# Bolts of light on a train

1. Jan 21, 2012

### 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?

Last edited: Jan 21, 2012
2. Jan 21, 2012

### Staff: Mentor

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

3. Jan 21, 2012

### kwestion

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.

Last edited: Jan 21, 2012
4. Jan 21, 2012

### Staff: Mentor

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."

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.

Yes.

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.

Me too.

5. Jan 21, 2012

### Staff: Mentor

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

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.

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.

6. Jan 21, 2012

### 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?

Last edited: Jan 21, 2012
7. Jan 21, 2012

### kwestion

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.

8. Jan 21, 2012

### 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

9. Jan 21, 2012

### kwestion

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.

Last edited: Jan 21, 2012
10. Jan 21, 2012

### kwestion

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

Last edited: Jan 21, 2012
11. Jan 21, 2012

### bobc2

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.

Last edited: Jan 21, 2012
12. Jan 21, 2012

### Staff: Mentor

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.

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

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.

13. Jan 21, 2012

### Staff: Mentor

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.

Thanks!

14. Jan 21, 2012

### 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.

15. Jan 21, 2012

### 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.

Last edited: Jan 21, 2012
16. Jan 21, 2012

### kwestion

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?

17. Jan 21, 2012

### bobc2

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).

18. Jan 21, 2012

### kwestion

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?

19. Jan 21, 2012

### kwestion

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...

20. Jan 22, 2012

### Staff: Mentor

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.

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.)

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.

Last edited: Jan 22, 2012