Did I Witness a Moving Train or a Stationary One? The Mystery of Bolts of Light

[kwestion]

Suppose I´m right in the middle of a train and suddenly bright light bolts out of both ends of my train. I swear that I saw both bolts of light at exactly the same time. Later I saw historical evidence of the char marks at the ends of my train.

Although my train seemed stationary to me, an outside observer in another train, pointed in the opposite direction, told me that my train was moving. Really it seemed like his train was the one that was moving. We haven´t concluded who is right or wrong regarding my train´s motion.

On further investigation, and unknown to me at the time of observation, we did find some char marks on the tracks that were separated by the same distance as the length of the train. Some say this is conclusive evidence that my train was stopped. However, the other observer has some credibility and I´d like to see if his perspective can also be true. Could my observations have been made while I was on a moving train even with this evidence on the tracks?

 

[Dale]

My account is that the originating events must have been simultaneous.

... we did find some char marks on the tracks that were separated by the same distance as the length of the train.

Your train was stationary wrt the tracks. If you were moving then so were the tracks.

 

[kwestion]

Your train was stationary wrt the tracks. If you were moving then so were the tracks.

I´m now trying to trace the events backwards: if the light hit my eyes at the same time, then I think the light originated from my train´s ends at the same time. I think that can be true whether I´m moving or not, since I´m equidistant from the ends of my train. In this case, the light source and I are not in motion relative to each other.

If the light originated from my train´s ends at the same time, then it seems that since the train´s ends are in contact with the rail, it would take essentially no time to imprint a mark on the rail regardless of whether I was moving. Those marks would then seem to need to be separated by the length of the train.

I don´t see the logical flaw in this reasoning. It must be that we rely on physical experiments to prove this thinking wrong. If so, I wonder about the value of the original thought experiment since thought doesn´t necessarily coincide with reality.

That is, it seems we must have foreknowledge of length changing in order to conclude that length changes. That foreknowledge must come from experiment, making the thought experiment seem useless to me.

 

[Dale]

I´m now trying to trace the events backwards: if the light hit my eyes at the same time, then I think the light originated from my train´s ends at the same time.

This should be: "the light hit my eyes at the same time, then [STRIKE]I think [/STRIKE]the light originated from my train´s ends at the same time in my frame."

I think that can be true whether I´m moving or not, since I´m equidistant from the ends of my train.

This is not correct. If you were equidistant between two simultaneous flashes in some frame, but moving wrt that frame, then you will receive light from the flash that you are moving towards before you receive light from the flash that you are moving away from. However, you are never moving wrt your own frame, by definition, so it doesn't really matter.

If the light originated from my train´s ends at the same time, then it seems that since the train´s ends are in contact with the rail, it would take essentially no time to imprint a mark on the rail regardless of whether I was moving.

Yes.

Those marks would then seem to need to be separated by the length of the train.

This should be: "Those marks would then [STRIKE]seem to[/STRIKE] need to be separated by the length of the train in the rail's frame". The length of the train in the rail's frame is only equal to the length of the train in your frame if you and the rails are stationary wrt each other.

I wonder about the value of the original thought experiment since thought doesn´t necessarily coincide with reality

Me too.

 

[Doc Al]

I´m now trying to trace the events backwards: if the light hit my eyes at the same time, then I think the light originated from my train´s ends at the same time. I think that can be true whether I´m moving or not, since I´m equidistant from the ends of my train. In this case, the light source and I are not in motion relative to each other.

Sounds good to me. The light struck the train at the same time, as measured by you in the train.

If the light originated from my train´s ends at the same time, then it seems that since the train´s ends are in contact with the rail, it would take essentially no time to imprint a mark on the rail regardless of whether I was moving. Those marks would then seem to need to be separated by the length of the train.

As measured by you, in the moving train. Someone at rest with the tracks would disagree. Unless, of course, your train was not moving along the tracks.

