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If an rigid rod a light year long was rotated, would the other end also rotate at the same time? If yes, that would mean, that the information to rotate the rod in the same direction would have to travel faster than the speed of light. thanks...
- mike (age 16)
toms river high school, new jersey
Right- so it canít happen. You've discovered the proof that, assuming Special Relativity is correct, there can be no rigid objects. The information telling the far-away end what to do when you push on the near end canít travel out there faster than the speed of light, so in the mean time the rod must deform.
(republished on 07/23/06)
Follow-Up #1: relativity implies no rigidity
My question goes back to the idea of the speed of light being the universal speed limit, specifically for information. What would happen if you took a long (say 1 light year) rod made of a sufficiently stiff material, and use it to push the button on a telegraph that is the rod's distance from Earth? If there was a sufficient force on Earth to push and pull the rod, could it potentially move at the other end fast enough to communicate with the telegraph faster than the speed of light?
- Nathan (age 21)
I've switched which question this follows-up to one more closely relevant. In fact, maybe the previous answer suffices.
(published on 12/30/11)
Follow-Up #2: No unstretchable cables
Think of a simple mind experiment. There is a flushing toilet in the space and a 1 000 000 km long flushing cable is held by a cosmonaut on the other side. Think of the cable to be perfectly inflexible. When cosmonaut pulls the cable it flushes the toilet instantly, so the information was propagated faster than speed of light which is about 300 thosands km/sec. I do not think this is an unrealistic experiment. Think of Earth stoping its rotation suddenly. Than all of us no matter in what country would know about it. I do not think this breaks relativity because no matter has been propagated faster than light, but maybe we should not say that information also cannot propagate faster than light.
Thanks for your answer.
- Jozef Tencer (age 29)
I've marked this as a follow-up to previous questions on hypothetical rigid rods. They can't exist for the same reason that the perfectly unstretchable cable can't exist.
(published on 08/19/12)
Follow-Up #3: suddenly stopping spin and relativity
Well think of the sphere size of our planet stopping its rotation suddenly. Each point on the sphere surface gets that information in the same time and faster than light. I guess that even very small sphere size of the hand when suddenly stopped rotating distributes this information among the atoms faster than light.
- Jozef Tencer (age 29)
How would the spin suddenly stop at the same time everywhere? You could distribute little rockets with timers all around, and then have them all fire at once. (We'll ignore the problem of how you get that to work inside the sphere.) But in that case the information was distributed slowly, ahead of time, when the instructions were sent out.
If you tried to stop all the parts at once by grabbing some particular part of the sphere, you'd see that other parts were affected only after a delay given by the light transmission time. The sphere, like anything else, cannot be rigid.
What's worse, even in the first case the different parts would stop spinning at different times as viewed by any observer moving with respect to the sphere. That's just how it is.
(published on 08/21/12)
Follow-Up #4: rotating a rigid rod
According to this question http://van.physics.illinois.edu/qa/listing.php?id=1398 does that mean that if a normal rigid rod about 10 cm long was rotated, that the end would move slighter slower than the closest end?
- Jess (age 13)
Sydney, NSW, Australia
What it says is more that if you start to twist on one end of the rod, there has to be a slight delay before the other end responds, since no information can travel faster than c. In principle that delay only has to be 10 cm/c ≈ 3.3*10-10 s. In practice, the forces are mostly transmitted by the same sort of material stiffness that gives rise to the speed of (transverse) sound in the rod. So the response really starts up after about 10 cm/(speed of sound), maybe around 10-4 s.
Assuming the rotation is at some reasonable rate, however, the speed of the different parts ends up being just what you'd get from a simple classical calculation.
Mike W. (posted without checking until Lee gets back)
p.s. For a very cool video of how influences propagate from one end of an object to the other, you might want to look at http://www.youtube.com/watch?v=wGIZKETKKdw. It uses a slinky, so the relevant waves propagate much slower than the sound waves in an ordinary rod.
(published on 05/27/13)
Follow-up on this answer.