# I Special Relatively Conundrum

1. May 26, 2017

### hatflyer

I can't reconcile how a slightly altered thought experiment can be explained.

It's the 1 where a train is going past, with an observer on the ground. Say instead of a train it's a cable car, held up by a cable in the front and 1 in the back to an overhead line.

The observer on the ground shoots 2 lasers simultaneously (to him) so that each laser destroys the support cables, the 1 in the front and the 1 in the back. To that observer, they get destroyed simultaneously, and so the cable car falls in a horizontal orientation.

But, to an observer in the middle of the cable car, the front cable snaps before the rear 1. So he sees the front of the cable car fall first, then the rear cable snaps and it falls a bit later. Thus the cable car would seem to fall with the front pointed downward, not horizontally as seen by the ground observer.

Those opposing views can't be, as the cable car falls in only 1 orientation.

Which is it?

Thanks.

2. May 26, 2017

### Ibix

You can't ignore the speed at which the cable relaxes. Basically the car won't fall until the information about the break propagates from the break to where the car is suspended. That happens at the speed of sound in the cable, which is much less than the speed of light and is frame dependent - and not the same speed in both directions in frames where the cable is moving. This will conspire with the relativity of simultaneity so that if the information about the cable breakages arrives simultaneously in one frame it will do so in all.

3. May 26, 2017

### Staff: Mentor

The orientation is not invariant. There is nothing wrong with two reference frames disagreeing about the orientation.

4. May 26, 2017

### phinds

I don't think the introduction of the speed of sound in the cable is really relevant to the OP's conundrum and his question could be reformulated to avoid any need for consideration of that. His problem, I think, is that he is ignoring (as you point out) the relativity of simultaneity but in the following way: he thinks that he can fire the lasers simultaneously AND have the return pulses hit his eyes at the same time AND have both of those event happen along with the pulses hitting the cables at the same time in the TRAIN's FOR so that it drops horizontally. The geometry of all that just doesn't work.

5. May 26, 2017

### phinds

NUTS ! I see that I overthought the problem.

6. May 26, 2017

### Mister T

If each end of the car hits the ground at the same time in one frame, then they can't hit at the same time in the other frame.

7. May 26, 2017

### hatflyer

I'm not quite getting it. The front cable is seen by the rider as snapping first. Doesn't he thus see the front cable itself collapse downward before he sees the rear cable collapse? Then I thought time frames in a direction perpendicular to the time frame in the direction of motion were the same to both observers, so that at least on the end of the cable car (not towards the observer) it would start to fall before the rear does.

Obviously that's wrong, but confused if we are talking about the ends of the car they would at least start at separate times.

8. May 26, 2017

### hatflyer

PS. So the observer in the car sees the cable in the front snap before he sees the rear cable snap (i.e. he sees the moment the laser hits the cables), yet he sees himself falling horizontally?

9. May 26, 2017

### Staff: Mentor

There are not different "time frames" in different directions. The spatial coordinates in directions perpendicular to the direction of motion are the same in both frames; but anything involving time is affected regardless of what direction it's in.

10. May 26, 2017

### hatflyer

Sorry, I meant velocities.

11. May 26, 2017

### phinds

velocities involve time, thus the relevance of Peter's comment

12. May 26, 2017

### hatflyer

So if the observer in the car shoots at gun outside the side window, don't both observers measure the speed of the bullet as the same speed?

13. May 26, 2017

### FactChecker

The orientation can only be defined by the positions of the front and end of the car at the same time. So coordinate systems that do not agree on what is simultaneous will not agree on the orientation.

14. May 26, 2017

### jartsa

A military helicopter has a propeller at the rear and at the front, enemy fire destroys first the front propeller, then after a short while the rear propeller is destroyed. Now we have helicopter that spins around, right?

That war story was told in the frame of the helicopter, I mean it was the point of view of the helicopter crew.

So the cable car also spins around, right?

15. May 26, 2017

### hatflyer

That doesn't seem possible. What if there was a marble at the center of the cable car. Both observers must agree on whether the marble stays at the center or rolls to the front of the car. So surely they agree on orientation of the car, right?