I don´t see the logical flaw in this reasoning. It must be that we rely on physical experiments to prove this thinking wrong. If so, I wonder about the value of the original thought experiment since thought doesn´t necessarily coincide with reality.

A thought experiment relies on application of certain physical principles. In this case, the principle that light travels at the same speed with respect to all observers.

That is, it seems we must have foreknowledge of length changing in order to conclude that length changes. That foreknowledge must come from experiment, making the thought experiment seem useless to me.

The point of this thought experiment is usually to illustrate that simultaneity is relative. If you conclude that the lightning struck the ends simultaneously, someone moving with respect to you must disagree.

 

[bahamagreen]

So... let's see if I have this straight...

If the train was not moving wrt the track:

Both you on the train and an observer opposite you on the track would see the same things - two simultaneous flashes, two char marks the same distance apart as the train is long.

If the train was moving wrt the tracks:

You see simultaneous flashes.

While standing by the track afterward, you see that the char marks on the track are further apart than the length of the train sitting still on the track.

You recall that the track ties appeared closer together while on the moving train at flash time than now while standing by the track looking at the track's char marks.

To you, the shorter distance between ties during the flash accounts for the difference between the resting train length and the distance between the char marks on the track (at the time you were on the moving train, there was more track between the ends of the train than when you looked at it at rest).

The observer by the tracks would see the flash at the back of the train occur first, then the one at the front.

If he had a way to do so, he would confirm that both flashes reached you at the same time.

He will recall that the train seemed to be shorter when moving compared to when it was at rest.

To the observer, the shorter length of the train when moving (and/or the staggered flashes and chars, (?)) accounts for the difference between the resting train length and the distance between the char marks on the track (at the time he observed the moving train, there was less length of train than when he looked at it at rest, and/or the train moved between separate flashes).

So... you have one reason the account for the difference, the observer has at least one reason, maybe two (both)?
Am I missing something the train rider should have noticed about time dilation wrt the track?

 

[kwestion]

The point of this thought experiment is usually to illustrate that simultaneity is relative. If you conclude that the lightning struck the ends simultaneously, someone moving with respect to you must disagree.

First, thanks for your thoughtful, nonconfusing comments.

I have been curious why the original author did not explore the ambiguity of rider's motion relative to the light source. Since both the track and train were charred, it seems that the rider has two possible realities to explore: a) that the rider is closing in on the source such as a point on the track and b) that the rider is stationary with respect to the source such as a point on the train. Both the train and track were charred, so both scenarios seem equally plausible.

Scenario (b) seems to have been hushed without explanation. The logical and physical principles used in the story don't seem to be sufficient to eliminate (b) as an option. If (b) is an option from the rider's perspective then so is simultaneity from the rider's perspective (at least from the physical principles revealed in the story).

Does that sound right? There isn't enough physics revealed in the original story to make the point that was intended on simultaneity? That is, there wasn't enough physics revealed in the story to eliminate (b), right?

To get where I'm coming from, I'm thinking that as long as the rider can view the source as being relatively stationary, then the author loses the ability to tell us that the rider saw the front flash first. The author's ability to make that claim hinges on the ability to tell us that the source of the flash was the rail and not the train. The author doesn't appear to have a legitimate reason for being biased towards the rail as the source. It seems that other complexities need to be examined in order to eliminate (b) and its not as simple as whisking it away.

 

[bahamagreen]

OK, so a and b are:

a - the flashes originate from the track
b - the flashes originate from the train

Either way, the flashes originate from the same place. The speed of each flash will propagate at c for both the train rider and the track side observer.

For train rider,
a = b = simultaneous flashes

For track side observer,
a = b = flash from back of train happens before flash at front

 

[kwestion]

OK, so a and b are:

a - the flashes originate from the track
b - the flashes originate from the train

Either way, the flashes originate from the same place. The speed of each flash will propagate at c for both the train rider and the track side observer.

