# I Simultaneity: Train and Lightning Thought Experiment

1. Nov 30, 2017

### Staff: Mentor

However, if you're thinking about it that way you're setting yourself up for future confusion. When you say "the IF which roughly contains the earth and the star", you seem to be suggesting that there might be an inertial frame (or non-inertial frame, for that matter) that does not "contain" the earth and the star. That's not right, because everything is always in all frames always - there's no such thing as being in one frame and not another.

There is such a thing as being at rest in one frame and not another, but that doesn't change any of the physics. In particular, the basic principle that the time something happened is the time at which it could be observed minus the light travel time between the event and the point of observation works in all inertial frames. Whether the source or the observer is at rest in the frame is irrelevant.

2. Dec 1, 2017

### 1977ub

I meant the IF in which the earth and the star are basically at rest. In this frame, the star explodes and the time it takes for that light to reach earth is 4 Y. In a different IF - traveling .999c, arriving at the star as it explodes, then passing the earth - the time between explosion and seeing on earth is miniscule.

3. Dec 1, 2017

### Staff: Mentor

As is the distance between the two events.

4. Dec 1, 2017

### Mister T

Yes, your meaning was clear from the context. That's usually referred to as the rest frame of those objects.

I think the point @Nugatory makes is that using the language one way signals an understanding, but using it another way signals, if not a misconception, then at least a warning that it might lead to a misconception.

And calculations done using that frame would also involve the delay due to light travel time.

5. Dec 8, 2017

### Josh_Seedman

OK. How about I back-peddle by a few steps and instead request the following assumption: The two clocks on the moving train are synchronized only after the train has reached its constant velocity. The sense I get is that it can be agreed that one or more valid procedures exist by which these two clocks can be synchronized to each other, in the IF of the moving train. Yes?

6. Dec 8, 2017

### Mister T

Yes, assuming you mean rest frame of the moving train when you say IF of the moving train.

But then they won't be synchronized in the rest frame of the platform. That's the point.

7. Jan 31, 2018

### Ziang

I found the thought experiment here http://www.bartleby.com/173/9.html
and Einstein concluded:" Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."

Now let me place a long seesaw on the embankment and parallel with the railway. This seesaw is working. I mean its both ends A & B are moving up and down continuously.
Let us consider two events: A is at high position and B is at low position. According to the relativity of simultaneity, these two events are simultaneous with reference to the embankment but are not simultaneous with respect to the train. Hence, the woman on the train claims that the seesaw is not straight up but it is curved up and down on its both ends A & B continuously. The lady questions why the seesaw is not broken?

8. Jan 31, 2018

### Ibix

Rotating objects generally look rather odd in relativity - you can't have rigid objects, so it's not that the seesaw is broken but rather that it is not rigid. A related phenomenon is the appearance of a wheel at relativistic speed. Even if the wheel is not itself rotating relativistically then it is length contracted into an ellipse as seen from a moving frame, yet it still rotates.

9. Jan 31, 2018

### Ibix

An important point to bear in mind, which I forgot to mention above, is that the seesaw is not straight even in the embankment frame. When one end strikes the ground a mechanical wave propagates up the beam at the speed of sound in the material and the other end doesn't stop rising until that wave reaches it. That's typically on a timescale of milliseconds, which is why you don't notice, but it's always going to be flexing.

Relativity forces you to pay attention to such details. Unfortunately that means that a formal analysis of this problem requires a detailed mechanical model of the seesaw and its reaction to applied forces.

10. Jan 31, 2018

### Peter Martin

The problem is in the description of the situation, which states that the lightening strikes are "simultaneous" without stating that the simultaneity is from the man's (bystander's) point of view. Let's re-describe the problem from the woman's (passenger's) point of view.

A woman sits at the middle of a train. Out the window she sees the countryside - which includes a man standing watching the train - rushing by in the direction of the rear of the train. Suddenly she sees lightening strike the front and rear cars of the train simultaneously. The question is: What does the man see?

Since he is rushing toward the rear of the train, he sees the lightening strike the rear car first because, as the light travels toward him, he is traveling toward the source of the light. By the same token, he is moving away from the strike on the front car so it takes longer for the light to reach him.

Since we typically spend more time on the landscape than on trains, we naturally take the man's point of view when describing this apparent paradox. So as soon as you read the (biased) description you are already on the "wrong track".

11. Jan 31, 2018

### PeroK

It's also a question of by how much the seesaw is out of sync. In the frame of the train, clocks at either end of the seesaw will be out of sync by $\frac{Lv}{c^2}$, where $L$ is the rest length of the seesaw and $v$ is the speed of the train. The train must be travelling at less than $c$, so an upper limit on this is $\frac{L}{c}$.

