Is relativity of simultaneity measurable?

In section 8 Einstein asserts that the lightning strikes are simultaneous! Elaborates on how and why, by explaining that the distance between A and M and B and M are equal... Light travels between the two in the same amount of time.
Thank you for rereading the chapter.

Now think about how we could then use this same procedure for the train: we have two lightning strikes that took place an equal distance apart, yet they arrive at the midpoint at different times, thus they are not simultaneous. If we use the definition of Chapter 8 like Einstein asks us, then the lightning strikes are not simultaneous in the reference frame associated with the train.

In that chapter he was first asserting that the lightning strikes were absolutely simultaneous and then connecting them to the embankment frame.
You need to reread the chapter yet again. He does not assign absolute simultaneity, he assigns a definition of simultaneity based on measurements of lengths, midpoints, and the arrival time of light. That is what simultaneous means by the end of that chapter and in the next.
As he begins section 9 he alters the definition slightly by defining the simultaneity, by the meeting of the two rays of light at M.
That is exactly what he lays out in the previous chapter. Perhaps you did not reread it.
That does not represent a direct measurement of the time of the lightning strikes. No synchronized clocks. And says that simutaneity can be determined in the train frame in the same manner.
Yes, in the manner of identifying equidistant points, only with respect to points given with reference to the train, not the embankment.

Since, at the time of the strikes, M' in the train frame is inline with M on the embankment and A and B in both frames are in line with each other, the train frame has all of the information required to determine simultaneity of the strikes, as described in section 8, for both frames. However, as defined in section 9 by the time the light reaches M' it is no longer between where the strikes occurred.....
You are imagining there is this thing called "the time of the strikes". There is only the strikes and the times assigned to them in different systems of coordinates. We know that in the reference frame of the train, there is no "the time of the strikes" as we know that the strikes take place at different times by the definition of simultaneity adopted in the previous chapter.

Einstein first established two events that are simultaneous and then demonstrated that due to time of light delays they would not be measured to be simultaneous in all frames.
No, he establishes that two events that are simultaneous in one frame are not simultaneous in both, which is what he explicitly says that he will do.

Go back and re read post 425, I quote most of the relevant parts of both sections, and explain why I have interpreted them as I have.
I have no idea why you insist on misrepresenting the thought experiment. You say, "The lightning strikes are simultaneous in both frames," even though you actually cut-and-paste from Einstein, "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)." This is either due to a simple mistake on your part or some sort of pathological problem that will not allow you to actually read the right words.

You are completely wrong: Einstein explicitly states the opposite of your claims and that you cling to your claims while quoting Einstein saying the opposite is baffling.
 
Now think about how we could then use this same procedure for the train: we have two lightning strikes that took place an equal distance apart, yet they arrive at the midpoint at different times, thus they are not simultaneous.

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.


If we use the definition of Chapter 8 like Einstein asks us, then the lightning strikes are not simultaneous in the reference frame associated with the train.

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.

He does not assign absolute simultaneity,

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.

he assigns a definition of simultaneity based on measurements of lengths, midpoints, and the arrival time of light. That is what simultaneous means by the end of that chapter and in the next.

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!

That is exactly what he lays out in the previous chapter. Perhaps you did not reread it.

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.

Yes, in the manner of identifying equidistant points, only with respect to points given with reference to the train, not the embankment.

Remember the train is moving relative to the embankment and the lighting strikes.

You are imagining there is this thing called "the time of the strikes".

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...​

Remember the footnote? The above statement says that just as the flashes of lightning occur M and M' naturally coincide. That establishes a simultaneous event.., the location of M and M', just as the lightning strikes happen. 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.

The event of the lightning strikes is given a time. It is the time when M and M' are in line with each other.., naturally coincide, as do A and B in both frames for that moment in time. Even when the train continues along the track, where it was remains a part of its past frame of reference.

There is only the strikes and the times assigned to them in different systems of coordinates.

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.

Even in Section 8 no time was given for when the strikes occurred.

We know that in the reference frame of the train, there is no "the time of the strikes" as we know that the strikes take place at different times by the definition of simultaneity adopted in the previous chapter.

No, we know that the lightning strikes occurred when M and M' were in line with each other. That is an un defined time of the event of the lighting strikes. The lightning strikes are given a time When M and M' coincide, the rays of light are recorded and given a time when they are perceived. In both frames the rays of light are perceived some time after the events (lightning strikes) from which they originated.

