What is an Inertial System?

Inertial systems are a skillful summary of objects, which facilitates the detections of the functions of the world for the intellect of man. It divides the very much of events of nature in individual divisible areas. Inertial systems with all its components can be regarded and treated as single compact bodies, what is the purpose of their invention. What happens in them, the inertial system is the reference. The reference for relations with the environment is the absolute fixed point of the world.
Inertial systems are tiny particles such as muons over interconnected parts (spaceship) and unconnected only equal moving objects up to the entirety of the earth's surface. The latter, however, with one exception: only in the horizontal plane. Why? That will answer the following "heart of the matter" of inertial systems.

In teaching inertial systems are defined as moving systems with constant speed, ie unaccelerated. Within an inertial system, it would be impossible to detect whether it is moving or not. But, constant speed and the impossibility to detect motions are given also in vehicles on earth as car, train, plane and also on the existing movement of the earth's surface by itself. Therefore also they are, contrary to the teaching dogma, inertial systems. Billiards for example can play only in an unaccelerated system, an inertial system. This is given in the horizontal direction at the earth's surface. A "billiard in a three dimensional room" is, of course, on the earth not possible, only in a not accelerating spaceship.

Which relations have inertial systems to the absolute zero point? Speed
with respect to the zero point leads to their definition. How can detected there speed? With the time dilation (see in the next chaptor), which owns inertial systems. Time dilation arises only by Newtonian movements and Newtonian movements are always movements against the zero point of the world.
What is, if an inertial system has no movement against the zero point? Then it is a so called "outstanding" system, a particlularly system. After teaching dogma there would not exist such an
"outstanding" system. What is "special" on it? It is characterized by that, that the time in it runs with the highest possible speed of these world, it has no time dilation. A second "outstanding" inertial system is that, what is moving with light speed, the time in it stands still

The result is a new basic definition of inertial systems with its true "heart of the matter":

Inertial systems are "isles of time"

Detecting the nature by all her single objects is impossible. Every interacting things in this cosmos happens in inertial systems. Depending on their Newtonian movements to absolute zero the time in inertial systems goes slower, caused by the time dilation. On earth the time dilation is the same for all objects. Smallest existing differences of gravitation in it are ignored, just as smallest differences of the objects in inertial systems by there motions against the system, otherwise an inertial system makes no sense. Ultimately, of course, each single object is an inertial system for itself. But by this the name sytem would be nonsensical. However, since a muon also is subject to the time dilation, it must be assumed that in its occur internal time-operations and so it is an inertial system. Its course of time can be recognized by its radioactivity. Whether particles, that have no course of time, can also be an inertial system, is unclear.

Inside inertial systems all operations runs by Newtonian physics. Namely with the time, which is running in the inertial system, arose by its movement by the time dilation. 
This implies that Newtonian physics is relativistic. Relativistic is, that natural events occur with different timings. But, an other physics than the Newtonian does not exist in this cosmos. The laws of Newtonian physics applies unchanged in inertial sytems! That means absolutely: in inertial systems it needs no correction caused by the time dilation, for all what happenis in it.

Corrections with the relativistic factor are required only when seen from one inertial system into an other. Corrected must the view of the observer and not the seen in the observed system. If, for example, in a very large fast spaceship a car drives against a wall, an observer sees from its location as if it runs in slow motion. But the resulting damages on the car did not fit to the seemingly too slow speed, how the observer is measuring with his faster running clock. However the speedometer in the car in the spaceship reveals indeed the very high speed that exactly arise the observed devastations.
The clock of the observer is running too fast for what is happening in the space ship, it must be adapted with the relativistic factor from the space ship. Observations from the zero point in moving inertial systems always shows slower sequences of events in them (slow motion). Observations from moving inertial systems in stationary or slower moving shows in contrast faster events in them (time-lapse).

