Can anyone show me some maths to explain the train problem with relative simultaneity

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):

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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:

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DaleSpam

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):

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Doc Al

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:

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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:

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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 ?

DaleSpam

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

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 [itex]t=0[/itex] and the beams return to him at some time [itex]t = 2 \delta[/itex], then he concludes that the mirrors were each a distance [itex]\delta[/itex] from him at time [itex]t = \delta[/itex] according to his watch.

Now, let us presume that, at the man's time [itex]t = \delta[/itex], 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 space ship 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

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.

Your 'simple triangle' is wrong.

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

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.