In this episode where they are talking about light bouncing between two mirrors while on a train, what would keep the light in tune with the mirrors. What I mean is, lets say the train was going at extremely high speeds like >50% of the speed of light, why would the light even travel back to the first mirror instead of just hitting the ceiling somewhere else further back. I suppose you might just have to have long enough mirrors to reflect the light back to its source . . . I guess the analogy was just not feasable to me.

Why wouldn't the light hit the mirror? If it hits in one frame, it needs to hit in all inertial frames.

Someone on a train tosses a ball straight up, and they see it drop straight down. Someone on the ground sees the ball travel in a parabola; it has a transverse velocity component along with the vertical one. Same basic concept, except the speed of the ball isn't constrained to be the same in all frames.

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It wasn't mentioned in the show but as the speed of Gravity is the same as for Light, it's [gravity] information also appears to slow down in an inertial system [train] when viewed from the field.

I was thinking about a sort of clock like the one used in the show except imagining a wave-front of Gravity instead of Light, though the gravity couldn't bounce back off the second mirror of course. If a mass is at mirror #1 it would be constantly propagating Gravity towards mirror #2 (and in every other direction as well). This force (and the information) would also appear to slow down just like the Light beams when viewed from the field.

well,concerning the momentum part of the podcast, i couldn't understand it, so i'd like anyone to help me witrh it.
thanx.