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

[Doc Al]

Okay. Erase my prior terminogy. I'll try to introduce as few of my own words as possible and borrow from the author's wording as much as possible in order to present my meaning. I'm supposing the author could have told the exact same story, but could have also included this alternate paragraph:

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 not approaching the light signal that travels toward him from the front end of the train. He’s also not moving away from the light signal that proceeds toward him from the back end of the train. Thus Trent [STRIKE]first[/STRIKE] intercepts the front-end light signal[STRIKE], while the back-end light signal is still catching up with him. An instant later in time,[/STRIKE] at the same time he receives the back-end signal.​

I'm supposing the word not is justifiable because a) the paragraph is said to be from the point of view (author's wording) of the observer in the train, and b) the paragraph states that the light is coming from the ends of the train. Together, (a) and (b) have the light approaching the observer who is just sitting there in his frame, without requiring that the observer be moving either toward or away from the light.

It's true that in Trent's frame the light simply travels toward him at speed c. Thus the travel time for each light signal must be the same--according to Trent's frame--since they travel the same distance (half the length of the train). But you cannot simply assume that the two light signals arrive at the middle of the train at the same time.

On the contrary, we already know--based on the analysis from the track frame--that the light signals cannot arrive at Trent's location at the same time. Thus Trent must conclude that the light flashes occurred at different times. (That's the point of this exercise--to show that simultaneity is frame dependent.)

 

[ghwellsjr]

Okay. Erase my prior terminogy. I'll try to introduce as few of my own words as possible and borrow from the author's wording as much as possible in order to present my meaning. I'm supposing the author could have told the exact same story, but could have also included this alternate paragraph:

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 not approaching the light signal that travels toward him from the front end of the train. He’s also not moving away from the light signal that proceeds toward him from the back end of the train. Thus Trent [STRIKE]first[/STRIKE] intercepts the front-end light signal[STRIKE], while the back-end light signal is still catching up with him. An instant later in time,[/STRIKE] at the same time he receives the back-end signal.​

I'm supposing the word not is justifiable because a) the paragraph is said to be from the point of view (author's wording) of the observer in the train, and b) the paragraph states that the light is coming from the ends of the train. Together, (a) and (b) have the light approaching the observer who is just sitting there in his frame, without requiring that the observer be moving either toward or away from the light.

You've just defined a different scenario. In this new scenario, the observer on the train sees the light reach him at the same time from the two bolts at opposite ends of the train in which he is at the midpoint. This means that in the rest frame of the train (and this observer), the lightning bolts occurred at the same time which means in the ground frame, they occurred at different times.

I think the problem you're having is that Einstein developed the train situation to help explain the relativity of simultaneity in an ongoing description throughout his book but your author just picked up this chapter out of context so it makes it rather confusing.

What you need to know is that in any frame, according to SR, if an observer sees light from two different directions hit him at the same time, and the sources of that light are equidistant from him, then they originated at the same time.

So let's say that at the moment the train observer reaches the same location as the ground observer, they both see the two flashes reaching them at the same time. The observer is always equidistant from the two ends of the train where the lightning bolts occurred but the ground observer is equidistant from the two ends of the train only at one moment in time, when they both see the two flashes.

Now we ask ourselves that question did the lightning strikes occur at the same time? You should see that as an ambiguous question because it will depend on which frame we want to use to answer it. If we use the train's frame, then the answer is yes because the midpoint of the train is alway equidistant from its two ends, correct?

But if we use the ground frame, it should be obvious that the answer is no because the ends of the train will have moved during the time that the light was propagating from the ends of the train to the observer on the ground. So in order for the two flashes to arrive at the same time at the observer, they must have started at different times. The lightning bolt at the rear of the train must have occurred earlier than the one at the front of the train.

Now you may wonder, how can the lightning bolts occur at the same time and at different times. It's because there are two definitions of time, one for the ground frame and one for the train frame.

 

[Dale]

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

OK, so here is how I would re-write it to avoid the inconsistency.

Let’s now consider a passenger on the moving train. The passenger will be Trent, who is located at the center of the train. In Stacy's frame, 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.

Let's now consider the events from Trent's perspective. In Trent's frame he is equidistant from both ends of the train and at rest wrt them. Since he received the front-end signal before he received the back-end signal and because the distance is the same and the speed of light is the same for both signals he therefore concludes that the front-end signal was emitted before the back-end signal.​

Is that more clear?

 

[bobc2]

OK, so here is how I would re-write it to avoid the inconsistency.

