Coexist vs Simultaneous

[vexspits]

In physics when we say two events occurred simultaneously at two locations--is that synonymous with saying they coexisted at those two locations? 

When we say the words “coterminous events”, it is taken for granted that we mean the two events coexist at a particular location and also that they occur simultaneously. However, to a layman like me, the advent of Special Relativity seems to have changed the concurrence between the two in the following way: We can no longer take it for granted that coexisting events that are not coterminous will also be simultaneous, because in Einstein’s original thought experiment (train/embankment) where he outlines his “most natural definition of simultaneity”, its determination depends on intervals, and the “how long” of these are shown to depend on the motion of the observer with respect to the wavefronts of light that inform him of the event’s “time”, and do not seem to serve as any indication of whether the events (in this case two bolts of lightning) coexisted.

I submit this to you all because it exposes the thinking of someone who is unable to understand how the relativity of simultaneity dispels any conceivable form of absolute coming-into-existence of events, or absolute “now”—perhaps creating an opportunity here to clear up misconceptions I suspect many laymen have. 

PS. I started this thread in the philosophy sub-forum, but it was automatically transferred to the physics sub-forum. 

 

Edited November 3, 2020 by vexspits

[studiot]

9 hours ago, vexspits said:

In physics when we say two events occurred simultaneously at two locations--is that synonymous with saying they coexisted at those two locations? 

When we say the words “coterminous events”, it is taken for granted that we mean the two events coexist at a particular location and also that they occur simultaneously. However, to a layman like me, the advent of Special Relativity seems to have changed the concurrence between the two in the following way: We can no longer take it for granted that coexisting events that are not coterminous will also be simultaneous, because in Einstein’s original thought experiment (train/embankment) where he outlines his “most natural definition of simultaneity”, its determination depends on intervals, and the “how long” of these are shown to depend on the motion of the observer with respect to the wavefronts of light that inform him of the event’s “time”, and do not seem to serve as any indication of whether the events (in this case two bolts of lightning) coexisted.

I submit this to you all because it exposes the thinking of someone who is unable to understand how the relativity of simultaneity dispels any conceivable form of absolute coming-into-existence of events, or absolute “now”—perhaps creating an opportunity here to clear up misconceptions I suspect many laymen have. 

PS. I started this thread in the philosophy sub-forum, but it was automatically transferred to the physics sub-forum. 

 

 

I think we should bear in mind that SR was originally written in German.
So any choice of English words in the translation depends partly upon the personal view of the translator.

Interestingly when I look up coterminous (in the OED) I find that the principal definition is

"Having a common boundary."

A secondary definition is also given "coextensive with in space, time or meaning"  -  A rather more general use.

So I agree with you that this is really a subject of the Philosophy of Physics and my interpretation is that what is trying to be conveyed is the idea that SR assigns a relationship between events.
Unsaid is that this idea is hard to define in English and most precisely and conveniently put in Mathematics.

The matter also brings into play the indea of continuity since in order to have a relation between events it must be possible to identify individual 'events'
This subject, in itself, has been the subject of intensive mathematical investigation and debate for centuries.

Edited November 3, 2020 by studiot

[Markus Hanke]

10 hours ago, vexspits said:

In physics when we say two events occurred simultaneously at two locations--is that synonymous with saying they coexisted at those two locations?

Coexistence and simultaneity are not interchangeable, in my opinion.

Example - consider two muons, which are unstable and short-lived particles. Suppose we have one muon around the time when the Earth begins to form, and one muon right now, here in your living room. Both of these come into existence, live for a short time, then decay. It is reasonable to now say that these muons coexist in spacetime, since spacetime is by definition the set of all events; however, there is no convention by which one can say that these events are simultaneous, because no physical clock can be constructed that shows them to be simultaneous - you can only make those events appear to happen in very quick succession, given the right setup, but they will never appear simultaneous. So these concepts aren't the same.

[swansont]

14 hours ago, vexspits said:

In physics when we say two events occurred simultaneously at two locations--is that synonymous with saying they coexisted at those two locations? 

When we say the words “coterminous events”, it is taken for granted that we mean the two events coexist at a particular location and also that they occur simultaneously.

That’s not a term I’ve run across in physics. We often approximate things as points, making the phrasing moot. Simultaneity for an extended object runs into issues, since the location of a point is a contributing factor in determining simultaneity.

 

 

3 hours ago, Markus Hanke said:

Coexistence and simultaneity are not interchangeable, in my opinion.

Agree. Coexistence would seem to refer to objects, while simultaneity refers to events.

