M' in the train frame is no longer at the midpoint of the lightning strikes, when the rays of light reach it. It is the train's velocity relative to the lightning strikes and the embankment frame that results in the rays of lights being recorded sequentially rather than simultaneously.
You are speaking like we can only measure distance with reference to the embankment. Yet if we use a system of measurement in which the train is at rest, then M' remains at the midpoint of the lightning strikes. This is inanely basic special relativity and, indeed, the point of the train thought experiment.
That becomes the definition of simultaneous within the context of SR. But you are cherry picking what Section 8 says about simultaneous events. You over look the footnote.
I am cherry-picking the only definition of simultaneity that Einstein provides. If you have another, please provide it. So far, all you have been able to provide is quotations that directly contradict your position.
8. ON THE IDEA OF TIME IN PHYSICS
Lightning has struck the rails on our railway embankment at two places A and B far distant from each other. I make the additional assertion that these two lightning flashes occurred simultaneously.
In the first two sentences of Section 8 Einstein asserts that the lightning flashes are simultaneous. He is not saying this is a definition. He is saying they are simultaneous.
You are talking about the introduction to the chapter! Einstein then goes on to explain what it means to say that two events are simultaneous. The entire next chapter is to show that the definition that he gives
after the very beginning of the chapter that you quoted. Please, read the chapter. All of it. In order.
This is one of the definitions at the end of Section 8. It is concluded from the hypothetical experiment designed to show that an observer at M sees both flashes at the same time. That is not where Section 8 leaves it though. Einstein goes on to introduce clocks and events at A, B and C. Take another look and pay special attention to the footnote. It is important!
No, it's not. You might have some kind of strange imagination that it does, but you are mistaken. The train example from Chapter 9 is only about the relationship between two events (and their midpoints in two different frames of reference), not three. A and B are
events, M and M' are
locations.
This is what is being referred to in Section 8,
If the observer perceives the two flashes of lightning at the same time, then they are simultaneous.
"They", refers to the flashes. Only through the knowledge that M is half way between A and B and the assumption that the speed of light is the same from A to M as it is from B to M, can the simultaneity of the perception of the flashes be attached to the lightning strikes.
Einstein is using poor wording. Sadly, he was not as clear a writer of physics as his idol, Maxwell. The "lightning flashes" are two events that occur spatially separated from an observer. The light from these flashes is what is being used to determine whether or not these events are simultaneous. Einstein is trying to define what it means for the lightning strikes to be simultaneous, yet you are claiming that now he is talking about something else entirely?
Remember the train is moving relative to the embankment and the lighting strikes.
But. Not. Relative. To. Itself.
Let M' be the midpoint of the distance A → B on the travelling train. Just when the flashes (as judged from the embankment) of lightning occur, this point M' naturally coincides with the point M...
"as judged from the embankment"
"as judged from the embankment"
"as judged from the embankment"
"as judged from the embankment"
"as judged from the embankment"
How many times do you have to see those words to have them sink in?
Remember the footnote? The above statement says that just as the flashes of lightning occur M and M' naturally coincide.
"as judged from the embankment"
That establishes a simultaneous event.., the location of M and M', just as the lightning strikes happen.
"as judged from the embankment"
Both M and M' record the resulting rays of light some time later. But in accordance with the footnote at the end of Section 8, since the lightning strikes can be determined to not only be perceived as simultaneous but be shown to be simultaneous, in the embankment frame, at that moment when M' and M coincide the lightning strikes are simultaneous in both frames. If A is simultaneous with B and B is simultaneous with C, then A is simultaneous with C.
"as judged from the embankment"
The event of the lightning strikes is given a time. It is the time when M and M' are in line with each other..,
"as judged from the embankment"
"as judged from the embankment"
as do A and B in both frames for that moment in time.
"as judged from the embankment"
Even when the train continues along the track, where it was remains a part of its past frame of reference.
When the train "continues along the track", it remains exactly where it was. The track moves past it and on to different coordinate values. Note the difference from the place of the train "as judged from the embankment".
Only the rays of light from the strikes are assigned times in either frame. And the times assigned to the rays of light are affected by where and when they were recorded in each frame. The only time given for the lightning strikes is that time when the locations of M and M' coincide.
"as judged from the embankment"
Why don't you try to work this out with actual math, assigning actual coordinate values to the different events in accord with the definition of simultaneity given? You will quickly find out that given the information about the times "as judged from the embankment", we can find out the times as judged from the train. These times are different.
Even in Section 8 no time was given for when the strikes occurred.
Because. It. Doesn't. Matter. In Chapter 8 we are only considering time "as judged from the embankment".
No, we know that the lightning strikes occurred when M and M' were in line with each other.
"as judged from the embankment"
The entire point of Chapter 9 is to demonstrate that simultaneity "as judged from the embankment" is not the same when judged from the train. As the quotations from Einstein that you provided indicate!
This is the conclusion, based on his final definition of simultaneous in SR. Events are defined as simultaneous when the information about the events reaches an observer simultaneously.
Exactly. So, judged from the train, the events of the lightning strikes
are not simultaneous. This is exactly the definition given in Chapter 8. Why you want to defend the opposite is baffling.
I suspect that you did not learn this stuff from having to work through it.
On the contrary, I worked through it carefully. You are the one writing direct contradictions of your own statements and quotations.
It continually seems you insist on interpreting this hypothetical from the context of some greater knowledge of SR than was present. Einstein was leading an interested lay audience through a series of examples and hypotheticals.
Yes, and he was clearly showing how the lightning strikes were not simultaneous in both frames. As he wrote. As you quoted.
In the case of RoS it was important to create a situation where two events were simultaneous and then demonstrate that two observer's would not agree, solely based on the information available at that point.
No. You are imagining something that is not the case. Something that you want to believe very, very strongly, but that is nonetheless false.