In Special relativity why the light clock is orthogonal to the direction of motion of the train?

Question

I tried to see if this question has been asked elsewhere in the forum, I couldn't find it, unless somehow I missed it.

I have always wondered why the light clock in the relativity train goes up and down and the train moves at 90 degrees to it and if there is specific reason why it is done that way. What would happen if the light clock was going back and forth along the direction of motion? I hope my question is clear and not ambiguous.

Thank you very much in advance.

Answer 1

As John says in his comment, the reason the light clock experiment is usually introduced with the light moving at right angles to the train is because it makes the maths simpler. You can derive the equations of special relativity by considering beams of light travelling parallel to the train, but it is a lot more complicated that way.