Trying to Understand Light in Motion: A Frustrating Puzzle

[Dale]

if the passenger on the train was equidistant from the flashes when they occurred in the platform frame - then by the time the flashes moved from the source to her eyes she will have moved towards one and away from the other. so she will see two flashes but not simultaneously.

OK, so now you agree that data point 6 above (post 127) is correct?

 

[solarflare]

The lightning strikes are events that happen. They occur in all frames!

yes they are events that happen in all frames - but they happen at different times in each frame.

when you look at the stars you are seeing light that was emitted millions of years ago - not at the point when you see it.

the light strikes the train - therefore that is the starting point

the platform observer sees the light after it has traveled from the train to his eyes

the strikes do not originate in his frame

 

[solarflare]

I made this spacetime diagram a while ago, and I *think* it corresponds to the original scenario that is being discussed here. Maybe it will help. The "worldline" of the train (which is its path through spacetime) is clearly indicated, and it of course coincides with the t' axis:

The worldline of the photon that is coming in from the front (i.e. from the positive side) clearly intercepts the worldline of the train before (i.e. at a smaller value of t') the worldline of photon that is coming in from the rear (negative side) does.

The coordinate grid I've drawn is for the train observer, in the primed (t',x') coordinate system.

this graph shows that at t=0 there are two strikes - indicating that the strikes wer simultaneous.

the two strikes actually happen on the train

follow the lines to the observer and he sees the flashes simultaneously also - after a set amount of time has passed.

now take this graph and make the strikes hit the platform - the platform is the platforms guys frame so that is where they originate -

he sees the light simultaneously but the train observer sees them seperately.

the video has put the lightning striking in the wrong place - it should strike the platform not the train

 

[solarflare]

Sure, but for simplicity let's set r1 to some small value, say 1 cm. Then it is reasonable to neglect it and also to consider the lightning strikes to have marked both the train and the platform.

you want to neglect a key factor

and to say that the strikes mark both the train and the platform means that they must happen simultaneously also

 

[Doc Al]

The lightning strikes are events that happen. They occur in all frames!

yes they are events that happen in all frames - but they happen at different times in each frame.

when you look at the stars you are seeing light that was emitted millions of years ago - not at the point when you see it.

the light strikes the train - therefore that is the starting point

the platform observer sees the light after it has traveled from the train to his eyes

the strikes do not originate in his frame

It's certainly true that the lightning must occur before anyone can see it, no matter what their frame. But that's a triviality. (No need for relativity to understand that!)

There are several distinct events that are of interest in this scenario:
(1) Lightning strikes the front of the train (and the section of platform under the front of the train at that moment)
(2) Lightning strikes the rear of the train (and the section of platform under the rear of the train at that moment)
(3) Light flash from the front of the train reaches the platform observer
(4) Light flash from the rear of the train reaches the platform observer
(5) Light flash from the front of the train reaches the train passenger
(6) Light flash from the rear of the train reaches the train passenger

Discuss the scenario in terms of these events (which occur in all frames, of course) and you will be less likely to stumble.

To start you off, here are the facts:
Events 1 & 2 occur at the same time in the platform frame. (This is given in the setup.)
Events 3 & 4 occur at the same time in every frame.
Events 5 & 6 occur at different times in every frame.

What's interesting is what these facts tell us about the times of events 1 & 2 in the train frame. That's where the relativity of simultaneity comes in.

 

[solarflare]

why put r1 = r2 in the video if if its of importance?

 

[solarflare]

if they happen at the same time in the platform guys frame then the guy that made the video needs to put the strikes happening before they reach the centre of the platform.

and r1 can not = r2

 

[Doc Al]

Sure, but for simplicity let's set r1 to some small value, say 1 cm. Then it is reasonable to neglect it and also to consider the lightning strikes to have marked both the train and the platform.

you want to neglect a key factor

If I recall from the video correctly, r1 and r2 are the distances from the lightning strikes to the platform observer according to the platform observer. It's kind of silly to think of them as being 1 cm. Is the train that tiny?