[J.C.MacSwell]

On 11/3/2020 at 7:20 AM, Markus Hanke said:

Coexistence and simultaneity are not interchangeable, in my opinion.

Example - consider two muons, which are unstable and short-lived particles. Suppose we have one muon around the time when the Earth begins to form, and one muon right now, here in your living room. Both of these come into existence, live for a short time, then decay. It is reasonable to now say that these muons coexist in spacetime, since spacetime is by definition the set of all events; however, there is no convention by which one can say that these events are simultaneous, because no physical clock can be constructed that shows them to be simultaneous - you can only make those events appear to happen in very quick succession, given the right setup, but they will never appear simultaneous. So these concepts aren't the same.

Fair comment, but coexist does not normally mean "coexist in spacetime". Generally speaking, I think they are somewhat interchangeable with "simultaneously" being more specific.

As a somewhat counter example...your same example...no one would claim they ever coexisted without that context modifier "in spacetime".

They would normally be an example of things that did not coexist.

As you essentially pointed out, there is no frame they could coexist in or be simultaneous in, notwithstanding they both exist in spacetime.

[Markus Hanke]

6 hours ago, J.C.MacSwell said:

As a somewhat counter example...your same example...no one would claim they ever coexisted without that context modifier "in spacetime".

It always depends which wider context these terms are used in. You are right that in colloquial speech, they are largely interchangeable; however, the OP specifically asked about the situation in physics, and here the context is always spacetime.

There are in fact many such terms that have specific meanings in physics, which differ from how these terms are used in normal everyday speech.

[J.C.MacSwell]

6 hours ago, Markus Hanke said:

It always depends which wider context these terms are used in. You are right that in colloquial speech, they are largely interchangeable; however, the OP specifically asked about the situation in physics, and here the context is always spacetime.

There are in fact many such terms that have specific meanings in physics, which differ from how these terms are used in normal everyday speech.

Granted, but is coexist really such a term?

What is the specific meaning of coexist in physics? Where would one find it?

 I expect you might know better than I, but I fail to see any advantage in defining the term such that it means objects that may never have overlapped in their existence.

I realize that's somewhat an argument from incredulity, thus the questions.

[Markus Hanke]

19 hours ago, J.C.MacSwell said:

I expect you might know better than I, but I fail to see any advantage in defining the term such that it means objects that may never have overlapped in their existence.

Well, it isn’t a common term that you’d come across frequently in the physics literature - it really belongs more to philosophy.
The advantage would be precisely to contrast it with simultaneity (which has a very specific meaning in physics) - events can coexist without being simultaneous; especially since there are scenarios where it is difficult or even impossible to even define a meaningful concept of simultaneity.

[studiot]

This issue, in Relativity, is complicated by the nature of the the subject.

 

Here is a short extract from Professor Schrodinger's explanation of 'the metric' in his book on the subject.

The book is not a textbook of Relativity, more of a commentary which contains some definite insights as might be expected from a Professor of Applied maths.

I have marked just such an insight.

 

[J.C.MacSwell]

4 hours ago, Markus Hanke said:

Well, it isn’t a common term that you’d come across frequently in the physics literature - it really belongs more to philosophy.
The advantage would be precisely to contrast it with simultaneity (which has a very specific meaning in physics) - events can coexist without being simultaneous; especially since there are scenarios where it is difficult or even impossible to even define a meaningful concept of simultaneity.

It's not uncommon, for example, to use it to refer to a substance in more than one phase. It is said that the phases coexist.

I would think that that would be using the default meaning of the term for physics. 

[studiot]

1 hour ago, J.C.MacSwell said:

It's not uncommon, for example, to use it to refer to a substance in more than one phase. It is said that the phases coexist.

I would think that that would be using the default meaning of the term for physics. 

That would indeed be a correct common use (in Thermodynamics and Physical Chemistry) use for co-exist.

Nice example +1

Another might be the co-existence of isotopes which account for the observation that measured atomic weights are often not whole numbers.

Edited November 10, 2020 by studiot

[md65536]

5 hours ago, studiot said:

This issue, in Relativity, is complicated by the nature of the the subject.

Here is a short extract from Professor Schrodinger's explanation of 'the metric' in his book on the subject.

Maybe I missed the point, but the extract is basically explaining that in relativity, you deal with spacetime, not just space or just time. When you do, the things described in the text become simple. It's simple and mathematical, and the nature of the subject doesn't complicate it. If anything it seems to make issues irrelevant.