16. May 26, 2017

### Staff: Mentor

17. May 26, 2017

### Staff: Mentor

Yes. But the direction the marble rolls does not depend only on the orientation.

18. May 26, 2017

### Staff: Mentor

Yes.

No. This scenario includes proper acceleration--the car is being accelerated upward as long as the cables hold--so you can't analyze it the way you would analyze purely inertial motion. In the frame in which the car is moving, because of the upward proper acceleration, its surface is not flat--it is concave upward. So even though the front end falls first in this frame, the concavity prevents the marble from moving forward.

19. May 26, 2017

### jartsa

In the ground frame the marble starts moving, because sound waves from the front reach the marble first, because of anisotropic speed of sound in the car structure.

And in the car frame the marble starts moving, because sound waves from the front reach the marble first, because of the non-simultaneity of the laser shots.

20. May 26, 2017

### Mister T

You don't need the cables to illustrate your paradox. Suppose the car is in free fall and hits Earth's surface. If the ends hit simultaneously in the car's rest frame, they don't hit simultaneously in Earth's rest frame. A marble on the floor of the car stays put in the car's rest frame because the car is level in that frame. It therefore stays put relative to the car's floor in Earth's rest frame, not because the car is level, but because both the car and the marble are in motion in Earth's rest frame.

21. May 26, 2017

### hatflyer

In the ground frame, doesn't the force translation from the sudden loss of upward force from the front and back reach the center simultaneously? You add the speed of the car to the speed of travel of the force effects atom by atom from the back, and subtract it from the front?

Anyway, I still can't see how an observer on the ground, seeing both cables snap simultaneously, would have any reason to believe the car would tilt forward. There is no introduction of rotation (i.e. the front falling more than the rear).

Likewise, if I'm in the car and see the car as being at rest (same thing), if I see my front cable snap first, I'm expecting at least the tip of the car to drop first.

Sorry if an above explanation set this straight for me, but it hasn't yet.

Last edited: May 26, 2017
22. May 26, 2017

### jartsa

Well I can understand the intuition that says that the car stays level in the ground frame. It's a good intuition. But there's this other intuition that says that the car starts spinning in the ground frame. See post #14. Now I just happen to be quite sure that the latter intuition is right, even though the first intuition and the other posters disagree, and even though there's no easy explanation for the spinning in the ground frame.

But how about a fighter jet that gets hit by a grenade on the front, and an identical grenade on the rear, simultaneously in the ground frame, and non-simultaneously in the jet frame. The rear and the front get the same upwards speed, so the jet does not spin, but moves upwards, front first in the jet frame, front and rear level in the ground frame.

Oh yes, there's the question what does a marble aboard the jet do, and why? I guess it does not roll anywhere, because the plane stays level in the ground frame, and the direction of gravity changes in the plane's frame. When the plane accelerates, the direction of gravity changes, right? I mean the direction depends on velocity.

Last edited: May 26, 2017
23. May 26, 2017

### bahamagreen

I think the problem is that "shoots 2 lasers simultaneously" and "the support cables...destroyed simultaneously" can not be the platform observer's experience.

The observer in the car will assume she is at rest and that the observer on the platform is in relative motion.

For the car observer, she observes that the concentric rings of leading edges of radio signals emitted by the platform observer will be closer together on her side than the far side.

If you draw this picture you will see that her exterior to interior interception of a circumference must always be with the front of her car first.

If you convert this to laser line distances, the platform observer must fire on the back cable attachment before firing on the front one in order to observe both release simultaneously; that is, if he fires the lasers simultaneously he will observe the front release being hit first.

24. May 26, 2017

### phinds

Yes. As I pointed out in post #4. I think the problem is that the OP is trying to use human "intuition" in a situation where it not only doesn't help, it actively hurts.

25. May 26, 2017

### hatflyer

I don't agree with that at all. Use bullets if somehow lasers and radio signals add complexity. The ground observer will indeed see both cables snap at the same time. It's simply 2 signals of light bouncing off the cables straight back to the observer at the simultaneous moment in his frame. Why would anything be different? You shoot at 2 things at the same time, they reflect right back that they just started to snap at the same time..It's not intuition. It's just following the events in time.

The moving observer will view the front and rear cables snap at different times. That's when things get confusing.