Now, for a seesaw of even $100m$, say, this is a very small time difference, less than a micro-second. The woman on the train will still measure the seesaw as being essentially in sync and observe nothing unusual.

Note that the seesaw will be curved in the platform frame as well, due to the forces along its length.

12. Jan 31, 2018

### Ziang

We don't have to use a seesaw moving up and down. Let us use a horizontal seesaw that its two ends move closer and farther from the railway. I mean the horizontal seesaw rotates freely an small angle during the experiment.

13. Jan 31, 2018

### Ziang

You can imagine a horizontal seesaw. And the seesaw rotates an angle freely during the experiment.

14. Jan 31, 2018

### pervect

Staff Emeritus
I would tend to believe the conclusion that the see-saw is curved, as "rigid objects" simply aren't compatible with special relativity. One can define Born-rigid motions in special relativity, but objects satisfying the necessary criterion to be Born-rigid can't change their state of rotation. Your see-saw is changing it's state of rotation, so it can't be Born-rigid.

You may not be familiar with Born rigidity. I don't see how you can learn about it before you learn about the relativity of simultaneity, though. So the process of learning special relativity involves first realizing that simultaneity is relative, then exploring all the logical consequences of this fact (along with the other aspects of SR such as length contraction and time dilation, though the relativity of simultaneity seems to be the hardest thing for people to learn). The lack of rigid objects is one of the logical consequences of special relativity, I'm unsure if it can be formally deduced solely from the relativity of simultaneity however.

I don't think your exposition isn't quite complete, a drawing of the seesaw from the perspective of the ground and from the train using the Lorentz transform would be interesting. I believe your conclusion is probably right, but the argument isn't quite rock solid yet.

15. Jan 31, 2018

### Janus

Staff Emeritus
This doesn't change anything about any of the arguments already made. For the seesaw to swing back and forth on any axis, some force must be applied to it at some point, and that force cannot propagate through the seesaw faster than c.

16. Feb 1, 2018

### Ziang

Let me say the seesaw is rotating at a constant angular speed (like the earth is spinning).
At the time point that the train is passing it, it is parallel with the railway (and is still rotating)

17. Feb 1, 2018

### Ibix

The seesaw will not appear straight. Also its length will vary as it rotates. You may wish to Google for "relativistic wheel" and look at the shapes of the spokes.

18. Feb 1, 2018

### Janus

Staff Emeritus
To build on Ibix's point, Let's consider the following two illustrations:

On the left we have our rotating pole (light blue bar), The tracks (black and brown lines), the train( green line) and our observers on the embankment and on the train (red circles), according to the embankment frame. This is the moment the observers pass each other. The pole is parallel to the tracks, and its ends line up with both the end of the train and particular points on the track (the white lines). The pole is rotating counter-clockwise as shown by the blue arrows.

One thing needs to be noted in this image, the train, since it is moving relative to this frame is length contracted. In other words, the length of the train as measured in this frame is shorter than the length of the train as measured in its own frame.

This becomes apparent when we look at the right image, which is drawn from the frame of the train. We are still dealing with the moment the two observers pass each other. In this frame the train measures its length as its proper length, while it measures the tracks and embankment, which is moving relative to it as being length contracted. As a result, the train no longer fits neatly between the white lines, but extends quite a bit beyond is both directions. This also means that one end ( the right end in this case) has already passed its white line before the other end hasn't reached its white line yet.

Also note that the bar appears as being curved, as per Ibex's post, and the right end of the pole has already gone past the point where it is adjacent to the tracks, while the left end has not yet reached that point. If this were an animation that we could run backwards and forwards, you would see the ends of the train lining up with a white line at the same moment that an end of the rod was adjacent to the same spot. This just happens at different times for each white line. Another thing to note here is that as the rod rotates in this frame, the curvature of the rod does not remain constant but changes from being curved as shown here to being straight when aligned vertically.

19. Feb 1, 2018

### Ziang

That is what I said: "the woman on the train claims that the seesaw is not straight up but it is curved up and down on its both ends A & B continuously. The lady questions why the seesaw is not broken?"

20. Feb 1, 2018

### Janus

Staff Emeritus
Just because the See-saw is curved in her frame does not mean that it is under stress in her frame.
In the following image we see the same diamond shape, in both its rest frame and according to a frame in which it is moving at 0.8c.
In the top image all the corner angles are 90 degrees, in the bottom image, one pair of corners is more than 90 degrees and the other pair is less than 90 degrees. But this does not mean that the shape is under some type of stress at the corner. Even if the shape was rotating, and thus constantly changing shape in the bottom frame, it would not be undergoing any stress.