longshinewoole
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Doc Al said:The two events in this scenario are the lightning strikes at each end of the train. There are only two events, viewable by all observers whether on the train or on the embankment. (The entire point of this discussion is that different observers can see the same events happening at different times!) Note that it is you, not Einstein, who refers to A' and B' as events.
Note the careful use of "at a particular point". A' and B' are particular points--the ends of the train--not events. (Sounds like you are the one flipflopping words around.) There are just two events: Embankment observers would naturally say that these events occurred at locations A and B with respect to the embankment; Train observers would naturally say that these same events--the lightning strikes--occurred at locations A' and B' with respect to the train.
Einstein said:
"People traveling in this train will with advantage view the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train."
The words "also takes place" in the second sentence obviously says there are events taking place on the train.
If there are only two events A and B on the embankment, he must say "Then every event which takes place along the line will NOT take place at a particular point of the train."
If there are only two events A and B, then his experiment should look like this:
embankment: A_________M_________B.
the train...:__________M'__________.
Then how could he use that "vise versa"?
Now you said "But M' knows exactly where the flashes occurred--according to his reference (the train, of course) they occurred at A' and B', the ends of the train!" To me you were saying the samething as Einstein did: events taking place on the embankment also take place on the train. Due to the movement of the train, will a total of 4 events be created?
Now you said this: "All the train observers have to go by is their own observations. They measure the location of the events (the lightning strikes) with respect to the train. Everyone agrees that the light from the two flashes arrives at M' at different times. But each frame will disagree as to why that is."
If what the train observer observed was the light from A' and B' [according to his reference (the train, of course) they occurred at A' and B'], how could they agree that the light from A' and B' arrives at DIFFERENT TIMES? To this question of mine, I request you use methematics to show how "they measure." Don't use affirmative but ambiguous sentences such "Everyone agrees that the light from the two flashes arrives at M' at different times." Ambiguous because the phrase "two flashes" could mean either A and B, or A' and B'.