I am trying to understand the implications of c being relative to the frame of reference. Is the following analysis correct?
N is on a slow train moving 3 m/s and M on the platform next to N both see a distance super nova ahead of the train. The supernova is an event that happened a million light years away, hence a million years ago.
Do they see it at (almost) the same time? Being slow moving, M & N's clocks can be easily synchronized to within milliseconds.
Common experience says yes they do see it at about the same time.
HOWEVER, Within a frame of reference,
Distance = Velocity * Time
So if a one particle P was to travel from the super nova to us as at 0.1c and another particle Q was to travel towards us at 0.1c + 1m/s, then over a million light years Q would arrive long before P even though the speed difference is very small.
M & N are slow, but there will be a tiny difference in their perceived value of C. he super nova is very far away, which will amplify even a tiny difference in velocity as measured in different frames. The speed of the super nova is irrelevant, this is not an emitter model.
Question, is the super nova closer in N's frame of reference than in M's. If not, how can M and N observe it at the same time?
Likewise if the super nova was behind the train, it would be further in N s frame than M's.
(I am trying to make sense of Einstein's train example, which I suspect he fudges.
His example as stated makes perfect sense if there is an aether, but not if c is relative to the frame of reference of the observer. I suspect other things are going on, like length reduction or time shifting.)