[studiot]

4 minutes ago, md65536 said:

Maybe I missed the point, but the extract is basically explaining that in relativity, you deal with spacetime, not just space or just time. When you do, the things described in the text become simple. It's simple and mathematical, and the nature of the subject doesn't complicate it. If anything it seems to make issues irrelevant.

 

On 11/3/2020 at 12:17 AM, vexspits said:

In physics when we say two events occurred simultaneously at two locations--is that synonymous with saying they coexisted at those two locations? 

 

I think his point is  "What two locations ?"

[vexspits]

On 11/3/2020 at 9:36 AM, swansont said:

Coexistence would seem to refer to objects, while simultaneity refers to events.

In the train/embankment thought experiment, might we, at the very least, say of the two events referred to as the lightning bolts striking the two locations on the train that they coexist at those respective locations—meaning that while there is a lightning bolt that exists at point A on the moving box car, there is also one that exists at point B on the moving box car? 

On 11/8/2020 at 6:46 PM, J.C.MacSwell said:

Fair comment, but coexist does not normally mean "coexist in spacetime". Generally speaking, I think they are somewhat interchangeable with "simultaneously" being more specific.

Yes @J.C.MacSwell  your discussion with @Markus Hanke clarifies the sense of “coexist” I had in mind: not the sense in which they coexist in spacetime. So in the example of decaying muons given by Markus—we’d be talking about two in my living room that both decayed there during the first 2 microseconds of the, say, 13 milliseconds it took my brain to visually process the first letter of this post. 

On 11/10/2020 at 11:38 AM, studiot said:

I think his point is  "What two locations ?"

@studiotYes, two events at the same location vs two events at different locations: So couched in the language of the text you cited: Two events that in one frame are at the same point in space envisaged at the same moment will—if I’m not mistaken—in another frame also be at the same point in space and envisaged at the same moment. Whereas “…what in one frame is the same moment at two different points, will in general be mapped in another frame as different moments…” 

Now I suppose two events (such as bolts of lightning) can’t share a point in space at the same point in time, but at the very least they may share a boundary, one so constricting as to approximate sharing a “point in space”. And it seems that whether “coexist” and “simultaneous” point to the same thing along every frame of axes depends on the degree to which the events are confined within such a boundary. If that is true, it means that any concurrence between the two is merely circumstantial; it no longer seems reasonable to say that “coexisting events” and “simultaneous events” are synonymous. 

As mentioned in the OP: I ask because, well, we have for instance this passage:

"The theory of relativity implies that simultaneity is relative to a frame of axes. If one frame of axes is moving relative to another, then events that are simultaneous relative to the first are not simultaneous relative to the second, and vice versa….Those who think that there is a continual coming into existence of events (as the present rushes onward into the future) can be asked “Which present?” It therefore seems difficult to make a distinction between a real present (and perhaps past) as against an as-yet-unreal future [italics are mine]".¹

And then we have a quote from Adrian Bardon:

"Just like 'here', 'now' is a term that has no application in a description of the world that excludes people’s subjective beliefs and attitudes. To include 'now' in that description would presume an absolute present that Einstein’s theory dispenses with when it dispenses with absolute simultaneity [italics are mine]".²

If simultaneity has no bearing on whether two or more events among many make up a succession of them (as in the Leibnizian definition of time), then how does the fact that it is relative dispel (or dispense with) such an absolute succession?

 

1 https://www.britannica.com/science/time/Contemporary-philosophies-of-time

2 Bardon, Adrian; A Brief History of the Philosophy of Time;  Oxford University Press 2013; p,94.
 

[swansont]

11 hours ago, vexspits said:

In the train/embankment thought experiment, might we, at the very least, say of the two events referred to as the lightning bolts striking the two locations on the train that they coexist at those respective locations—meaning that while there is a lightning bolt that exists at point A on the moving box car, there is also one that exists at point B on the moving box car? 

If you make a statement like this without referring to a frame in which the statement is true, it has to be true for all observers. Depending on details, this statement might not be true for all observers, since the strikes are simultaneous in only one frame.

”Coexist” is not something I’ve run across in relativity before, as I noted. It needs to be rigorously defined. Probably related to having a space-like interval.

[vexspits]

On 11/17/2020 at 6:54 AM, swansont said:

If you make a statement like this without referring to a frame in which the statement is true, it has to be true for all observers. Depending on details, this statement might not be true for all observers, since the strikes are simultaneous in only one frame.

”Coexist” is not something I’ve run across in relativity before, as I noted. It needs to be rigorously defined. Probably related to having a space-like interval.