You'll have a much easier time of it if you think of the train as being miles long.

and to say that the strikes mark both the train and the platform means that they must happen simultaneously also

Think of the lightning bolts as being huge sparks that hit the ends of the train and the platform (wherever the ends of the train happens to be at that moment) at the same time.

 

[Muphrid]

the video has put the lightning striking in the wrong place - it should strike the platform not the train

It does not matter whether the strikes actually hit the train or the platform, solarflare. This is why someone else was saying consider the simplest case, which is when the strikes actually hit both in one event. All that matters are the x-coordinates of the strikes.

you want to neglect a key factor

and to say that the strikes mark both the train and the platform means that they must happen simultaneously also

No, it doesn't mean simultaneity in the train's frame. Why do you think it does?

the light strikes the train - therefore that is the starting point

the platform observer sees the light after it has traveled from the train to his eyes

the strikes do not originate in his frame

The strikes are events; they do not belong in any frame. You can just as easily talk about two moving, omni-directional sources of light. These sources do not have to move the same as the train--or even as the platform! All that matters is that the platform observer perceives both of them to have been equidistant from him when he receives each source's light pulse.

the strikes happen in one frame first - the trains frame
they then occur in the platform guys frame only after the light has traveled from the trains frame to the platform frame.

See above; the strikes are events that do not belong to any specific frame. They may have coordinates according to frames, but the strikes themselves (not just when the flashes from those strikes reach observers) have the same time coordinates in the platform frame, yet the forward strike has a different, earlier time coordinate from the rear strike.

 

[Dale]

you want to neglect a key factor

It is not a key factor.

why put r1 = r2 in the video if if its of importance?

What is r2? You defined r1 as the distance between the train tracks and the platform, but you never defined r2. According to your definition of r1, it is not important and can be made as small as we like.

I don't recall the video ever discussing the distance between the tracks and the platform, but again, no mistakes in the video eliminate the errors that YOU are making.

 

[solarflare]

finally Doc al agrees with somthing i said :-)

it wasnt me that said to think of the distance as really tiny.

 

[solarflare]

if you do not know what r2 is - then you obv have not watched the video - r2 is defined in the video as being = to r1

 

[solarflare]

the train is on the tracks - not the platform - r1 is the distance from the rear strike to the platform guy - r2 is the distance from the front strike to the platform guy

 

[Muphrid]

the train is on the tracks - not the platform - r1 is the distance from the rear strike to the platform guy - r2 is the distance from the front strike to the platform guy

Now that you've clarified what you think these distances are, I agree. You gave the impression you thought that r1 was the distance from the platform observer to the track, which is why I said "there is no r1". This problem is almost always done in only 1 dimension for clarity.

 

[Dale]

the train is on the tracks - not the platform - r1 is the distance from the rear strike to the platform guy - r2 is the distance from the front strike to the platform guy

OK, then this statement of yours is not correct:

the train is on tracks that are a distance from the platform r1

The distance from the tracks to the platform is not the same as the distance from the rear strike to the platform guy.

For clarity, from now on, let's call the distance from the tracks to the platform d. That distance, d, can be made as small as desired and can be neglected. Also, for clarity, it would help if you would use the quote feature to identify things that you are quoting.

Do you now agree with all of the data presented in post 127?

 

[cepheid]

this graph shows that at t=0 there are two strikes - indicating that the strikes wer simultaneous.

The graph indicates that the strikes both occur at t = 0, meaning that they were both simultaneous in the platform frame. The graph also clearly shows that the two strikes DON'T occur at the same value of t'. One occurs at t' < 0, and the other one at t' > 0, as I explained extensively in my accompanying explanation, and in the second version of the diagram that I posted later. Did you actually read any of that, or are you just interested in using the diagram to perpetuate your own false assertions?

the two strikes actually happen on the train

In the scenario I envisioned, the strikes occur along the rails at x = ±4, x being position values in the platform frame, with the platform observer at x = 0. Whether the train is long enough that these strikes actually hit the front and rear of it, or whether they occur on the rails just ahead of the train and just behind it, is irrelevant.

follow the lines to the observer and he sees the flashes simultaneously also - after a set amount of time has passed.

