31.2. THINKING WITH FIELDS IN MIND

I cannot, of course, claim that what I told about fields is absolutely correct. But it is a fact that, if you think with the LOGIC OF FIELDS that I covered before and will cover here, you can interpret (c+v) (c-v) mathematics more easily. You can reach consistent predictions on how to find results while analyzing an event. 

Thinking with fields in mind…

We can combine the fields of atoms that make up of an object in our minds and deal with it like a single field such as field of a plane, field of an observer, field of Earth. To reach the result in (c+v) (c-v) mathematics, thinking with objects and their fields in mind is sufficient in most cases. 

The answer to the question “What is a reference system?” is as follows: An object and the field that belongs to it together forms the reference system of the object.

We can break any object into smaller pieces in our minds, as well. Each piece we have will be an object, as well; it will have its own field and it will have a reference system of its own. In the figure, a few fields that belong to parts of the bodies of the runners are described. When we think with fields in mind, we can easily notice which behavior does the light that goes towards the runners have.

In the figure above, when the observer defines the coordinates of the plane that he sees as (x₁,y₁,z₁) relative to its own coordinate system, he actually defines a point on its own field without noticing it. The coordinate value he writes is a coordinate value on the observer’s own field. 

Thinking with fields in mind gives certain and clear information on where the image of an object will be seen. In the figure on the left, the plane (the Source Object) sends signals that form its own image when it is at point A. While these signals that are released on the field of the observer are coming towards the observer, they will follow the AO line in the field of the observer. In the figure on the right, however, the situation when the signals have reached the observer is shown. The observer will see the Image Object of the plane at point A because signals came from the point A that belongs to its own field. Even if the observer is in motion, the location of point A will never change relative to the observer because, when the observer is in motion, it carries its field along with itself. When it moves in a specific direction and at a specific speed, its field will also move in the same direction and at the same speed. Therefore, when the observer carries the field, it will carry point A together with itself. 

Thinking with fields in mind makes invisible events visible for us. Let’s go back to our Byte Shift example. Fields that belong to signal receivers are seen in the figure. The fields that belong to the planes are carried in the direction of the movement of the planes. Since the speed of each signal group relative to the field it travels in is c, the receivers always receive the INCOMING signal that comes to them at c speed. However, since the fields that belong to the planes are carried in the direction of the movement of planes, relative to the reference system of the signal transmitter, the speed of the OUTGOING signal that goes to the plane is (c+v) and the speed of the OUTGOING signal that goes to the approaching plane is (c-v). The fact that signal groups gradually draw apart from each other as they move in the sky is seen very clearly when thinking with the field in mind. 

The fields being carried in the direction of the movement leads to Doppler Shift, that is, the wavelength change during the emission of the electromagnetic wave. The fields being carried during the release of the signal on the field leads to compression or dilation of the signal wavelength. Imagine you take a handful of sand in your hand. By loosening your fingers a little, slowly pour the sand onto a conveyor belt. When the sand in your hand finishes, measure the length of the sand line formed on the conveyor belt. Then, do the same thing but this time the conveyor belt is moved forward or backward by a person. Then the speed of the conveyor belt will change relative to your hand. If the speed of the conveyor belt increases relative to your hand, then the sand you pour forms a longer line. If the speed of the conveyor belt decreases, then the length of the sand line is shorter. Wavelength change works with a completely similar mechanism. When we think with fields in mind, you easily notice that signal wavelength changes during the emission of the signal.