I’ve been thinking about it more, and I’m having trouble with the train example.
First let’s take a simple case: Light travels 186,282 miles per second. Let’s say I’m running in a straight line at 1000 miles per second, and lightning strikes exactly 186,282 miles ahead of me. How much time passes (on my watch) before I see the lightning? The answer, I believe, is exactly 1 second, because light travels the same speed in every reference frame – that’s Einstein’s chiddush.
So now the train example. To make it simpler, lets say the train is 372,564 miles long (2 x 186,282 miles). The guy on the platform sees both lightning strikes simultaneously after 1 second – simple. But why doesn’t the guy on the train also see them simultaneously? Why is it different from my case? Is my conclusion in my case incorrect?