Simultaneity: Train and Lightning Thought Experiment

[Ibix]

So I can say that according to SR,
If a medium is moving straight at a constant velocity, the velocity of mechanic waves in/on the medium depends on the direction of wave propagation.
For an example, if the water was touched at the center of a moving pool, then the waves look like eggs instead of circles.

Yes.

I don't really understand what you are trying to get out of this. SR does produce counterintuitive results, yes, but that's just because your intuition isn't developed to handle extreme situations. Can you explain to us what you hope to learn by posting scenarios where SR's predictions are surprising to you?

 

[Ziang]

The Einstein's train is now railing along a long and very light box. At the center of the box, we install two identical spring guns in opposite directions.
On the ground, these two guns shoot two identical balls at the same time. These balls also hit the opposite walls at the same time. The observer standing on the ground claim that the box is sitting still.
On the train, according to SR, the two balls do not hit the opposite walls simultaneously. So the box would be moving jerkily with respect to the lady sitting on the train, right?

 

[jbriggs444]

The Einstein's train is now railing along a long and very light box.

But you proceed to assume that the box is rigid. It is not.

 

[Ibix]

So the box would be moving jerkily with respect to the lady sitting on the train, right?

The box is not perfectly rigid since this would imply an infinite speed of sound, so this is exactly the same as your previous scenario. The shock waves from the impacts will always meet in the middle. The parts of the box not yet reached by the shock wave are not in motion.

I repeat: what are you hoping to learn by this process?

 

[Nugatory]

There's no acceleration involved here, so the box is analogous to the rails the train in the original experiment rides on - its rigidity is not a concern and can be safely assumed. The problem is the erroneous conclusion

So the box would be moving jerkily with respect to the lady sitting on the train, right?

No, all the motion is perfectly smooth. The two events "first ball hits front wall" and "second ball hits rear wall" do not happen at the same time in the frame in which the train and the lady are at rest, while they do happen at the same time in the frame in which the box is at rest.

 

[jbriggs444]

Rigidity comes in because of the assumption of a "very light box" and the conclusion that the box [apparently assumed to be a rigid whole] would be "moving jerkily". The two ends might each move jerkily, but they would not move rigidly and simultaneously in all frames.

 

[Ibix]

There's no acceleration involved here, so the box is analogous to the rails the train in the original experiment rides on - its rigidity is not a concern and can be safely assumed.

I disagree, although I suspect as a point of language. I think Ziang is imagining that the box remains stationary in the frame where the ends are hit simultaneously, but jerks one way then the other in other frames. The reality, of course, is that the impact events are space-like separated so the ends move independently at least until they enter the future light cone of the other end's impact event. And in practice much longer than that because the shock wave propagation is so slow compared to light. That's why I said that rigidity (or lack thereof) is important here.

 

[Peter Martin]

To restate what Orodruin and Janus have said - it doesn't. The point is that when you set up the experiment, you choose in which frame the flashes are simultaneous.

That frame is significant to this experiment alone. It's not significant to any physics. For example you could rig red flashlamps that fire simultaneously in the train frame and blue flashlamps that fire simultaneously in the ground frame and run both experiments (i.e., a "ground is at rest" and a "train is at rest" version) in one pass by the embankment.

In your reply you state, "The point is that when you set up the experiment, you choose in which frame the flashes are simultaneous." So please answer my question in this scenario.

You are Zeus, the god of thunder and lightening. You can cause a bolt of lightning simply by pointing a finger at a location. You are hovering over the railroad tracks crossing a countryside. A man stands beside the tracks waiting for a train to pass.

Scenario 1: From your right, a high-speed train approaches. You can see a woman passenger’s head sticking out a window at the train’s midpoint. As the two observers come face-to-face, you intend for lightning to strike the tracks just ahead of and behind the train such that the man sees the two flashes as simultaneous. How do you time the lightning bolts?

Scenario 2: This time you are hovering over the high-speed train. The countryside is slipping by from left to right. As the two observers come face-to-face, you intend for lightning to strike the tracks just ahead of and behind the train such that the woman sees the two flashes as simultaneous. What do you differently from what you did the first time?

Many thanks for your time and attention.

 

[Janus]

In your reply you state, "The point is that when you set up the experiment, you choose in which frame the flashes are simultaneous." So please answer my question in this scenario.

You are Zeus, the god of thunder and lightening. You can cause a bolt of lightning simply by pointing a finger at a location. You are hovering over the railroad tracks crossing a countryside. A man stands beside the tracks waiting for a train to pass.

Scenario 1: From your right, a high-speed train approaches. You can see a woman passenger’s head sticking out a window at the train’s midpoint. As the two observers come face-to-face, you intend for lightning to strike the tracks just ahead of and behind the train such that the man sees the two flashes as simultaneous. How do you time the lightning bolts?

Scenario 2: This time you are hovering over the high-speed train. The countryside is slipping by from left to right. As the two observers come face-to-face, you intend for lightning to strike the tracks just ahead of and behind the train such that the woman sees the two flashes as simultaneous. What do you differently from what you did the first time?

Many thanks for your time and attention.

You'd aim at different points of the tracks.
Example: In scenario 1, the train, as measured by Zeus, is 10 km long. The tracks also has kilometer markers along it. So, for example, if the track observer is stationed at the 45 km marker, he would aim so that one lightning bolt strikes the 40 km marker at the moment the rear of the train is next to it and the other bolt strikes the 50 km marker when the front of the train is next to it.
Now we will also assume that the relative velocity between train and tracks is 0.866c

Now we switch to the second scenario. The train is not 10 km long. The 10 km measured in scenario 1 was due to length contraction. In scenario 2, Zeus measures the proper length of the train, which is 20 km. He also now measures the tracks as length contracted and the km placed along it as being only 1/2 km apart. Now, in order to hit the tracks just in front of the train as the train observer passes the 45 km mark, He has to aim at the 25 and 65 km markers on the tracks.

