The Lorentz transformetion is non physical - the correct transformation and a new rule of composition velocities

Since the velocity is the measure of an angle between the trajectories of bodies (it is equal to the sinus of an angle between the trajectories) then the composition of the velocities can be described by the sum of the angles between the trajectories of bodies. This rule is also a base of derivating of transforamtion of coordinates - the alternative to the hitherto Lorentz Transformation

Let us consider the following example:Two observers, moving along red and green trajectory, are observing the same body - dashed trajectory in black. Green trajectory is the one of the observer in rest. The second observer of this body is moving along the red trajectry with the velocity, in relation to the observer in rest (green), equal to sinβ.


 

The new transformation of velocities:

 
 
 
 

The new transformation of coordinates:

 
 
 
 

The resultant velocity as a function of composed velocities. Both composed velocities are equal. Three cases of composition of the velocities are shown in the diagram: according to non-relativistic, Galilean transformation, according to SRT and according to the theory presented here.

More: See Is the Lorentz Transformation a Physically Correct Solution of the Spacetime Interval Equation?
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