Let’s now consider a passenger on the moving train. The passenger will be Trent, who is located at the center of the train. In Stacy's frame, because Trent is moving with the train, he is approaching the light signal that travels toward him from the front end of the train.​

DaleSpam, I may have gotten my own head turned around here, but let me go one step at a time with you. I agree at this point.

He’s also moving away from the light signal that proceeds toward him from the back end of the train.

I'm still with you at this point.

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.

This is where I'm not quite following. Remember that in the rest frame (Stacey's) the rear train flash happened first, followed by the later flash at the front of the train. And the net result is that both flashes arrive at Trent's position at the middle of the train at the same time. This is event C in the space-time diagram. Stacey (rest system) doesn't actually receive the light flashes from event C until event E (we will assume that the light from the rear of the train reflected off of Trent so that both reflected rear flash and front end flash arrive together at event E in the space-time diagram.

Let's now consider the events from Trent's perspective. In Trent's frame he is equidistant from both ends of the train and at rest wrt them. Since he received the front-end signal before he received the back-end signal and because the distance is the same and the speed of light is the same for both signals he therefore concludes that the front-end signal was emitted before the back-end signal.

Is that more clear?

Here again, I'm thinking that Trent received both flashes at the same time. Both Stacey and Trent will agree that an event C has occurred.

 

[bahamagreen]

The storyline also left out a small detail - that Trent happened to be cat sitting for Schrodinger that day, the mechanism having been modified to trigger on receipt of simultaneous flashes from opposite sides... with the sensors not in the center of the train, but at the train's ends.

When this is all straightened out I'd be interested in knowing what Trent and Stacey told Schrodinger happened to his cat.

 

[ghwellsjr]

DaleSpam, I may have gotten my own head turned around here...
...
I'm thinking that Trent received both flashes at the same time. Both Stacey and Trent will agree that an event C has occurred.

You are discussing kwestion's original scenario from post #1, DaleSpan is discussing the author's scenario from post #24.

 

[bobc2]

You are discussing kwestion's original scenario from post #1, DaleSpan is discussing the author's scenario from post #24.

My bad. Sorry, I wasn't paying very good attention. Appologies, DaleSpam. (Actually, I knew there was no way DaleSpam was going to mess up on your basic train example)

 

[Dale]

This is where I'm not quite following. Remember that in the rest frame (Stacey's) the rear train flash happened first, followed by the later flash at the front of the train. And the net result is that both flashes arrive at Trent's position at the middle of the train at the same time.

Sorry about the confusion, there are too many versions of the scenario flying around in this thread. I was rewording the post 24 version:
https://www.physicsforums.com/showpost.php?p=3723123&postcount=24

 

[kwestion]

You've just defined a different scenario.

It's not a conclusion, it's part of the way the story line was set up.

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 think this is the area that I need to focus on for understanding.

I've been thinking that the story had its light source intentionally set up in an ambiguous or symmetrical way so that the the light could be interpretted as interchangeably coming from the track or the train. I'm gathering that, no, at the time the story is set up, it is defined to be unambigously coming from either the track or the train. Once the definition has been made, the story must continue with that unambigous definition and not try to equate the light source as equally being from the train and the track.

Along with that unambiguous commitment to the light source's location, I would continue on to be sure that Einstein's personal definition of simultaneity also used that same unambiguos, pre-defined, train-or-track source of light.

It may be that I can construct a scenario where both observers receive light at the same time, but depending on the pre-defined knowledge of whether the light came from train or track, Einstein's personal definition of simultaneity will come out with different conclusions.

Do I sound like I'm getting it? Maybe the author's intent of the char marks on both the track and train was for other purposes such as measuring, but that I interpretted the char marks to be evidence that the source of the light was ambiguous and therefore interchangeable at some level.

 

[Dale]

I've been thinking that the story had its light source intentionally set up in an ambiguous or symmetrical way so that the the light could be interpretted as interchangeably coming from the track or the train. I'm gathering that, no, at the time the story is set up, it is defined to be unambigously coming from either the track or the train. Once the definition has been made, the story must continue with that unambigous definition and not try to equate the light source as equally being from the train and the track.

This goes back to my post 12. It is not that the source of light is ambiguous, it is irrelevant.

In relativity there is a very important concept called an "event". It is the equivalent of a point in spacetime. It has four coordinates, the usual 3 spatial coordinates and one time coordinate (t,x,y,z). An event is something that happens at a given point in space and a given instant of time.

Events simply do not have rest frames. They do not have velocity in any frame.

A flash of light, considered as an event, marks a particular time and location. Different frames will disagree on the time and the location. It does not identify a velocity, it makes no sense to talk about whether or not it is at rest in a given frame.