For train rider,
a = b = simultaneous flashes

For track side observer,
a = b = flash from back of train happens before flash at front

I´m not sure why you said that: In the version of the thought experiment that I recently read, only (a) was explored, and it was done in a way such that the track-side observer concluded simultaneity and train rider concluded non-simultaneity.

I don't think scenario a=scenario b. The author took advantage of that fact by pointing out that the rider was closing in on the source in (a). That key part of the story cannot be said for scenario (b). It appears to me then that for the rider (a) supports non-simultaneity and (b) supports simultaneity.

 

[kwestion]

DaleSpam: Regarding your correction. I think your leading me to this:
As long as the light and I are relatively stationary on that train, it doesn't really matter if another observer thinks the set of me and the light sources are moving. For me, in these relatively stationary circumstances, the light will behave the same whether the other observer agrees with me that the set is stationary or if they see the set as moving at a constant velocity.

oh, and congrats on the 10000 mark

 

[bobc2]

Suppose I´m right in the middle of a train and suddenly bright light bolts out of both ends of my train. I swear that I saw both bolts of light at exactly the same time. Later I saw historical evidence of the char marks at the ends of my train.

I'm not sure this space-time diagram is very easy to follow, but it attempts to depict an observer riding in the middle of a moving (relativistic velocity) train car (represented by the red slanted line). The frame of reference for the train and rider is represented by the blue coordinates. Another observer is standing by the tracks in the black rest frame as the train passes. Lightning flashes simultaneously at the front and rear of the train car in the blue frame of reference. However, the flash at the front of the train is delayed in the black rest system.

The train tracks are charred adjacent to front and back of train at the lightning flash events. These charred marks are represented by the two purple vertical lines in the sketch.

Notice in this space-time diagram the train tracks extend indefinitely along the X1 direction (for both frames). To show the whole track in the diagram you would have to start with an extended line along the X1 axis and then extrude it along the 4th dimension, essentially covering the whole screen with whatever color you choose to represent it. So, I just left the screen white for the extruded steel track. But, I wanted to show explicitly the purple charred marks as they extend into the 4th dimension.

 

[Dale]

I have been curious why the original author did not explore the ambiguity of rider's motion relative to the light source.

The flashes are generally assumed to be instantaneous, so the light source's velocity is effectively irrelevant. Remember, in order to define a velocity you need at least two positions at two times (i.e. two events) at least infinitessimally separated. For an ideal single event you don't have that. That is why it doesn't factor into the usual analysis.

Scenario (b) seems to have been hushed without explanation.

I am a little puzzled as to why you think that.

To get where I'm coming from, I'm thinking that as long as the rider can view the source as being relatively stationary, then the author loses the ability to tell us that the rider saw the front flash first.

The speed of the source is irrelevant, only the distance to the source and the speed of light matter for determining that they are simultaneous. You could replace the lightning strike with a pair of flashbulbs, one mounted on the train and one on the tracks, all of the conclusions about simultaneity would be the same.

 

[Dale]

DaleSpam: Regarding your correction. I think your leading me to this:
As long as the light and I are relatively stationary on that train, it doesn't really matter if another observer thinks the set of me and the light sources are moving. For me, in these relatively stationary circumstances, the light will behave the same whether the other observer agrees with me that the set is stationary or if they see the set as moving at a constant velocity.

That's true, although I wasn't actually being that insightful. I was merely pointing out that when you are describing frame-variant quantities you need to specify which frame they are measured relative to.

I am glad that you got more from what I wrote than intended.

oh, and congrats on the 10000 mark

Thanks!

 

[bahamagreen]

I´m not sure why you said that: In the original thought experiment, only (a) was explored, and it was done in a way such that the track-side observer concluded simultaneity and train rider concluded non-simultaneity.

