Quote by mangaroosh
Thanks Agerhall, I am familiat with the thought experiment alright, and it is essentially the same one that James posted, I think.
What phenomena occur that means the speed of light is c "in any inertial frame"? We would, ordinarily, expect the moving observer to measure a different speed of light  why is this not the case?

If you first assume that the speed of light is c in relation to the guy standing on the platform. The guy on the platform would classically expect that it takes longer time for the light from the guy on the train to reach the back and front wall and bounce back towards the guy on the train than if the train had not been moving. You can do the math, it is simple.
However, in Special Relativity the Time Dilation formula kicks in and it so happens that if the guy on the platform would expect it to take a factor k longer for the light to reach the back and front wall and get back to the guy on the train again, then the time for the guy on the train slows down with the same factor k so he thinks the two way speed of light has the same value, c, no matter what the velocity of the train relative to the ground is...
In this way the "twoway speed of light is the same in all inertial frames".
I belive this is how it is always explained...