No, he establishes that two events that are simultaneous in one frame are not simultaneous in both, which is what he explicitly says that he will do.

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.

I have no idea why you insist on misrepresenting the thought experiment. You say, "The lightning strikes are simultaneous in both frames," even though you actually cut-and-paste from Einstein, "Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)." This is either due to a simple mistake on your part or some sort of pathological problem that will not allow you to actually read the right words.

You are completely wrong: Einstein explicitly states the opposite of your claims and that you cling to your claims while quoting Einstein saying the opposite is baffling.

I suspect that you did not learn this stuff from having to work through it. 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.

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.

He later introduces the tools necessary to reconcile the observations of observers in different inertial frames.., but that was not present this early in his presentation.

In order to demonstrate RoS you first have to establish simultaneous events. This cannot be done in any practical way... We cannot in practice know that two remote events are in fact simultaneous, all we can know is whether the information about those events is perceived, recorded or measure to be simultaneous.
 
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"

naturally coincide,
"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.
 
There really is no point in continuing this discussion with you. You seem to be incapable of any interpretation of what Einstein was presenting except from the basis of his final conclusion.

You have done a lot of saying you are wrong and offered no alternate interpretation. You are stuck at the end looking back and cannot see the pieces that he (Einstein) was assembling to get there. There is more than one place in the whole of that book where he presents something and then later shows why it is not an accurate account within the context of SR.

He was attempting to lead a lay oriented audience who were used to a Newtonian view of the world, toward a new way of understanding.

Anyway since you offer nothing and it is clear you understand little of the historical context, there is no further point to this...
 
There really is no point in continuing this discussion with you. You seem to be incapable of any interpretation of what Einstein was presenting except from the basis of his final conclusion.
How funny of me, to think that the final conclusion of what Einstein wrote is what Einstein wrote. I suppose I should, like you, decide that his conclusion was the opposite of what he wrote.

You have done a lot of saying you are wrong and offered no alternate interpretation.
Really? Please wait for the drugs or alcohol you have consumed to leave your system and then read what I wrote again.

To be clear: I am offering the interpretation that when Einstein wrote that the two lightning strikes were not simultaneous when viewed from a reference frame in which the train was stationary, he meant that the two lightning strikes were not simultaneous when viewed from a reference frame in which the train was stationary.

You are stuck at the end looking back and cannot see the pieces that he (Einstein) was assembling to get there.
Indeed, I can.

Chapter 8: When I, Einstein, say, "simultaneous", I mean that the light from two events reaches a midpoint at the same time.
Chapter 9a: What if we think of two midpoints moving relative to one another? Is simultaneity absolute?
Chapter 9b:One is a midpoint on the embankment, we have simultaneity.
Chapter 9c:One is a midpoint on the train. We see from the embankment that the light reaches that midpoint at different times.
Chapter 9d: So by our definition, the two events are not simultaneous from the midpoint determined on the train.

There is more than one place in the whole of that book where he presents something and then later shows why it is not an accurate account within the context of SR.
But that's not here.
He was attempting to lead a lay oriented audience who were used to a Newtonian view of the world, toward a new way of understanding.
By explicitly writing one thing but meaning the opposite?

Anyway since you offer nothing and it is clear you understand little of the historical context, there is no further point to this...
I'm sorry to have embarrassed you.
 
My shortest explanation is that he defines two events to be simultaneous in any given inertial reference frame IF the light from those two events would arrive simultaneously at the midpoint between the events.
Without isotropy of c, there may not be RoS.


I agree that your experiment demonstrates that relativity of simultaneity (RoS) can be measured. I don't think your experiment measures isotropy of light speed, though.
Yeah, but it measures velocity transformations. Just plug in c, and get c. Isotropy of c! :)
 
It is important to keep in mind the difference between what is a construction of the hypothetical and what ultimately can be reproduced experimentally. Much of how Einstein constructed his hypothetical acts as a teaching tool as far as RoS is concerned and becomes more important later as other aspects of SR are being explored and explained. Einstein's RoS hypothetical does not require a complete knowledge of SR. It is only a component of SR.

Einstein's words...

Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment.

