TRANSITION TO (C+V) (C-V) MATHEMATICS

In this section, we will see that (c+v) (c-v) mathematics is valid for The Electromagnetic Theory, based on both the Galilean Relativity Principle and Albert Einstein's Principle of The speed of light Constant. First of all, I am writing a rule for the Galilean Relativity Principle we have just mentioned. I'll make use of this rule when showing you how (c+v) (c-v) mathematics came into being.

RULE: Let's have two reference systems moving in uniform linear movement relative to each other. Each of these reference systems can say the following for their own reference system: "My reference system stands still. The moving one is the other reference system."

Now let's use our imagination. A man suddenly finds himself in a box in a deserted corner of space. He panics, but after a short while, he understands he is safe and calms down. The first thing that comes to his mind is to try to figure out where he is going. Curiously, he looks through the window of the box and tries to understand where he is going. But this effort is in vain; he cannot get any results. The lights coming from the stars he sees far, far away does not give him any ideas.

Could the man say the box is moving in space? If the box is in an inert motion, which it is, he cannot. Looking at the stars, we might think that he could maybe say something, but he cannot understand whether the box he is in is moving in space or not, or in what direction he is going, based only on his own reference system.

After a while, he looks out of the windows again and sees another box approaching him. There is a woman inside. The man tries to find out whether he is moving towards the woman or the woman is moving towards him, but he again cannot figure it out. He thinks “Maybe I am standing still and she is moving towards me.”

The principles of physics give the explanation for this situation as follows: "In this example, there are two inert reference systems moving relative to each other, and there is no answer to the question: Which one is in motion?". Meanwhile, the principles of physics also say: "All physical laws valid for the box in which the man is in are equally valid for the woman in the other box. If the man carries out a measurement and gets whatever result, the woman in the other box will reach the same result if she carries out the measurement in the same way. "

Now, having the box example we have seen here in mind, we are moving on to the (c+v) (c-v) mathematics for The Electromagnetic Theory. The observers in the boxes think that the box they are in is still and that the one in motion is the other box.

Let’s make our example a bit more abstract and define the boxes as "Frame A" and "Frame B". The event takes place in the following way:

The boxes are in a linear motion relative to each other; that is, they are in inert motion. When the distance between the boxes is d₀, the observers transmit a light signal to the other box. The figure below depicts the starting position of the event.

In our observation relative to the reference system of both the observers, we will study;
1) The speed of the INCOMING signal from the other box to themselves,
2) The speed of the OUTGOING signal that they send to the other box.

As we can see, the result of this observation will lead us to (c+v) (c-v) mathematics.