1. COORDINATE SYSTEMS
Space is unlimited and man has, since the distant past, had a problem
in defining his position or the position of a point in that given infinity.
With time he found that space is three - dimensional, and that the position
of a point in relation to another point in space can be determined by three
length values. This method was first formulated by Descartes, and the first
rectangular coordinate system appeared. As is well known, it consists of
three axes 
, 
, 
,
which intersect at the origin of the
coordinates under a right angle. In this rectangular coordinate system
the position of each point in space is defined, in relation to the origin,
with three lengths, that is, with three coordinate points ,
, .
In Fig. 1.1 the position of the point 
is shown in
space in relation to the origin, and from there we can see that
|
 |
(1.1) |
In Fig. 1.2 the position of the point 
in
the 
plane is shown and in that case we have
|
 |
(1.2) |
 |
 |
| Fig. 1.1 |
Fig. 1.2 |
If point 
lies on one of the axes
of the coordinate system,
for example on the -axis, then 
,
that is 
. Beside
the above mentioned coordinate system there are others such as the polar,
the cylindrical, and the spherical etc. They are not important for the
further presentation, however.
The coordinate system, besides making it possible to define the position
of a body in space, also makes it easier to study its motion in space.
The origin of the system is connected to some reference point or body.
So, for example, when studying the earth's motion round the sun, the origin
is taken to be the center of the sun. A passenger aboard a ship, stands
still in relation to the ship, but together with the ship is in motion
in relation to the coast. If the coordinate system is connected to the
ship then the passenger will be at rest in the given coordinate system.
But, on the other hand, if we connect the coordinate system to some point
on the coast, then the passenger will move in that new coordinate system.
Thus, the passenger can either be at rest or in motion while remaining
in the same situation, depending on which body of reference (coordinate
system) he uses to define his state of motion. In this way the relativity
of motion was recognized. In fact, every motion is relative, something
which was known in Aristotle's time.
The theory of relativity is based on the Lorentz
transformation of coordinates. In that transformation and in the theory
of relativity are used two coordinate systems. One of them is at rest and
the other is moved uniformly and translatory relative to the first.
In addition to the relativity of motion there are relativity of time
and many other kinds of relativity. Broadly speaking, every measurement
or determination of magnitude or quality is relative, that is in relation
to some other magnitude or quality that we have defined as absolute or
in some other way.
Today the notion of relativity has become connected exclusively with
the name of Einstein. Simply said, it became in some way his property.
Many indeed believe that Einstein was the first to understand relativity
and that it had not been defined correctly before him. This is, of course,
a great mistake and an injustice to Galileo, Newton and Lorentz.
When reader read this book, carefully and with the understanding, then,
to him will be clear that Einstein's relativity is big illusion, which
we should reject and return to Galilean and Newtonian relativity.
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