Well, I'm not sure why you said that!
The story was that the train rider observed and concluded simultaneity.
The track side observer's conclusions were not presented, but if they were they would be in agreement with simultaneity because the observation that the distance between the char marks on the track matched the length of the train leads to the conclusion that the train was at rest on the tracks during the flashes.

If char length was train length,
Both measured at rest,
Both frames were the same,
SR saw no test.

 

[kwestion]

Bahamagreen: Ah, I started to realize that I had recently read an impure version of the experiment. I guess my version reversed the roles. I tried to edit to clarify, but not quick enough. Sorry and thanks.

 

[kwestion]

The flashes are generally assumed to be instantaneous, so the light source's velocity is effectively irrelevant. Remember, in order to define a velocity you need at least two positions at two times (i.e. two events) at least infinitessimally separated. For an ideal single event you don't have that. That is why it doesn't factor into the usual analysis.

Here´s where I need clarification. It's not so much the velocity of the light source at the moment of emission, but the closing velocity of the rider on that light that I think matters. In the version I recently read, there seemed to be emphasis that the rider was closing in on the light during its travel, shortening the travel distance of the light which in turn caused an important conclusion in the story.

In the case where the source is taken to be the train and the observer is on the train, I don't currently think that the observer is closing in on the light, shortening its path. I'm thinking that case is different and the light travels the full distance of the 1/2 train.

The two cases seem different to me deserving separate analysis. No?

 

[bobc2]

Here´s where I need clarification. It's not so much the velocity of the light source at the moment of emission, but the closing velocity of the rider on that light that I think matters. In the version I recently read, there seemed to be emphasis that the rider was closing in on the light during its travel, shortening the travel distance of the light which in turn caused an important conclusion in the story.

In the case where the source is taken to be the train and the observer is on the train, I don't currently think that the observer is closing in on the light, shortening its path. I'm thinking that case is different and the light travels the full distance of the 1/2 train.

The two cases seem different to me deserving separate analysis. No?

I'm not sure if you can read the post #11 space-time diagram, but it is clear that both light flashes arrive at the middle of the passenger car at the same instant (the two photon world lines intersect at the middle, right where the observer is sitting).

 

[kwestion]

...But, I wanted to show explicitly the purple charred marks...

I'm not quite ready to get into the side question that I'm about to ask, but the horizontal distance between the blue lines is the length between the moving char marks, while the horizontal distance between F & G is the length between stationary train's char marks as well as the track char marks? Did I get that right?

 

[kwestion]

I'm not sure if you can read the post #11 space-time diagram, but it is clear that both light flashes arrive at the middle of the passenger car at the same instant (the two photon world lines intersect at the middle, right where the observer is sitting).

I´ll have to gnaw on that. This diagram seems to be drawn from the perspective that it is known that event a and event b occurred at different times and that the observer at c had experienced an illusion of simultaneity. It seems that there should be a way to also draw the events as truly simultaneous on the timeline and also received at the same time. I guess that would be equivalent to redrawing it from the perspective that the train is stationary and the tracks are what is moving. Thinking...

 

[Doc Al]

Here´s where I need clarification. It's not so much the velocity of the light source at the moment of emission, but the closing velocity of the rider on that light that I think matters. In the version I recently read, there seemed to be emphasis that the rider was closing in on the light during its travel, shortening the travel distance of the light which in turn caused an important conclusion in the story.

It depends on the frame doing the analysis. From the viewpoint of the rider in the middle of the train, the light travels at speed c with respect to him. But from the view of someone on the tracks, the rider is moving toward one flash of light and away from the other.

In the case where the source is taken to be the train and the observer is on the train, I don't currently think that the observer is closing in on the light, shortening its path. I'm thinking that case is different and the light travels the full distance of the 1/2 train.

Right! In the frame of the train, each flash of light travels a distance equal to half the train length. (Note that this has nothing to do with the movement of the 'source', but everything to do with the movement of the light and the rider. Whether the 'source' is on the train or on the track--or both--doesn't matter.)

