I’d like to discuss the event of Angle Shift one more time here. I will now tell you about the event of Angle Shift with the help of the Field Concept. 

In the figure above, the field of the plane is represented by a graph paper.

  • In the first visual: When the plane is at (x1,y1,z1) coordinates, the signal station releases the signal on the field of the plane. Red d1 line belongs to the field of the plane. The signal will reach the plane following this line. 

  • In the second visual: While the signal is traveling to the plane on d1 line, the plane continues its movement on its own direction. Since the plane carries its field along with it, the signal that travels inside the field of the plane and follows d1 line is carried in the direction of the plane, as well.

  • In the third visual: The signal comes following the direction of the red d1 line and reaches the plane when it is at (x2,y2,z2) coordinates. The black d1, d2, d3 lines are the lines that form the Doppler Triangle that we came across in the previous topics. d3 line gives us the direction of the movement of the signal relative to the reference system of the signal station. However, since signal travels in the field of the plane, the determinant for the signal is naturally the red d1 line.

Let’s ask a question now: “Does an event of Angle Shift take place relative to the reference system of the plane?” No, it doesn’t. The signal straightforwardly came to it following the red d1 line; it doesn’t change direction in any way. 

On the other hand, Angle Shift relative to the reference system of the tower that emits the signal bears as absolute reality. While the signal had to follow the black d1 line, it reached the plane by following the direction of d3 line. The field of the plane is in motion in the same direction and at the same speed as the plane and the plane carries its own field along with itself. The signal that is emitted by the tower, as a result of being released on this field that is in motion and because of the movement of the field, has to change direction. The signal, in fact, doesn’t change direction, but, relative to the reference system of the signal tower, such a result comes out and the event of Angle Shift occurs. 

It is not complicated, is it? You just need to think with the field in mind. Thinking with fields in mind along with (c+v) (c-v) mathematics is a method of thinking that needs to be based upon. 

Of course, there is a reason I showed you the figure above this late. I couldn’t have started telling you about Alice Law with the topic of fields. In that case, Alice Law would be incomprehensible to you. I needed to tell you about the results of (c+v) (c-v) mathematics first. As (c+v) (c-v) mathematics is a highly consistent mathematics, it doesn’t need the Field Concept or any other similar concept. For this reason, I didn’t mention the Field Concept the first or second chapters. In the discussions where we covered our topics here, I made an introduction to the topic of fields together with the occurrence of the signs that indicate the existence of fields. (c+v) (c-v) mathematics is a mathematics that is valid and that can be understood without the concept of fields; however, using it along with the Field Concept significantly facilitates and clarifies thinking. The Field Concept is a result that (c+v) (c-v) mathematics points out. Of course, when we say the concept of fields, I am talking about a Field Concept as the one mentioned here. (c+v) (c-v) mathematics provides us with unique opportunities that guide us on how to interpret fields. But, of course, you don’t have to think like I do.