 

[kwestion]

OK, so here is how I would re-write it to avoid the inconsistency.

Let’s now consider a passenger on the moving train. The passenger will be Trent, who is located at the center of the train. In Stacy's frame, 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.

Let's now consider the events from Trent's perspective. In Trent's frame he is equidistant from both ends of the train and at rest wrt them. Since he received the front-end signal before he received the back-end signal and because the distance is the same and the speed of light is the same for both signals he therefore concludes that the front-end signal was emitted before the back-end signal.​

Is that more clear?

Something's still nagging me to think that the words in blue are essential:

Let’s now consider a passenger on the moving train. The passenger will be Trent, who is located at the center of the train. In Stacy's frame, 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, in Stacy's frame, 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.

Let's now consider the events from Trent's perspective. In Trent's frame he is equidistant from both ends of the train and at rest wrt them. Since he received the front-end signal before he received the back-end signal (according to Stacy's perspective) and because the distance is the same and the speed of light is the same for both signals he therefore concludes that the front-end signal was emitted before the back-end signal.​

I'm still stuck on the idea that Trent must inherit his perspective from Stacy in this story. I don't see that there is independent analysis from Trent's perspective. In other words, Trent's perspective is really Stacy's perspective of what Trent's perspective should be. This bothers me. The conclusion of the story is that Trent and Stacy don't agree on what should be obvious matters, so I question whether we can conclude that Trent agrees with Stacy on this particular matter of perspective.

Can you share further insight on this? Is it possible for the story to include Trent's perspective on arrival time without having Stacy first tell us what Trent's perspective will be?

 

[Dale]

The whole point of the story is to explain it from one person's perspective, translate the same scenario to another person's perspective, and show how different observers disagree about the simultaneity of the same events. In order to connect the two perspectives and show that they are observing the same scenario you have to describe the second person's perspective in terms of the first.

You could describe Trents perspective without reference to Stacy, but it would not mean much:

Trent receives the front flash before the back flash. Trent is equidistant between the flashes. Therefore, he concludes that the front flash occurred before the back flash.

 

[Last_Exile]

Trent receives the front flash before the back flash. Trent is equidistant between the flashes. Therefore, he concludes that the front flash occurred before the back flash.

Pardon me for butting in here, but if Trent is equidistant between the flashes and the speed of light, c , is a constant for all inertial frames how would he see the front flash before the back one? In what sense would he be hastening toward or away from either flash?

 

[Doc Al]

Pardon me for butting in here, but if Trent is equidistant between the flashes and the speed of light, c , is a constant for all inertial frames how would he see the front flash before the back one? In what sense would he be hastening toward or away from either flash?

All you can deduce from that is that in Trent's frame the flashes take the same time to travel from the ends of the train to him at the middle. They would only arrive simultaneously if they left simultaneously (in Trent's frame).

 

[ghwellsjr]

Trent receives the front flash before the back flash. Trent is equidistant between the flashes. Therefore, he concludes that the front flash occurred before the back flash.

Pardon me for butting in here, but if Trent is equidistant between the flashes and the speed of light, c , is a constant for all inertial frames how would he see the front flash before the back one?

If the front flash occurs before the back flash in a frame in which Trent is stationary, then he will see the front flash first and the back flash second.

In what sense would he be hastening toward or away from either flash?

In a frame in which Trent is stationary, he is not hastening toward or away from either flash. That's why we can say if the two sources of the flashes are the same distance from him and he sees one before the other then it occurred before the other.

By the way, this is illustrating the definition of simultaneity and the definition of a frame of reference. Did you read Einstein's book referenced in post #26?

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

 

[Dale]

Pardon me for butting in here, but if Trent is equidistant between the flashes and the speed of light, c , is a constant for all inertial frames how would he see the front flash before the back one?

Suppose the two flashes are located 20 ft apart (c = 1 ft/ns). If the front flash goes off at t = 0 and the back flash goes off at t = 1 ns then he will receive the light from the front flash at t = 10 ns and he will receive the light from the back flash at t = 11 ns. Conversely, if he receives the light from the front flash at t = 10 ns he will determine that it went off at t = 0, and if he receives the light from the back flash at t = 11 ns then he will determine that it went off at t = 1 ns.

In what sense would he be hastening toward or away from either flash?

In his frame he is at rest (by definition), neither hastening toward nor away.

EDIT: guess I was slow on the draw here

 

[kwestion]

Thanks to all. Lots of valuable replies. I think I now have firmed up where I have been parting with what should seem obvious (Stacy's observation translating to Trent's experience). Thanks for patience and willingness to get through. I willl have followup questions later and hope I'm as lucky next time.