Error in special relativity

albert einstein assumed (in the time dilation) a box-car moving with velocity V with a mirror in its ceiling and observer 1 sitting in the box car holding flash light vertically so when he sends a flash pulse , this pulse will go vertically , hit the mirror , and return back to the observer 1 so delta time = 2d/c.

while according to observer 2 who is outside the box car what he have seen is that the flash light starts from observer 1 old position , and ends in observer 1 new position . (where difference in the distance is (delta time)*V) so according to observer 1 the light pulse has moved a longer distance than 2d.

where delta time can be calculated afterward using pythogeran therom.

and here lies the error

that pulse went vertically , hit the mirror , and returned back , it didnt return back to observer 1 but it returned back to its same starting position as y vector of velocity of this light pulse is equal to c , while the x-vector is equal to zero(not affected by V of the box-car, and it has to be un-affected because if x-vector of the light pulse velocity has a value then the total V of the light will be more than c and its a fact for observer 1 and 2 that light velocity is c)

so since x-vector is zero the light didnt change its x-coordinate so when light pulse returned back to its position (which was observer 1 oldpostion) the distance between the light pulse and observer 1 after delta time is (delta time * V) since the box car moved.

while according to observer 2 the light pulse starts from observer 1 old position , and ends in observer 1 old position so simply delta time according to observer 2 the light pulse moved 2d

so to both observer the light pulse moved the same distance. with the same velocity so equal delta time.

This not an argue , i just wantto know whats wrong in the above...so i am not gonna argue just asking to understand.

albert einstein assumed (in the time dilation) a box-car moving with velocity V with a mirror in its ceiling and observer 1 sitting in the box car holding flash light vertically so when he sends a flash pulse , this pulse will go vertically , hit the mirror , and return back to the observer 1 so delta time = 2d/c.

while according to observer 2 who is outside the box car what he have seen is that the flash light starts from observer 1 old position , and ends in observer 1 new position . (where difference in the distance is (delta time)*V) so according to observer 1 the light pulse has moved a longer distance than 2d.

where delta time can be calculated afterward using pythogeran therom.

and here lies the error

that pulse went vertically , hit the mirror , and returned back , it didnt return back to observer 1 but it returned back to its same starting position as y vector of velocity of this light pulse is equal to c , while the x-vector is equal to zero(not affected by V of the box-car, and it has to be un-affected because if x-vector of the light pulse velocity has a value then the total V of the light will be more than c and its a fact for observer 1 and 2 that light velocity is c)

so since x-vector is zero the light didnt change its x-coordinate so when light pulse returned back to its position (which was observer 1 oldpostion) the distance between the light pulse and observer 1 after delta time is (delta time * V) since the box car moved.

while according to observer 2 the light pulse starts from observer 1 old position , and ends in observer 1 old position so simply delta time according to observer 2 the light pulse moved 2d

so to both observer the light pulse moved the same distance. with the same velocity so equal delta time.

This not an argue , i just wantto know whats wrong in the above...so i am not gonna argue just asking to understand.

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