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There is a natural constant that shows what velocities are related to. This constant is the fastest possible time. Practically spoken, the fastest possible clock. This is the one, which is not subject to time dilation, ie it has a time dilation of zero. Such a clock does not exist on Earth, since there is a general gravitational time dilation. However, a clock can theoretically be set to the fasted possible, the zero time.

Measurements with this clock gives the absolute velocities, since the clock and the movements measured with it have the same reference. What this is, is not determinant for the following. But it is named nevertheless, it is the ether, which Einstein unjustly abolished.

If velocities are not measured with a clock without time dilation, then they are relativistic velocities. These are measured with clocks that have time dilations.
If velocities are measured with a clock without time dilation, then they are the one with which objects moves based on the geometry of the cosmos. These are also based of the ether. This area, apart from all gravitational influences, is also the basis of the special relativity theory.

If an observer is standing in rest against the space coordinates in free space, he measures with his clock without time dilation the absolute velocities of objects against him, that is against the space and the ether.
The differential velocities of two objects, which moves to the observer, is the sum of there individual velocities. This means, that two objects, which each have the light velocity, have a differential speed of:

light velocity plus light velocity
equals twice light velocity

The objection, that differential velocities must not exceed the speed of light is wrong. Why?
Differential velocities are mathematical values, but no physical velocities. Obviously, differential velocities up to twice the speed of light are possible, and these are also directly observable when the light front from one supernova flows to the light front of another.

No impulse can arise by differential velocities. This does not prevent, that mathematics does it. The quantitative results are even correct, but nature is not so: each object has its own impulse, resulting by its own absolute velocity. This is that, which is measured with a clock without time dilation and is defined based on the space, that is also based on the ether.

On the other hand, science and teaching says, that the differential velocity of two objects which move toward another with the speed of light is also only the velocity of light. This false faith has its foundation by a widespread misunderstanding about that, what relativistic
If the velocities of objects are measured with their own clocks, they have a slower time sequence dependent on the speed of the objects. Speeds measured with these clocks are relativistic and have higher values at increasingly higher velocities than those of the absolute velocities at which the objects are actually moving toward the space. At light speed the clocks of the objects no longer have a time, they stand still. Thus, for the relativistic velocities of the objects with the speed of light, a relativistic velocity value of infinite is obtained: at the high velocity with light speed no time is "consumed".

The speed difference between two objects to be moved towards each other at a respective speed of light is also the sum of the individual speeds: light speed plus light speed equal to twice the light speed.
However, the use of the light velocity is no longer permitted: the speed of light is limited to its absolute velocity (defined). This is the one that is measured with the dormant clock without time dilation, that is the absolute velocity. The relativistic differential velocity of two objects to be moved towards another at the speed of light is:

Infinity + infinity = infinity

Only for this purpose can we say synonymous: 1 + 1 = 1.

This leads to new rules for velocities:

Absolute velocities add up absolutly,
Relativistic velocities add up relativistically.

Relativistic velocities are fictitious, that are untrue velocities, not based on the geometry of the cosmos, only on other times, although these other times actually being present in the moving objects. But just these other times are astonishingly these velocities, that determine the Newtonian impulses of objects!
This is a fact that must be taken. First one must believe the nature and then theories, not vice versa!

That the relativistic increase of the impulse would be result by a relativistic mass increase is definitly wrong. The relativistic factor comes from the time dilatation and is thus firmly bound to the time.
This also applies to its application in the formula for the relativistic impulse. The relativistic factor must not be taken away from the nature varable time! The relativistic factor can by mathematical factor rules also be assigned to the mass and the length, but mathematics must adhere in physics to what is possible in the nature.
Mathematics can not determine in nature what is possible or impossible, that can only the nature by itself. Mathematics does not understand nature, it can only describe it like a photo. Modern theoretical physics does not care all physically rules and: the replacement of the mathematical variables by physical quantities let mathematics not became to physics. Richard Feynman: mathematics is mathematics and physics ist physics.

The first, who can be to disprove the aforementioned rules for the addition of speeds
will receive a bonus of  5,000 Euros from me during my lifetime.

Refutations of theories can only occur physically, ie only verbally and only within the theories. Comparisons with externals or other theories are not permissible. There are no package deals between theories: no theory has anything to do with any other. A correct physical theory is objectively defined and consistent in itself. If it is not, it is wrong. These also are rules of physics.
The examination of a theory must also be done physically and not mathematically. Mathematics is not the supervisor of physics. The physical correctness of a theory is proved only by the fact that it can answer all questions in its sphere of responsibility by a physically based way with its basic principle.