As a further clue, he goes on to define simutaneity, in the embankment frame, not as when the lightning strikes happen, but when the onserver at M, observers them to happen at the same time.... The hypothetical Ws constructed with an imaginary absolute simultaneity of the lightning strikes built in.., and then defines simultaneity, as when the flashes of light are later observed.

Even though the train is moving relative to the embankment, at the moment that the lightning strikes occur, simultaneous in the embankment frame, points A, B and M' of the train frame line up with their counterparts on the embankment. The lightning strikes occur atthe tick of a clock not over several ticks....... An instant in time and thus the strikes are simultaneous in both frames. This is something that can only be stipulated in a hypothetical, for many of the reasons that were raised earlier inthe tread.

That is how Einstein constructed the hypothetical. Then he demonstrated how those events would be measured by two observers who were not at the location of either event.

He goes onto say that what he means by simultaneous in the embankment frame is that the observer at M, observes the flashes at the same time. And that because the observer at M' on the train was inline with M when the lightning strikes occurred, but was moving such the he/she observed the flashes first one and the the other..., simultaneity of two events is relative to the frame of reference from which they are observed.

Sorry, I'm afraid I don't understand the above at all.
 
What role is it that you are assigning to coordinate time, with respect to RoS? I ask only so everyone is on the same page and referring to the same measurement.

Just tell me whether it can be or not and then i will show the relationship..
 
I hope your, "Ok" means that you do agree that RoS is being measured.

Sorry for that.. don't consider that word at all.




I don't understand why you want to restrict this to a single observer. There is an observer (M) located at rest with the embankment, and there is an observer (M') located at rest with the train. One of them (M) receives the light from both lighting strikes simultaneously, and the other (M') receives the light from the stikes at two different times. Are you suggesting that observer M has no way of "measuring" that the light from the lightning strikes would be received by observer M' at two different times? If so, then that is not correct. Of course M could determine that.

But observers can only measure "proper" time and Not "co-ordinate" time.

In the both cases,there are two observers and two observers are measuring their proper time.

Really That is not a good book.. Please read Space-time Physics.
 
Okay, I hope you have the same reasons as me.

What reason do you mean? I know this one. If one measures that light speed travels at less speed and more speed,that means there in no Time Dilation,Length Contraction and No Relativity Of Simultaneity.
 
What reason do you mean? I know this one. If one measures that light speed travels at less speed and more speed,that means there in no Time Dilation,Length Contraction and No Relativity Of Simultaneity.

Yes, but that is if I said "will not", I said "may not".

Never mind, it's difficult for me to explain to you.
 
Just tell me whether it can be or not and then i will show the relationship..

Proper time is the elapsed time between two events, in which the clock is collocated with each of those events. "Elapsed", is key here.

Coordinate time is a specific time coordinate, associated with a location in a spacetime coordinate system. Observers cannot measure the coordinate time of remote events, but they can measure or determine the coordinate time of an event collocated with their clock.

As this relates to RoS and specifically Einstein's hypothetical, the following assumes that M and M' had clocks. (In the hypothetical they just perceive the rays of light.)

M and M' record the coordinate time that they perceived the rays of light. That was a single time coordinate, for each observation.

M' could record the proper time between when the rays of light were perceived in the train frame.

There is no elapsed or proper time measured by M.
 
Sorry, I'm afraid I don't understand the above at all.

Eram, I am willing to give it one more try, but since it has become obvious that I have been doing a poor job, trying to explain this as a whole, I believe it would be best to go one step at a time.

Before beginning with Einstein's hypothetical, I would add, what I have been attempting to explain is how Einstein constructed his thought experiment in Sections 8 & 9, to arrive at that definition in the end... And why some of the assumptions which cannot be experimentally proven in practice were important to that process. The SR definition of RoS, is not really in question. SR defines RoS based on when the information about events reaches an observer in any frame of reference.

With that in mind the first issue is that Einstein began Section 8, by just asserting that the two lightning strikes were simultaneous.

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.

Can you see and agree that in the statement in bold above he was simply asserting that the lightning strikes are or were simultaneous? Nothing that follows or his final conclusion, is important at this point. Only that he is referring to the lighting strike events specifically. Not to the rays of light.
 
Eram, I am willing to give it one more try, but since it has become obvious that I have been doing a poor job, trying to explain this as a whole, I believe it would be best to go one step at a time.