If you're referring to the platform observer, then sure, I agree. If you're referring to the train observer, then no. The diagram clearly shows that the strikes reach the train observer at different times, because they strike at different times.

now take this graph and make the strikes hit the platform - the platform is the platforms guys frame so that is where they originate -

he sees the light simultaneously but the train observer sees them seperately.

the video has put the lightning striking in the wrong place - it should strike the platform not the train

Neither of the statements in bold make any sense whatsoever. It makes no difference whether the strikes hit the train in particular, or the platform ahead of the train and behind it. ANY scenario in which the lightning strikes at points equidistant from the platform observer, and in which the positions of the platform observer and train observer coincide at the origin at t = t' = 0, will result in the spacetime diagram I drew, which shows that the strikes occur simultaneously for the platform observer, and not for the train observer.

I also don't understand what you mean about the strikes "originating" in a particular frame. I'm not sure what you think an inertial reference frame is, but it is just a coordinate system that is rigidly attached to some unaccelerated body. You can conceptualize it as a rigid latticework of rods and clocks used for making physical measurements of distance and time. One such coordinate system (with the unprimed coordinates) is rigidly attached to the track or platform, and the other one (with the primed coordinates) is rigidly attached to the train. It's not like as if they are two alternate realities or something, so it's not possible to assert that something can "happen" in one frame and not in another. As Doc Al has repeatedly tried to convince you, the strikes are events that must occur in both frames. An event is something that occurs at a definite spacetime location. In the platform frame, it would have definite spacetime coordinates (t,x,y,z). This event must also have definite spacetime coordinates (t',x',y',z') in the train frame. What special relativity says is that these sets of coordinates are, in general, different from each other for two inertial frames that are in relative motion. I.e. the events can occur at different places and at different times as measured in the two frames. The two sets of coordinates are related to each other by a Lorentz transformation.

 

[solarflare]

if the lightning strikes the train - then it will mean that the train is considered stationary and the platform is moving

 

[Doc Al]

if the lightning strikes the train - then it will mean that the train is considered stationary and the platform is moving

Why in the world do you think that?

Viewed from the platform, the train is always moving; viewed from the train, the platform is moving. Nothing to do with the lightning striking the train or not.

 

[Dale]

if the lightning strikes the train - then it will mean that the train is considered stationary and the platform is moving

Nonsense. Lightning can strike moving objects.

Consider the lightning strikes to leave a char mark such that the size of the mark is greater than d. Then one strike can leave a mark on both the platform and the train.

 

[ghwellsjr]

Here is the transcript for the first minute of the video devoted exclusively to the platform frame:

Imagine two observers, one seated in the center of a speeding train car, and another standing on the platform as the train races by. As the center of the car passes the observer on the platform, he sees two bolts of lightning strike the car - one on the front, and one on the rear. The flashes of light from each strike reach him at the same time, so he concludes that the bolts were simultaneous, since he knows that the light from both strikes traveled the same distance at the same speed, the speed of light. He also predicts that his friend on the train will notice the front strike before the rear strike, because from her perspective on the platform the train is moving to meet the flash from the front, and moving away from the flash from the rear.

This states in no uncertain terms that when the center of the car (where the passenger is) passes the platform observer, the flashes of light from the strikes reach him at the same time. Therefore, they also reach the passenger at the same time (as long as there is no distance between them which is the only way you can meaningfully interpret this statement apart from seeing the video).

And what does the video show?