The two cases seem different to me deserving separate analysis. No?

Those aren't different cases, but the very same situation analyzed from different frames of reference. That's the whole point! Observers on the train are forced to conclude that the lightning strikes occurred simultaneously. But observers on the track, who see the rider moving, draw a different conclusion.

 

[bobc2]

...the horizontal distance between the blue lines is the length between the moving char marks

Yes. Char marks were made at the front an rear of the moving train (it's also the distance from the rear end of the train to the front of the train).

...while the horizontal distance between F & G is the length between stationary train's char marks...

The train is not stationary. The vertical purple lines are the char marks on the stationary tracks extended into the 4th dimension. However, once the train stops, then the distance between front and rear train char marks will be the same as the F to G distance.

...as well as the track char marks? Did I get that right?

Got this part right. Track char marks are staionary, therefore the 4-D picture of the char marks are two purple lines extended vertically into the 4th dimension of the rest system (black coordinates).

To repeat the point about the observer sitting at the middle of the train passenger car: Notice that the photons arrive at the passenger's position at event C simultaneously. The observer on the ground would agree on that as well (ground observer agrees that the passenger witnessed both flashes simultaneously--that is, the ground observer agrees that the two photons intersect at the middle of the passenger car).

 

[ghwellsjr]

I have been curious why the original author...

The logical and physical principles used in the story don't seem to be sufficient...

There isn't enough physics revealed in the original story...

That is, there wasn't enough physics revealed in the story...

...the author loses the ability to tell us...

The author's ability to make that claim...

The author doesn't appear to have a legitimate reason...

In the version of the thought experiment that I recently read...

The author took advantage of that fact...

...I started to realize that I had recently read an impure version of the experiment. I guess my version reversed the roles. I tried to edit to clarify, but not quick enough. Sorry and thanks.

...In the version I recently read...

It would help if you would quote the original author so we can know what you're talking about. Please give the whole statement of the problem and the author's solution or provide a link.

Thanks.

 

[Dale]

Here´s where I need clarification. It's not so much the velocity of the light source at the moment of emission, but the closing velocity of the rider on that light that I think matters.

Sure, that works too. In the frame where the rider is at rest the closing velocity is c for both the front and the back flashes, and in the frame where the rider is moving at velocity v the closing velocity is c±v and is different for the front and the back.

The two cases seem different to me deserving separate analysis. No?

They seem to be the same case described from two different frames, but it is hard to tell without seeing the full description.

 

[kwestion]

It would help if you would quote the original author so we can know what you're talking about. Please give the whole statement of the problem and the author's solution or provide a link.

Okay, here's the story line I'm considering. Its from pages 10-12 of the book PHYSICS FOR THE REST OF US Ten Basic Ideas of 20th Century Physics by Roger S Jones.

[…] We shall again employ one of Einstein’s famous thought experiments: Imagine one observer—Stacy, let’s say—standing on the platform in a railroad station while a train is passing by. As luck would have it, two lightning bolts strike—one at the front end and one at the back end of the train—as it passes Stacy. Fortunately, no one is hurt, but the lightning leaves telltale char marks at both ends of the train and also at two corresponding points on the platform. Stacy takes advantage of the situation to make an observation. She notices that the light from the two bolts reached her at the same instant. She then paces off the distance between her point of observation and each of the char marks on the platform and discovers that the two distances are equal. In other words, Stacy was exactly equidistant from the two ends of the passing train as the lightning bolts struck. What does Stacy conclude?

Stacy received the light from the two lightning events at the same instant. The distances between Stacy and the two events are equal, and the speed at which light traveled to her from the two events is, of course, the same. So the two light signals Stacy received traveled equal distances in equal times and reached her at the same instant. The two original events (the emission of the light by the two bolts) must have occurred at the same time, and therefore they were simultaneous.