Yes the lack of a rigorous definition is a problem. I certainly can’t define it mathematically. If I say, “…while there is a lightning bolt…”—what does that mean? What is this “while” business? I can’t say “at the same time” because that brings us right back to what you noted about the strikes both occurring at a shared t_x point in only one frame. 

I guess what I’m trying to point to when I say, “coexisting events” is something that cannot be confirmed to be the case for two events distanced from one another in Einstein’s thought experiment due to the limiting velocity of information. You would have to collapse the interval between the event itself and the event of its observation which would require some form of information transmission of infinite velocity—impossible. 

So if I ask the question: “Is there some definite fact of the matter regarding Einstein’s bolts of lightning quite apart from the “time order” in which they are deemed to occur in different frames of reference according to the time of physics?” What would this fact be and how would I find it out? 

Apart from a mathematical definition, the only thing I can come up with involves information transmission that “belongs” to a given frame of reference. So if, along with the mirrors “inclined at 90 degrees” which Einstein allotted, we equipped both observer M on the embankment and observer M₁ on the train with two light bulbs connected to transformers connected to two electrodes that “coincide” with the two bolts of lightning, then both M and M₁ would see the bulbs next to them light up “at the same time”. Yet, relying on the reflected light from the mirrors, M1 would reach a different conclusion. Both forms of information transmission (EM energy wave along reference-frame wire and light wave through the air) seem to point to something different. It’s this “something different” I’m trying to get a grip on. 
 

[md65536]

1 hour ago, vexspits said:

I can’t say “at the same time” because that brings us right back to what you noted about the strikes both occurring at a shared t_x point in only one frame. 

I guess what I’m trying to point to when I say, “coexisting events” is something that cannot be confirmed to be the case for two events distanced from one another in Einstein’s thought experiment due to the limiting velocity of information.

"The interval between the two events is space-like" describes everything you're talking about here, and it has a precise definition. "Event" has a precise definition as well. There no problem here.

A lightning bolt could also be described not as a single event, but as something with spatial and temporal extent. Then it could be described with some other precise definitions that effectively describe sets of events, such as "world line".

If "coexist" is given a precise definition, it would be fine, but there are already words that suffice, and it's a problem if you want it to mean something more or other than the definition you give it.

[studiot]

9 hours ago, vexspits said:

So if I ask the question: “Is there some definite fact of the matter regarding Einstein’s bolts of lightning quite apart from the “time order” in which they are deemed to occur in different frames of reference according to the time of physics?” What would this fact be and how would I find it out? 

This is a much better question than the wooly one you originally posted. +1

Now go back and read Einstein's train example again, armed with the following:

The point of the example is that the lightning bolts strike and marks permanently  both the train and the platform together, although they 'are in different frames', since the train is travelling and the platform is not.

Because the marks are permanent it is then possible to stand the train next to the platform, in the same frame (ie at rest) and compare the distances between the marks on the platform and the train.

Thus distance measured in a moving and rest frame may be directly compared.

 

[swansont]

13 hours ago, vexspits said:

Yes the lack of a rigorous definition is a problem. I certainly can’t define it mathematically. If I say, “…while there is a lightning bolt…”—what does that mean? What is this “while” business? I can’t say “at the same time” because that brings us right back to what you noted about the strikes both occurring at a shared t_x point in only one frame. 

I guess what I’m trying to point to when I say, “coexisting events” is something that cannot be confirmed to be the case for two events distanced from one another in Einstein’s thought experiment due to the limiting velocity of information. You would have to collapse the interval between the event itself and the event of its observation which would require some form of information transmission of infinite velocity—impossible. 

Events are typically not extended in time, so this simply reduces to simultaneity.

You can evaluate this after the fact, so transmission of information isn’t really an issue.

 

13 hours ago, vexspits said:

So if I ask the question: “Is there some definite fact of the matter regarding Einstein’s bolts of lightning quite apart from the “time order” in which they are deemed to occur in different frames of reference according to the time of physics?” What would this fact be and how would I find it out? 

For the train moving at v relative to the platform, you have x and t. Those are your measurables, in each frame.

You can ask about the time order and location. That’s all relativity tells you.