At 20 seconds into the video are these three images captured in rapid succession:

 

[solarflare]

posts 164 and 165

1 agrees with me and the other doesnt

 

[ghwellsjr]

Then the video goes back and repeats the sequence of the platform observer seeing the lightning flashes by panning up above him (unfortunately, I can only put three videos on a single post so this will be scattered among several posts):

 

[ghwellsjr]

Notice how in the first image here, they depict the progress of the two flashes of light hitting the window in which the observer is (although they don't show her, it's the second window from the front of the train car-the second window from the right). They hit simultaneously. Then in the next image, the two flashes hit the platform observer:

 

[Dale]

posts 164 and 165

1 agrees with me and the other doesnt

They are both pointing out that you made a mistake in calling the distance between the track and the platform "r1". Do you understand that r1 is not the same as the distance between the track and the platform, which I suggest we call "d"?

 

[ghwellsjr]

Here's where they show that the platform observer is equidistant from the two lightning strikes that hit the moving train car (at an earlier time but they have not shown this):

 

[Doc Al]

Here is the transcript for the first minute of the video devoted exclusively to the platform frame:

Imagine two observers, one seated in the center of a speeding train car, and another standing on the platform as the train races by. As the center of the car passes the observer on the platform, he sees two bolts of lightning strike the car - one on the front, and one on the rear. The flashes of light from each strike reach him at the same time, so he concludes that the bolts were simultaneous, since he knows that the light from both strikes traveled the same distance at the same speed, the speed of light. He also predicts that his friend on the train will notice the front strike before the rear strike, because from her perspective on the platform the train is moving to meet the flash from the front, and moving away from the flash from the rear.​

I agree, sloppy use of the term 'see' in the second sentence. And sloppy illustration of the light flash reaching the platform observer while the train just sits there.

 

[ghwellsjr]

Now here's where they repeat the sequence again but this time it is an animation and it shows something different than what they showed earlier. And note the platform observer is not present so we can't tell exactly when he is supposed to see the flashes of light. This is further complicated by the fact that they are panning the image from left to right so the perspective is changing making it impossible to know where the platform observer is. The last image is where they "light up" the passenger to show that she sees the front flash first:

 

[ghwellsjr]

And now with further panning, they show the rear flash arriving at the train passenger in the last of these images but note the lightning strikes have disappeared:

 

[Doc Al]

Why don't we scrap the video and just discuss the scenario that the video was trying (badly) to illustrate, which is what we've actually been discussing for the most part. It's the standard Einstein train thought experiment, of course.

A train passes by a person on the platform. At the instant the center of the train passes the person, lightning strikes both ends of the train according to the platform frame. (These are the two events that I label #1 and #2 in post 155.)

Solarflare, given this setup, can you comment on my statements in post #155?

 

[solarflare]

how can you say scrap the video when my whole point is that the video is wrong ?

 

[Dale]

Your statements are also wrong, independently of any errors in the video. Your original mistakes were not even involving the same scenario as the one in the video.

 

[Muphrid]

how can you say scrap the video when my whole point is that the video is wrong ?

The situation the video describes is essentially correct; we want to do away with it anyway because the small flaws do not seriously jeopardize the larger argument, which is what you seem to have an issue with.

Nevertheless, it may help to start from a clean slate so we can pick out exactly what the issue is. So let's draw up a new scenario.

A man is rafting on a narrow stream. He moves at a constant velocity. There are two other boats, one downstream of the man and one upstream, both with mirrors. These boats (and the mirrors attached to them) move in some arbitrary, unspecified manner. They may decelerate and accelerate at will.

The man uses two lasers to shine beams off both mirrors. If these beams both return to him at the same moment, then he concludes that he must have been equidistant from both mirrors at the time the beams hit the mirrors. If he shines both beams at some time t=0 and the beams return to him at some time t = 2 \delta, then he concludes that the mirrors were each a distance \delta from him at time t = \delta according to his watch.

Now, let us presume that, at the man's time t = \delta, there is a child in another raft just beside him, except the child has some constant velocity downstream relative to the man.

Now, solarflare, some questions for you:
a) Would the child believe the man emitted both laser pulses at the same moment?
b) Would the child say that the pulses reflected off both mirrors at the same time according to his (the child's) watch?
c) Would the child receive both reflected pulses at his boat at the same moment?

