Lorentz's error
Lorentz's relativism is based on the formula:$$x^2-(ct)^2=(x')^2-(ct')^2$$
But this formula is lying.
The correct formula is as follows:$$x^2-(ct)^2=(x'-vt')^2-(ct')^2$$
Why not?
I'll give the answer below:
I remind to you of a school-task about the two foot-passengers and the dog:
1. Two travelers go on the road with the same velocity ($$v$$) at a distance ($$L$$) from each other (one behind the other).
2. A dog runs between travelers (at velocity $$c$$).
QUESTION: how long time the dog ran ahead, and how long - ago.
Every schoolboy knows the answer to this ask: ldog's time will be different because:
1. When the dog runs back (to meet to lagging-traveler) - the dog's time will be the lesser: $$T_1=L/(c+v)$$.
2. When the dog runs forward (to rush to the advance-traveler) - the dog's time will be the greater: $$T_2=L/(c-v)$$.
Let the two mirrors will be in place of travelers.
Let the photon will be in place of dog.
So as it shown in this picture:
Please note: photon's time are different.
$$t_1=L/(c+v)$$
$$t_2=L/(c-v)$$
These two values are the roots of the equation:
$$(x-vt)^2-(ct)^2=0$$
for $$x=\pm L$$
Einstein, Lorentz, Minkowski argued that dog's times (on both sides) is the same:
$$x^2-(ct)^2=0$$
$$t_1=L/c$$
$$t_2=L/c$$
_______________________
In the problem of the two travelers and the dog: L '= L.
This little problem only shows that dog's times (in different directions) will be different:
$$t'_1=L/(c+v)$$
$$t'_2=L/(c-v)$$
In the problem (with two mirrors, with a photon and with a moving observer) times will be different too, but to this added to the visual relativistic effect: the distance between the mirrors will become smaller (visual). Therefore:
$$L'=L(1-v^2/c^2)$$
$$t'_1=L'/(c+v)=L(1+v/c)/c$$
$$t'_2=L'/(c-v)=L(1-v/c)/c$$
TEST:
$$t'_1+t'_2=L(1+v/c)/c+L(1-v/c)/c=2L/c=t_1+t_2$$ - is true!