4. TRANSITION
TO (C+V) (C-V) MATHEMATICS IN ELECTROMAGNETIC THEORY
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.