 

[solarflare]

take the position of the train when it is in the centre of the platform -

and run the scenario for both observers - the result comes out the same.

if the strikes occur when r1 = r2 then a simple triangle shows that they must occur in both frames simultaneously but at different times.

take a spaceship with two lasers - one on each wing

observer 1 is in the centre moving directly away from the ship in another smaller ship
observer 2 is stationary also in the centre but at a greater distance.

the spaceship fires its lasers -

observer 1 sees the two lasers pass simultaneously before observer 2

observer 2 sees the two lasers pass him simultaneously also

 

[solarflare]

they both say the lasers pass them simultaneously but they disagree on the time that they pass

 

[Doc Al]

take the position of the train when it is in the centre of the platform -

and run the scenario for both observers - the result comes out the same.

Don't know what you mean by 'run the scenario for both observers'. There is just one scenario, described from two different frames of reference.

if the strikes occur when r1 = r2 then a simple triangle shows that they must occur in both frames simultaneously but at different times.

Your 'simple triangle' is wrong.

take a spaceship with two lasers - one on each wing

observer 1 is in the centre moving directly away from the ship in another smaller ship
observer 2 is stationary also in the centre but at a greater distance.

the spaceship fires its lasers -

observer 1 sees the two lasers pass simultaneously before observer 2

observer 2 sees the two lasers pass him simultaneously also

Your scenario is somewhat ambiguous:

Do you mean:

(A) At the moment that the ship fires its two lasers towards the middle, there is an observer sitting in the middle of the ship (observer 2) and a second observer (observer 1) in a small ship moving parallel to the big ship just passing the middle of the ship at that moment (according to the big ship frame).

In this case the light flashes from each laser reach the middle of the big ship at the same time, but they reach the small ship at different times. In any case, the observers in the small ship do not agree that the lasers were fired at the same time.

Or do you mean:

(B) The ship fires its two lasers towards the middle. There is an observer sitting in the middle of the ship (observer 2) and a second observer (observer 1) in a small ship moving parallel to the big ship who happens to pass by the middle point just as the light reaches the middle point.

In this case both observers see the light simultaneously (since they are at the middle when the light arrives). But the observers in the small ship do not agree that the lasers were fired at the same time.

Note that in either scenario the lasers are only fired simultaneously in the frame of the big ship. The small ship will think that they were fired at different times.

 

[Doc Al]

they both say the lasers pass them simultaneously but they disagree on the time that they pass

If you say they reach the observers simultaneously, then you are talking about the second version (B) of the scenario (per my last post).

Again, you are hung up on the times at which the light flashes reach the observer. But the real interesting deal is what they conclude about whether the lasers fired at the same or different times. The different frames disagree about that!

 

[Muphrid]

Solar, the lasers have to point in opposite directions to to see the difference we're talking about.

You understand that the point if the train example is that the light from the strikes approach the observers from two different directions, right?


You also keep talking about triangles. There are no triangles necessary. Put the platform and train observers right next to each other.

 

[solarflare]

ok
A--------------------B------------------------------------- C

---------------------0 -------------------------------------
)-------------------/---------------------------------------/
)-----------------I----------------------------------------D
)-------------------\---------------------------------------\
---------------------0 -------------------------------------

the big ship fires two lasers at the two tragets from position A
the smaller ship that flying away from the big ship with velocity V sees the targets get hit by the lasers at position B
the targets are the 0
the pilot of the small ship reports that the lasers hit the targets simultaneously
the observer at position C sees the two targets get hit simultaneously also

 

[Doc Al]

Please choose one of the two laser scenarios that I offered in post #185, A or B. (They are both similar to the train example.)

If you insist on creating yet another scenario, please describe it in complete detail.

 

[Muphrid]

What you describe is correct; it's also nothing like the train situation because there is no light ray moving opposite the the small ship. Why do you think this illustrates the same thing as the train?