There seems to be nothing too surprising in all of this. As far as Stacy is concerned, two bolts struck at equal distances from her, and since she received the light signals at the same instant, the bolts must have struck simultaneously.

Let’s now look at the same two events from the point of view of an observer in the reference frame of the moving train. Our second observer will be Trent, who is located at the center of the train. Because Trent is moving with the train, he is approaching the light signal that travels toward him from the front end of the train. He’s also moving away from the light signal that proceeds toward him from the back end of the train. Thus Trent first intercepts the front-end light signal, while the back-end light signal is still catching up with him. An instant later in time, he receives the back-end signal.[8]

Afterwards, Trent also paces off the distance between his point of observation and the char marks at each end of the train. He, too, finds that the two distances are equal.[9] What then does Trent conclude? He is equidistant from the two events, and the speed of light is the same for him as it is for Stacy. (Here is where the crucial second postulate comes in: the speed of light is exactly the same in the train and in the station reference frames.) The two light signals traveled equal distances to Trent in equal times. But the light from the front event reached him earlier than the light from the rear event. Therefore the front event must have occurred earlier than the rear event.

The two events that are simultaneous for Stacy are not simultaneous for Trent. Stacy claims that the two bolts struck a the same instant; Trent says they occurred at different times. Who is right?

Einstein's surprising answer is that they are both right.[...]
​

Edit: the author also had some footnotes in this section that I am now later adding:

[8] The time delay between these signals will admittedly be very small because of the hight speed of light. But we can imagine that Trent is also moving at a very high speed-- half or three-quarters of the speed of light. In any case, there is a time delay, no matter how small, as long as Trent is moving.
[9] The equality of the two distances that Stacy and Trent measure is not critical to the argument; it’s just a convenience. They can infer the time intervals from whatever distances they measure. But since this is a thought experiment, we might as well keep things simple.​

 

[kwestion]

They seem to be the same case described from two different frames, but it is hard to tell without seeing the full description.

I recently posted the description of the scenario that I've been thinking about. Typically, I think the two perspectives are taken to be from two different observers, in my case, I'm wondering why a single observer can't have two different perspectives on the situation.

In the above-posted story line, my puzzle centers on this statement: "[...]Because Trent is moving with the train, he is approaching the light signal[...]"

I don't see how that conclusion about Trent's approach can be reached. The light in this case offers a nice ambiguity, because both the train and platform are involved in the source of the light.

I would have expected something like this: "[...]Because Trent is moving with the train, there are two possibilities: 1) he is approaching the light signal as envisioned as being from the platform, and 2) he is not approaching the light signal as envisioned as being from the train[...]"

 

[ghwellsjr]

Thanks for quoting the original author. His story is exactly the same as Einstein's:

http://www.bartleby.com/173/9.html

I'm not sure your author made clear in his discussion preceding this story what Einstein made clear in the previous chapters of his book: the "description" of how light travels and therefore what is simultaneous according to the two different frames is not a characteristic of nature but merely a matter of Einstein's personal definition of simultaneity and the propagation of light. But otherwise, there is nothing wrong with the author' story--how could it be, it's identical to Einstein's? I would just add something that was not clear, which is that although both observers measured themself to be equidistant from the two char marks, the distances are different for the two observers. I think this point may have provided confusion for you.

I recently posted the description of the scenario that I've been thinking about. Typically, I think the two perspectives are taken to be from two different observers, in my case, I'm wondering why a single observer can't have two different perspectives on the situation.

Do you see the huge difference between the author's (and Einstein's) scenario and the one in your original post? Yours had to do with what the train observer could see and not what was defined about the simultaneity of the distant lighting bolts.

In the above-posted story line, my puzzle centers on this statement: "[...]Because Trent is moving with the train, he is approaching the light signal[...]"

I don't see how that conclusion about Trent's approach can be reached. The light in this case offers a nice ambiguity, because both the train and platform are involved in the source of the light.

