Definition of the light circle :
This circle will be used to simulate the relativistic deviations in the case of a static source and a moving observer (direct deviation or counterclockwise deviation) or in the case of a moving source and a static observer (inverse deviation or clockwise deviation). The circle has for radius the lenght of the speed vector OC. The mobile speeds are submultiples of this vector.
The observer is on the circle so we can vary the angle of emission r with respect to the direction of movement. We can also vary the value of the mobile speed by moving the cursor Va on the light vector OC.
Direct deviation (Static source, moving observer) :
The speed vector of the mobile is drawn from point A. The deviation is oriented backwards wrt the direction of motion. So the observer at point A must look in the parallel direction (i.e towards a point before source S).
We can simulate the particular case of Bradley's effect of stellar abberation with an emission angle of 90°. But the speed of our Earth (30km/s) is too small to be represented with our cursor of speed. The angle r may be varied by moving A on the light circle.
In this case, the source S moves and the observer is at rest.
The path of the light emitted by moving source S is in fact the result of direct deviation of a light path emitted by a static source S towards point G. This point G is a special point. It is the real local geodesic point for all the rays emitted by a absolute static source S in direction of A. From this absolute path, we can get all the "observed paths" for different relative speeds by direct deviation.
So, on the circle, the geodesic path SG gives path SA by counterclockwise deviation for a static source and an observer at speed Vs then conversely, the path SG is the "inverse clockwise deviation" of path SA for a moving source at same speed Vs and viewed by an static observer.
Hereby, we can see that Einstein was wrong about symmetry of relativity.
In the case we have 2 mobiles (A and B), the simulation of the direct deviation using the relative speed between A and B (Vb-Va) for a light ray emitted by A could be false. In fact, we can consider that the ray seen by B is the result of :
- inverse deviation of a light ray emitted by A at speed Va and that gives SG
- followed by a direct deviation of SG at speed Vb.
The angle obtained by this combinaison is different from the angle computed from SA at relative speed (Vb-Va). We have to correct this error.
I define the correction factore K to be :
k = Angle obtained with (Vb-Va)/Combined angle of 2 deviations
Determination of point G of the local geodesic path :
What if the speeds of A and B are not absolute ones ? Then, the computing by combinaison method will be incorrect. Fortunately, we still find the G point by deduction from the angle of the measured path of a ray emitted by A and observed by B.