 

[solarflare]

my ship scenario shows that two observers in drifferent inertial frames of reference can agree that an event was was simultaneous

 

[solarflare]

but the event itself is relative to the time that they see it

 

[Doc Al]

my ship scenario shows that two observers in drifferent inertial frames of reference can agree that an event was was simultaneous

That's easy to arrange. One way: As long as two events take place at the same time and place, they will be simultaneous in all frames. But that's not particularly interesting.

Events 3 & 4 in the train example, for instance. (Post #155)

 

[Muphrid]

my ship scenario shows that two observers in drifferent inertial frames of reference can agree that an event was was simultaneous

While observers in two different frames of reference can agree that two events are simultaneous, the point of the train example is to show that there are circumstances where they don't agree.

In your example, the observers agree on simultaneity because the targets are separated in a direction perpendicular to the velocities of the observers.

In the train example, the observers disagree on simultaneity because the places the lightning bolts strike are separated in a direction parallel to the velocities of the observers.

 

[Nugatory]

they must occur in both frames simultaneously but at different times.

OK, I think I've found the problem here.
----------------------------------------

(Expanding a bit: Dude, "simultaneously" means "at the same time". Thus, the text above says "they must occur in both frames at the same time but at different times", which is of course nonsense. Is it possible that you're thinking that there's a single "real" time out there in which events can "really" be simultaneous, although that may disagree with what the observers observe?)

 

[Doc Al]

In your example, the observers agree on simultaneity because the targets are separated in a direction perpendicular to the velocities of the observers.

Ah... I'm glad you were able to decipher what that example was all about.

 

[solarflare]

What you describe is correct; it's also nothing like the train situation because there is no light ray moving opposite the the small ship. Why do you think this illustrates the same thing as the train?

because the train and the observers in the video are all lined up like my ship scenario -

by saying r1 = r2 the person who made the video is describing the same thing as my ship scenario.

 

[Muphrid]

because the train and the observers in the video are all lined up like my ship scenario -

by saying r1 = r2 the person who made the video is describing the same thing as my ship scenario.

No, the scenarios are nothing alike. Let's look at it again:

A--------------------B------------------------------------- C

---------------------0 -------------------------------------
)-------------------/---------------------------------------/
)-----------------I----------------------------------------D
)-------------------\---------------------------------------\
---------------------0 -------------------------------------

the big ship fires two lasers at the two tragets from position A
the smaller ship that flying away from the big ship with velocity V sees the targets get hit by the lasers at position B
the targets are the 0
the pilot of the small ship reports that the lasers hit the targets simultaneously
the observer at position C sees the two targets get hit simultaneously also

If points A, B, and C all lie along the x-direction, are the targets (0 and 0) separated in the y-direction? Is the velocity of the small ship in the x-direction?

If you answered yes to both, then this situation is nothing like the train, where the "targets" (the points the lightning bolts strike) are separated in the same direction as the velocity.

Contrast with the train diagram:

                   Train observer
                          T
 Rear of train R==========|==========F  Front of train
                          P
                  Platform observer

T & P need not be separated by any actual distance in the y-direction. The train moves left to right. F and R are separated left to right.

 

[solarflare]

No, the scenarios are nothing alike. Let's look at it again:



If points A, B, and C all lie along the x-direction, are the targets (0 and 0) separated in the y-direction? Is the velocity of the small ship in the x-direction?

If you answered yes to both, then this situation is nothing like the train, where the "targets" (the points the lightning bolts strike) are separated in the same direction as the velocity.

the pilot is positioned where the I is - therefore the light from the targets will travel in the y direction to get to his eyes - in the same way light hitting a platform will travel to the platform observer

 

[Doc Al]

the pilot is positioned where the I is - therefore the light from the targets will travel in the y direction to get to his eyes - in the same way light hitting a platform will travel to the platform observer

That's a red herring in the train scenario. Imagine the platform observer one inch from the tracks, but one mile from the ends of the train (at the moment of interest). You can safely ignore that one inch. The only distance of interest is along the direction of travel.