings up and down in a constant speed and constant frequency and draws the moving paper below.

The shape of the drawing will change according to the speed of the paper.

For the horizontal movements, the fact that the paper moves or that the paper stands still while the pencil moves gives exactly similar results.

Figure 2, The Doppler Effect

We see the previous animation created with electromagnetic waves here. There is a magnet instead of a pencil. The magnet vibrates properly. These vibrations are sent to the spaceship by its field in electromagnetic waves.

Each effect occurring on the field goes to the spaceship with the c speed (light speed constant). Here, c is the speed of electromagnetic wave according to the field. The direction of movement and the speed of the spaceship do not change the speed of the electromagnetic wave according to the field. However, the speed and direction of the spaceship changes the shape that the magnet draws (the electromagnetic waves undergo a change) because the spaceship carries its field along with itself. The change in the shape of the drawing, as we can see, occurs as the change of the wavelength. If the spaceship is moving, it will see that the length of the electromagnetic waves that come to it change; in other words, it will see a Doppler Effect. We should pay attention to the fact that the Doppler Effect occurs on the source (at the side of the magnet) while electromagnetic waves are emitted.

As can be seen, in case the spaceship approaches to the source, the wavelengths diminish (BLUSHIFT), and in case the spaceship moves away from the source, the wavelengths extend (REDSHIFT).

The values in the animation are pixel/second. In an attempt to make the animation realistic, the speed of light are set to 299,792458 pixel/sec. In order to comment on the animation correctly, after setting the speed value, wait until all the wavelengths are equal.
Figure 3, Doppler Effect

We see a more sophisticated animation created with light compared to the previous one here. With regards to the occurring of the Doppler Effect, the events that the observer moves and the lamp stands still or that the lamp moves and the observer stands still come to a similar conclusion.

Although the light (photon) is an electromagnetic wave, it is an energy bundle independent of other photons. Accordingly, the most realistic animation is the drawing in the fourth choice. As we can classify the electromagnetic waves according to their frequencies, it is also possible to think together with the first, second and the third choices.

If we pay attention to the fourth choice, we can see another important result of the Doppler Effect. The power of the light (the light lumen) that occurs as a result of the Doppler Effect increases or decreases. While the observer is coming closer to the source, the number of photons arriving to the observer increases in unit of time and while is moving away, the number of photons decreases.

The Doppler Effect has a second effect on photons. While the observer is coming closer to the source, the photons that are coming to it are more energetic. While the photons are moving away, the effect is just the opposite.

Figure 4, THE RELATIONSHIP BETWEEN (c+v)(c-v) MATHEMATICS AND WAVELENGTH, FREQUENCY

We see the relationship between the wavelength and frequency with (c+v)(c-v) mathematics here.
The change on the wavelength and frequency is directly dependent on (c+v)(c-v) mathematics.
Figure 5, The Relationship between the Wavelength and Frequency

When we look at the figure, we can see that the light travels the distance equal to a wavelength on the field with c speed in t time. Namely; λ = c. t. Therefore, t = λ/c. This t time is also the period (T) of an electromagnetic wave that is λ in length. Namely, t = T.

There is the equation T = 1/f also between the period and the frequency. We can write down T and t. Frequency is the repetition number in 1 unit time. If we write down 1/f instead of t in the equation λ = c. t, we obtain λ = c. f or f= λ/c.

At the bottom of the page, we can see the equations belonging to the Doppler Effect as a summary. We have obtained these equations in the previous page.
Figure 6, The direct relationship between the Doppler Effect and the Relativity Effects and Erim Equations

The relativity effects length deformation, time dilation, and change in perception speed  can never be present alone. If a time dilation occurs, it means that other effects also occur at the same time. If the Doppler Effect is confirmed in an observation, it indicates that there are relativity effects because the reasons of the formation of the Doppler Effect are same with those of the relativity effects and the Doppler Effect occurs with other relativity effects at the same time.

We have already seen how the relativity effects are formulated in the sections of length deformation, time dilation and simultaneity. As the Doppler Effect also uses the same mathematical equations, the relationship can be recognized easily. If we see RedShift or BlueShift in one of our observations, we can easily find out to what extent other relativity effects occur by benefiting from the change in the wavelength.

As a result of my noticing the relationship between the Doppler Effect and the relativity effects, this table came out. I wanted to give a name to this table and I named it ERIM, which is my last name.

By using the buttons on the table, you may go to relevant pages of each section and see the relations one-to-one.

The maximum and minimum limits for wavelength and frequency

The Doppler Effect occurs in certain limits. These limits come about as a result of the fact that the difference in speed between the reference systems has a limit. As far as we know, the movement speed of any material object cannot exceed the c light speed limit. It is possible to make various assumptions in this area, but we will not mention them here.

When we use the c speed limit as base for material objects, we may say that two reference systems approach each other or move away from each other with c speed at the most. In this case, v value that shows the difference in speed between the frames in (c+v)(c-v) mathematic will change between +c and c (*).
If we write down +c and c instead of v in the equations, we obtain maximum and minimum limits.
Accordingly, the change ranges of an electromagnetic wave are:
For wavelength:
0 ≤ λ ≤ 2 λ

For frequency:
/2 ≤  ≤ ∞

You must have already seen and felt the change limits in frequency and wavelengths in the animations in this section. These limits also determine limits of the relativity effects. For instance, the dilation of ticktack intervals of a clock can only be possible up to twice.

(*) Please take a look at the section of the Alice Equation.

Figure 7, The Doppler Effect and the Force Effect

As the speed value changes in the movements in the force effect, the Doppler Effect, as you guess, increase or decrease according to time. We see this situation in the graphics.

Now, we have come to a very interesting spot here because this spot is the GENERAL RELATIVITY. Generalizing (c+v)(c-v) mathematics by adding the force effect means the General Relativity. The graphic on this page is a very good example that shows what General Relativity is. From now on, the General Relativity will be as simple as this.

We will continue our journey with the Alice Equation.

Establish: December 2001