Before beginning with Einstein's hypothetical, I would add, what I have been attempting to explain is how Einstein constructed his thought experiment in Sections 8 & 9, to arrive at that definition in the end... And why some of the assumptions which cannot be experimentally proven in practice were important to that process. The SR definition of RoS, is not really in question. SR defines RoS based on when the information about events reaches an observer in any frame of reference.

With that in mind the first issue is that Einstein began Section 8, by just asserting that the two lightning strikes were simultaneous.

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.

Can you see and agree that in the statement in bold above he was simply asserting that the lightning strikes are or were simultaneous? Nothing that follows or his final conclusion, is important at this point. Only that he is referring to the lighting strike events specifically. Not to the rays of light.

It's alright, I appreciate the effort.

Which book or paper does this come from?
 
It's alright, I appreciate the effort.

Which book or paper does this come from?

Sorry I should have added a link. http://www.gutenberg.org/ebooks/30155 For the purposes of quoting I downloaded a copy of Relativity: the special and general theory, by Einstein from project Gutenberg.

I first read this in the mid 1960's, probably before the first publication of Talor and Wheeler's, Space Time Physics... And before I had begun any classes in physics. I would not say that at that time I fully understood, what Einstein was presenting. There are still parts that give me trouble and I have to think about.

If you agree with the assertion that the lightning strikes were simultaneous, I will move on to the next significant point.
 
If you agree with the assertion that the lightning strikes were simultaneous, I will move on to the next significant point.
This train gedanken has been widely discussed.

In the embankment frame, the lightning strikes are simultaneous, the embankment dude observes them simultaneously, the train dude does not.

In the train frame, the lightning strikes are non-simultaneous, the train dude does not observe them simultaneously, the embankment dude still does.




I first read this in the mid 1960's, probably before the first publication of Talor and Wheeler's, Space Time Physics... And before I had begun any classes in physics.
Just a couple of years after Einstein's death.

I was just reading through Einstein's 1905 SR paper, and I realized that I had a few questions to ask him! But he's dead, and all the other people I could've asked are dead too. :eek:
 
This train gedanken has been widely discussed.

In the embankment frame, the lightning strikes are simultaneous, the embankment dude observes them simultaneously, the train dude does not.

In the train frame, the lightning strikes are non-simultaneous, the train dude does not observe them simultaneously, the embankment dude still does.

This agrees with the conclusion of Section 9 and the definition of simultaneous, as the simultaneous observation of the rays of light. But the observation of the rays of light are not simutaneous with the remote events.

In practical terms, when an observer records the light rays from two remote events to be simultaneous, they cannot know that the two events, that the light rays come from, are not different distances away and that the light from one started toward the observer before the light from the other. All they know is that they record both rays at the same time or one before the other.

That is way Einstein, went to the trouble to assert simultaneous events to begin with, it is important to know that two remote events can be simultaneous and that there is some way to test that, even if only in a hypothetical, before the definition of simultaneous within SR, is of any value.

We measure remote events only as the information from those events reaches us, which at best is at the speed of light.

The definition of simultaneous within SR, does not say anything about the timing of the events in the frame of the events. It does. It even say that two separated events cannot have a common coordinate time while having different spacial coordinates. It just says the simultaneous in SR is defined by when the information about the remote events reaches the observer or measuring device.


Just a couple of years after Einstein's death.

I was just reading through Einstein's 1905 SR paper, and I realized that I had a few questions to ask him! But he's dead, and all the other people I could've asked are dead too. :eek:

Open a thread and ask the question(s). There are people posting on this forum that do have a solid background and/or understanding of the subject.
__________

I think one of the things that is hard for some to grasp is that the definition of simultaneous in SR is not saying with certainty that the remote events are simultaneous. Again it only defines the simultaneous record of when the information about the events reaches the observer.
 
I think one of the things that is hard for some to grasp is that the definition of simultaneous in SR is not saying with certainty that the remote events are simultaneous. Again it only defines the simultaneous record of when the information about the events reaches the observer.

Maybe you can answer something that's been puzzling me about your definition. According to you, RoS is about the simultaneity of the information about events reaching observers, not about the simultaneity of the events themselves. Right? But if that's RoS, how does it have anything to do with relativity? Even if you treat the flashes from the lightning strikes as classical projectiles, you can get two observers to disagree about which flash arrived first just by putting them in different places. The results only become interesting and relativistic if you have each observer account for the speed of light and interpolate back to when the strikes themselves happened.
 
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