 

13 hours ago, vexspits said:

Apart from a mathematical definition, the only thing I can come up with involves information transmission that “belongs” to a given frame of reference. So if, along with the mirrors “inclined at 90 degrees” which Einstein allotted, we equipped both observer M on the embankment and observer M₁ on the train with two light bulbs connected to transformers connected to two electrodes that “coincide” with the two bolts of lightning, then both M and M₁ would see the bulbs next to them light up “at the same time”. Yet, relying on the reflected light from the mirrors, M1 would reach a different conclusion. Both forms of information transmission (EM energy wave along reference-frame wire and light wave through the air) seem to point to something different. It’s this “something different” I’m trying to get a grip on. 
 

No, this can’t be correct. If the means of information transmission changes the answer, then you have a flaw in your apparatus, or your interpretation of the information

[md65536]

15 hours ago, vexspits said:

So if, along with the mirrors “inclined at 90 degrees” which Einstein allotted, we equipped both observer M on the embankment and observer M₁ on the train with two light bulbs connected to transformers connected to two electrodes that “coincide” with the two bolts of lightning, then both M and M₁ would see the bulbs next to them light up “at the same time”. Yet, relying on the reflected light from the mirrors, M1 would reach a different conclusion. Both forms of information transmission (EM energy wave along reference-frame wire and light wave through the air) seem to point to something different. It’s this “something different” I’m trying to get a grip on.

Based on others' answers, I think I'm misunderstanding what you mean by this.

What you described here is fine, if you set up the experiment to get those results. Having the lightbulbs next to the observer is a good idea, because if they light up at the same time and at the same place, that can be considered a single event, and then everyone in every reference frame will agree on whether the bulbs lit at the same time or not. Similarly you can set it up so that M and M1 are at the same place at the moments the light bulbs light (ie. their world lines intersect at that event) and then everyone can agree on the simultaneity of those events. Is that what you are describing?

On the other hand, adding transformers and bulbs can unnecessarily complicate things, and obfuscate what you're trying to get a grip on. Simplification is usually better.

What you might be missing, is that just because the two light bulbs light at the same time, the events that caused them (in this case the lightning bolts) might not have occurred at the same time, because the information from the 2 events might not have taken the same time to get to the 2 bulbs. The simpler case is that M and M1 can both see the lightning bolts appearing simultaneous, but still disagree on whether they're "really" simultaneous, because they can disagree on their distances to the two lightning bolts. It applies the same to wires and bulbs, because you can measure the timing of the signals through the wires using light signals, and you'll get consistent results.

So that suggests some "definite facts" that you're looking for: The events you're describing, and the causal relationships between them, and the light cones describing those relations, are all definite and not dependent on frame of reference.

 

[vexspits]

On 12/1/2020 at 12:10 PM, md65536 said:

Based on others' answers, I think I'm misunderstanding what you mean by this.

What you described here is fine, if you set up the experiment to get those results. Having the lightbulbs next to the observer is a good idea, because if they light up at the same time and at the same place, that can be considered a single event, and then everyone in every reference frame will agree on whether the bulbs lit at the same time or not. Similarly you can set it up so that M and M1 are at the same place at the moments the light bulbs light (ie. their world lines intersect at that event) and then everyone can agree on the simultaneity of those events. Is that what you are describing?

I’m not sure. But I don’t think it matters. I think what you said here:

On 12/1/2020 at 12:10 PM, md65536 said:

On the other hand, adding transformers and bulbs can unnecessarily complicate things, and obfuscate what you're trying to get a grip on. Simplification is usually better.

is good advice, and what all three of you (yourself, @studiot, and @swansont) are pointing to: the fixed distances comparable after the fact, is exactly what I have in mind. M₁ and M would find themselves right smack-dab in the middle of the char marks left by the lightning bolts. 

As to how this applies to “coexisting events” is another matter; something that, I suppose, should be placed in philosophy. 

Thank you (and also both @studiot and @swansont) for your engagement and your patience.  
 

[md65536]

1 hour ago, vexspits said:

the fixed distances comparable after the fact, is exactly what I have in mind. M₁ and M would find themselves right smack-dab in the middle of the char marks left by the lightning bolts.

Yessssss... but

What you described can be true, but there are complications you should understand. Lets say the lightning bolts hit the 2 ends of the train simultaneously in the train frame, and M1 is in the middle of the train, and sees the lightning bolts simultaneously at the same moment M passes on the embankment (at a negligible distance from M1). Then M also sees them simultaneously. And yes, each says "The ends of the train where the char marks are, are both the same distance from me at the moment that I see the lightning."

First, because of length contraction, there isn't a fixed distance they agree on. M1 might say "Both ends of the train are 100m away from me and are at rest." M might say "Both ends of the train are 80m (say) away from me and are moving."

