I have a question after John Rennie's answer of this post Light & Observer moving perpendicular to each other.
Imagine a train station and a train passing very fast. There are two frames of reference: the train frame and the platform frame. We will look at the situation from above (from the sky view).
We turn on a laser in the platform (in the direction perpendicular to the direction of the train), creating a light ray. In the platform frame the light ray is vertical and in the train frame we can calculate the angle of the light ray to the vertical with Lorentz transformations.
In the same way, now we turn on the laser inside the train. In the train frame the light ray is vertical and in the platform frame we can calculate the angle of the light ray to the vertical with Lorentz transformations. So far so good.
Here come my questions. It seems that the direction of the light ray depends on the movement of the laser in the precise moment in which the light ray was created. But knowing that in both cases the light ray is created absolutely perpendicular, it seems like if the light ray had a kind of "inertia" in the sense of the Newton's first law, as throwing a ball through the window of the train. So, How is it possible? Why light "knows" how its source was moving? Why light does not move relative to some static fundamental medium (ignore this parenthesis: even though this medium could move relative to the space somehow)? How does it work? How this is explained? I think this leads to another question: What is the physical nature of light and through which physical tangible medium it is transmitted? (first it was thought that a real physical Ether existed, now is something like an unreal physical field modeled with mathematics). Thanks.
PS: This situation is used to informally obtain the Lorentz factor. It is assumed that the light ray (created inside the train) accompanies the train. I was just pondering this fact.