Why does the light beam move with the lightclock? A flat platform is moving in a tunnel with velocity V relative to the tunnel. A stationary reference frame S1 is attached to the tunnel and a reference frame S2 is attached to the moving platform.
On the platform floor there is a light source perpendicular to the platform which turns on at the moment that S2 coincides with S1 (point O in the figure). The coordinates of O are:
In S1: (X1=0;Y1=0) ;   In S2: (X2=0;Y2=0) ;
As the light beam is not affected by the light source velocity, the light beam touches the tunnel ceiling at point B with S1 coordinates:
(X1=0;Y1=y) .
In the meantime, the platform has moved to point C with S1 coordinates:
(X1=x;Y1=0)
and S2 coordinates:
(X2=0;Y2=0) ,
because the platform didn’t move in its frame. Thus, point B on the ceiling is seen from S2 with coordinates:
(X2=-x;Y2=y) .
However, according to Einstein’s light clock, the light beam would touch the ceiling perpendicular to point C, at point D with S2 coordinates: (X2=0;Y2=y)  .
So which is the right answer?
I know that in Einstein’s clock the ceiling is attached to the moving frame S2,  but this shouldn’t change the light beam trail.

 A: 
As the light beam is not affected by the light source velocity

This is an incorrect statement of the second postulate. It is only the speed of light that is invariant, not the velocity.
Since the inner workings of a laser is a little complicated, think of a simpler beam of light: consider a spherical source with a narrow aperture a small distance away.
In the rest frame the spherical source emits a spherical pulse of light. All of the light is blocked except for the ray that hits the spot on the ceiling.
In the moving frame as the spherical pulse of light expands the hole moves. In this frame, the ray of light that passes through the hole is one that moves diagonally. This same ray of light passes the same hole and hits the same spot on the ceiling, but in this frame the angle of travel is different.
A: The reason is quite simple. The source of light moves along with the mirror. Hence in the reference frame of the mirror the light must be moving in straight lines, this corresponds to light moving along with the mirror.
Think of it this way, the light source moves up and down in the frame of the mirrors, just like a ball moves up and down in a train (while it looks parabolic to an outside observer)
Because the motion of light isn't an accelerated one in the vertical direction, it is seen as a straight line.
A: While photons have no rest mass, they have momentum p. Its components px,py,pz are changing with the Lorentz transformation in different frames, so that the light beam is moving with S2 in both frames. This corresponds to the relativistic aberration of light, where the angle of light propagation depends on the inertial frame.