Besides the outstanding inertial systems arised by the limit conditions in relation to the absolute reference point of the world, which are the one at rest and the other one at maximum possible speed, there is a "special" inertial system, which is characterized by the fact that we live in it. For us it is the one that determines our live and our technology.
How is to find out which motion the own inertial system has? The own clock does not say. A local clock without time dilation can not be in an inertial system. A look to a clock in rest is influenced by the own time dilation. There is only one way, to measure an object whose velocity is known. And there is only one, the velocity of light. A measurement of the velocity of light led to the run of the own clock.

For all externals, which we observed from this earth's inertial or coordinate system, we used it as a zero point. An early observation from this "zero point" was the wrong circulating of heaven about us. It was recognized with most difficult birth pangs after millennia. But the idea that there still could arise further errors does not even arise for centuries. Only after this centuries Einstein came up to a new point of reference, a force-free body on its geodesic. But, that his reference point is not free of movements,  he did not realize. Surely this was his biggest mistake. Thus he found not the both special inertial systems determined by the movement limits.

How is to handle the inertia system earth's surface?
It has a constant Newton's basic speed, the escape velocity of the earth. Accordingly to it is its time dilation. For everything that happens in it, it provides the zero point. Movements against it therefore are also referred as absolute. (For the "absolute" of the entire cosmos the language has no additional term, it was not known.)
The difference compared to a "normal" inertial system with only evenly motion, however, is, that an acceleration exists in the vertical direction. It is one with which it will be accelerated continuously and constantly upward. It is the same, as if this system were in Einsteinīs empty space steadily accelerating elevator. Therefore in it the laws for inertial systems apply only in the horizontal direction. For all vertical parts of movements must be considered, that they are influences by acceleration. Nevertheless humans intellect was found a clear view, he can think separately in horizontal and vertical direction. The formation of the physics succeeded here on earth, so, how it is valid in all inertial systems without any accelerations in any direction.

But, what man does not creates up today, is to distinguish relatively from absolute, ie fictitious from true. Bike- and car-drivers and airplane pilots can see the air coming against her and they believe that is true. But, just as the term "absolute" in its highest meaning is related to the fixed point of the whole world, must it at lack of other expressions, how is written before to the fixed point "inertial system", now even deeper on yet another, also relate to single natural event. From the participating objects must be found the one, to which relate a cause-effect principle of only a single nature event.
For this problem as example the nature event flying. By it only two objects are involved, the flying object and the air. Because a flying object without support falls down, it must do something to prevent it. Therefore it needs energy with which it can nourish a cause-effect-process that holds it up. For this function can be either the flying object or the air the reference. Because flying is a moving event, the reference point for its movements must be found. Movements against this "point to find" are absolutely.
To find the reference point of a single event, the rule is, that the object, that brings in the energy, is the moving object. This object is "doing something", is active. The other object only reacts, is passive. The passive object is always the object of reference of a natural events, no matter whether it is moving against the earth's surface or not! It hosts the most important question: what happens with it? And that has to be observed on it from its state before. Chop the wood, for example, the wood is the passive object. The ax is the active, it has the energy in its movement, with which it splits the wood. The ax is moving through the wood and not the wood along the ax. As accurately not the air flows past a plane, but the aircraft through the air. An airplane has the absolute motion.

For flying, the air is therefore the reference point, it is the passive object. The flying object is the active, it has the powered movement that brings the air to a reaction, so that arise a force by the air. So, not the air moves past a flying object, but rather a flying object moves against the air, it has the absolute movement for this natural event. From the perspective of a pilot, air flows past him, but only relatively, fictitious, untrue. The copy of flying with the wind tunnel with its exchange of cause and effect supports the relative view that the air passing a flying object would be a true flow. The crucial question for flying is: what happens with the air? The answer lays only in the observation of the air with the view from its state before, so, as if no plane or bird or bumble bee would come to the observed location. This represents, that man has infinite difficulties in the nature to distinguish
absolutly from relative, ie right from wrong.

The insights into the world must be divided into absolute absolutely, these are the ones in relation to the fixed point of the world, in absolutely in relation to inertial systems, valid for the inner of inertial systems, and in relatively out of movements towards inertial systems or the fixed point of the world. Never a correct theory can be found from a relative perspective.