Second, because the train is moving for M, the locations of the char marks are not the locations of the lightning strikes! M can say "The lightning struck at locations x1 and x2, but by the time I'd seen them, the char marks (which were equidistant from me when I saw the lightning) had moved to locations x1+delta and x2+delta." Observer M is not at the midpoint of x1 and x2 in her frame, but at that point plus delta. M and M1, while momentarily at the same location, do not agree that that location is the midpoint of the lightning strikes, in their respective frames.

Edited December 10, 2020 by md65536

[vexspits]

13 hours ago, md65536 said:

Yessssss... but

What you described can be true, but there are complications you should understand. Lets say the lightning bolts hit the 2 ends of the train simultaneously in the train frame, and M1 is in the middle of the train, and sees the lightning bolts simultaneously at the same moment M passes on the embankment (at a negligible distance from M1). Then M also sees them simultaneously. And yes, each says "The ends of the train where the char marks are, are both the same distance from me at the moment that I see the lightning."

First, because of length contraction, there isn't a fixed distance they agree on. M1 might say "Both ends of the train are 100m away from me and are at rest." M might say "Both ends of the train are 80m (say) away from me and are moving."

Second, because the train is moving for M, the locations of the char marks are not the locations of the lightning strikes! M can say "The lightning struck at locations x1 and x2, but by the time I'd seen them, the char marks (which were equidistant from me when I saw the lightning) had moved to locations x1+delta and x2+delta." Observer M is not at the midpoint of x1 and x2 in her frame, but at that point plus delta. M and M1, while momentarily at the same location, do not agree that that location is the midpoint of the lightning strikes, in their respective frames.

Sorry, I was thinking of @studiot's post: “The point of the example is that the lightning bolts strike and mark permanently both the train and the platform together…”

So what I meant was: M₁ (train) finds herself in the middle of the char marks left on the train, while M (embankment) finds himself in the middle of the char marks left on the embankment. 

Now that is assuming the scenario described in the original thought experiment: where the strokes of lighting are simultaneous with respect to the embankment according to Einstein’s definition:

“…A and B are simultaneous with respect to the embankment [if]…the rays of light emitted at the places A and B… meet each other at the mid-point M of the length A —> B of the embankment.”¹

Again, despite the fact that the strokes are not simultaneous in M₁’s frame, she would still find herself in the middle of the char marks left aboard the train; and that’s because her position, in Einstein’s words, “naturally coincides with” M’s position when the flashes of lighting occur.  

It seems like a commonality between the frames despite the time order discrepancy between them. 

¹ https://www.bartleby.com/173/9.html

[md65536]

2 hours ago, vexspits said:

So what I meant was: M₁ (train) finds herself in the middle of the char marks left on the train, while M (embankment) finds himself in the middle of the char marks left on the embankment.

[...]

It seems like a commonality between the frames despite the time order discrepancy between them.

Ah, okay, that experiment can be set up in a lot of different ways and the details will be different.

If you mean it's common that each is positioned at their respective midpoints between the events when they pass, it's only because you've chosen those observers. You could choose other observers who don't have that in common.

If you mean that both frames agree on where the midpoint of the train and platform are located relative to their ends, yes that's true because the length contraction factor in the direction of motion is the same everywhere (the front half and back half of the train are length-contracted by the same factor).

But it is true, if you had a bunch of trains running parallel at different speeds, the 'midpoints' on each train between the two events, would all momentarily coincide. Basically, all observers would agree that the "forward" char marks on all trains line up together at some time (at the moment the lightning strikes them, of course!), and the middles line up at some time, and the "rear" char marks line up at some time. Also, a 1/4 mark of the length between the marks lines up at some time, etc.

Edited December 10, 2020 by md65536

[vexspits]

On 12/10/2020 at 12:07 PM, md65536 said:

Ah, okay, that experiment can be set up in a lot of different ways and the details will be different.

If you mean it's common that each is positioned at their respective midpoints between the events when they pass, it's only because you've chosen those observers. You could choose other observers who don't have that in common.

Yes true. But I needed this setup and this choice of observers because I thought it was the only way to highlight what I am trying to point to: A spatial relationship between whatever exists while both lightning strikes do —something etched that would not be affected by an interval of time; something that points to “a time” that differs from an ordinal t_x point assigned through the use of a clock interval. I’m kind of at a loss as to how to say it other than a state of affairs consisting of a bolt here, one there, two observers here, char marks on the train and on the embankment there etc. They all exist in a particular spatial relationship to one another, and they don’t have this relationship “at a time”; the relationship itself constitutes “a time”.