It's not a conclusion, it's part of the way the story line was set up. But again, you need to have the background that Einstein provided in his earlier chapters. I would suggest that you read the previous chapter of his book and then see if this story line makes sense.

I would have expected something like this: "[...]Because Trent is moving with the train, there are two possibilities: 1) he is approaching the light signal as envisioned as being from the platform, and 2) he is not approaching the light signal as envisioned as being from the train[...]"

You can envision any scenario from any frame of reference but if it is defined according to one frame of reference, you need to use the Lorentz Transform to envision the same scenario in a different frame of reference. If you define the scenario in a different frame of reference to begin with, then of course things can happen differently.

 

[Dale]

I recently posted the description of the scenario that I've been thinking about. Typically, I think the two perspectives are taken to be from two different observers, in my case, I'm wondering why a single observer can't have two different perspectives on the situation.

In relativity an "observer's perspective" is just verbal shorthand for "the inertial frame where the observer is at rest". There is no reason that an observer has to analyze a situation from a reference frame where he/she is at rest, but when you talk about the "observer's perspective", that is what you are referring to.

In the above-posted story line, my puzzle centers on this statement: "[...]Because Trent is moving with the train, he is approaching the light signal[...]"

I don't see how that conclusion about Trent's approach can be reached.

I don't understand your concern here. Trent's movement is not a conclusion, it is part of the problem setup. I.e. "Let observer T be an observer which is at rest wrt the train". His motion is a given, not a conclusion.

I would have expected something like this: "[...]Because Trent is moving with the train, there are two possibilities: 1) he is approaching the light signal as envisioned as being from the platform, and 2) he is not approaching the light signal as envisioned as being from the train[...]"

Yes, both 1 and 2 are correct.

 

[Dale]

Let’s now look at the same two events from the point of view of an observer in the reference frame of the moving train. Our second observer will be Trent, who is located at the center of the train. Because Trent is moving with the train, he is approaching the light signal that travels toward him from the front end of the train. He’s also moving away from the light signal that proceeds toward him from the back end of the train. Thus Trent first intercepts the front-end light signal, while the back-end light signal is still catching up with him. An instant later in time, he receives the back-end signal.[8]

Hmm, I think I may see a possible source of your confusion. The first sentence, in red, mentions that we will do the analysis in Trent's frame, but the third and fourth sentences, in blue, are given in Stacy's frame. And the other sentences apply to both frames.

That is somewhat confusing.

 

[kwestion]

Hmm, I think I may see a possible source of your confusion. The first sentence, in red, mentions that we will do the analysis in Trent's frame, but the third and fourth sentences, in blue, are given in Stacy's frame. And the other sentences apply to both frames.

That is somewhat confusing.

Thanks for hanging in there with me. I see that you've given real effort into understanding where I'm coming from. I appreciate that.

You've highlighted what I see as the disconnect well.

 

[kwestion]

It's not a conclusion, it's part of the way the story line was set up. But again, you need to have the background that Einstein provided in his earlier chapters. I would suggest that you read the previous chapter of his book and then see if this story line makes sense.

You and DaleSpam made similar comments regarding it not being a conclusion. I may not be communicating well, or may not be understanding some facet of the story. Somehow though, between post #27 and #28, DaleSpam seems to have connected to my thoughts. Would you mind reviewing those posts in case they help my outward communication more clearly?

I have reviewed chapters VIII and IX in the link that you included. Among other things, it stated this:

People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train.

That may underscore the disconnect that I'm having as mentioned in post #28.

With that statement in mind, the story line seems to be setting up the idea that the on-train observer could (and maybe should) envision the light source as being like a point on the train and therefore correspondingly the on-train observer should not be envisioned as approaching the light in this case.

Note that I'm not trying to invalidate the other perspective that the on-train observer could envision the light like a point on the track and therefore closing in on that light, but examining an additional perspective which the story line seems to set up, but mysteriously abandon.