There is one thing to that also has to be accounted for in both of these scenarios Even Zeus' power to create lightning bolts is subject to the laws of Relativity. In other words, when he points his finger at a spot, the lightning can not strike at that spot any sooner than it would take for light to travel the distance between his finger and the spot. If you try to assert that it is instantaneous, then you are violating the rules you are intending to test. This means that the "Zeus" scenarios are really no different than scenarios where our train and track observers are given switches that they use to trigger the flashes, with the signals traveling along the wires at c.

 

[Ziang]

No, all the motion is perfectly smooth.

Now I install two laser guns instead of spring guns. Two light beams carry momentums and hit the mirror-walls of the box at different time points with respect to the train.
Is the box still moving smoothly with respect to the lady sitting on the train?

 

[Ibix]

You are Zeus, the god of thunder and lightening. You can cause a bolt of lightning simply by pointing a finger at a location. You are hovering over the railroad tracks crossing a countryside. A man stands beside the tracks waiting for a train to pass.

It's impossible to discuss a supernatural entity interacting with reality. What I can tell you is how an SFX guy would rig his squibs so that when Lawrence Olivier points his finger somebody somewhere records simultaneous strikes.

Let's define time zero to be the moment that the man and the woman pass. In both your scenarios, you rig the squibs to detonate at time zero. The only difference is whether you sync the squibs' clocks to train clocks or trackside clocks - that's the choice you make.

As Janus points out, the tricky part is where to place the squibs, but since I believe we rigged the scenario so that the train and embankment were the same length in the embankment frame you can just attach the squibs to the train when you want simultaneity in the train frame and to the embankment when you want simultaneity in the embankment frame.

 

[Ibix]

Now I install two laser guns instead of spring guns. Two light beams carry momentums and hit the mirror-walls of the box at different time points with respect to the train.
Is the box still moving smoothly with respect to the lady sitting on the train?

Same answer as before. Why do you think this changes anything?

 

[Peter Martin]

Janus, I can't thank you enough for your time and effort to explain the train-lightening experiment to me. I'm still processing your reply, so I'll thank you properly when I finish. I believe your explanation is the first time anyone on PF has introduced length contraction into their explanation of this thought experiment.

On another (sort of) note, I understand time dilation based on Einstein's "light clock". I've even done the algebra. What I don't get is how length contraction is derived from time dilation. I'd appreciate any thoughts you care to offer.

 

[vanhees71]

Janus, I can't thank you enough for your time and effort to explain the train-lightening experiment to me. I'm still processing your reply, so I'll thank you properly when I finish. I believe your explanation is the first time anyone on PF has introduced length contraction into their explanation of this thought experiment.

On another (sort of) note, I understand time dilation based on Einstein's "light clock". I've even done the algebra. What I don't get is how length contraction is derived from time dilation. I'd appreciate any thoughts you care to offer.

Maybe this helps?

https://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf

 

[jbriggs444]

On another (sort of) note, I understand time dilation based on Einstein's "light clock". I've even done the algebra. What I don't get is how length contraction is derived from time dilation. I'd appreciate any thoughts you care to offer.

There are three pieces. Length contraction, time dilation and relativity of simultaneity. Ignore anyone of the three and the other two will not make coherent sense.

 

[Janus]

Janus, I can't thank you enough for your time and effort to explain the train-lightening experiment to me. I'm still processing your reply, so I'll thank you properly when I finish. I believe your explanation is the first time anyone on PF has introduced length contraction into their explanation of this thought experiment.

On another (sort of) note, I understand time dilation based on Einstein's "light clock". I've even done the algebra. What I don't get is how length contraction is derived from time dilation. I'd appreciate any thoughts you care to offer.

First consider the standard light clock demonstration like the one shown here with a relative velocity of 0.866 c

Now modify it by adding mirrors aligned parallel to the motion as well as perpendicular.
If we assume no length contraction for the "moving" mirrors you would get the following :

Note that the horizontally traveling pulse for the moving mirrors doesn't even complete 1 leg of the round trip before the stationary mirror's pulses make their two round trips. More importantly, the vertical and horizontal pulses for the moving mirrors do not return to the starting point together. If this were true, then you would have a test that someone at rest with respect to the moving mirrors could use to tell that they were in absolute motion. (This is basically what the Michelson Morley experiment was looking for.)

If however, the moving mirrors are length contracted as measured in the frame of the stationary mirrors by the same factor as the time dilation, you get this.

Now the horizontal pulse for the moving mirrors complete the round trip in the same time as the vertical one does. The horizontal pulse does hit the right mirror after the vertical one hits the bottom mirror, but this is just the relativity of simultaneity being expressed. These events are not simultaneous according the the frame from which the animation is seen, but they would be for someone riding along with the moving mirrors.

 

[Nugatory]

On another (sort of) note, I understand time dilation based on Einstein's "light clock". I've even done the algebra. What I don't get is how length contraction is derived from time dilation.

The length of something is the distance between where its two endpoints are at the same time. Relativity of simultaneity, as shown by the train/lightning experiment, tells us that "at the same time" is frame-dependent, and therefore lengths also must be frame-dependent.

The easiest way to work out the exact formula is to start with the Lorentz transformation, from which both length contraction and time dilation follow.