A question regarding relativity and information transport

[janakiraman]

i posted this also in general physics, but I'm posting it here as well. sorry if I'm breaking the community rules

Well this is not my question, but i thought i would ask this in this forum to find a solution regarding the same.

Imagine a very long rod that extends between the Earth and upto sun (imagine that the material cannot melt even at the temp of sun). Now the rod is placed in an inclined position with a fulcrum in the middle of the rod about which the rod can move. Now if a person moves the end of the rod near the earth, the rod losses the balance and hence as a result the other end of the rod near the sun moves accordingly to balance itself.

Now though the rod moves at a very very small velocity compared to that of light, the information i.e., the imbalance travels almost instantaneously at infinite speed and makes the other end of the rod near the sun to move in accordance to the movement happened in the end near the earth

Now my question is, is this allowed by relativity? i don't know much regarding relativity theory, I would be happy if people here can answer to my query in more layman terms

 

[Doc Al]

Now though the rod moves at a very very small velocity compared to that of light, the information i.e., the imbalance travels almost instantaneously at infinite speed

No. Any stress applied to one end of the rod will travel at the speed of sound through the rod, far slower than the speed of light--never mind "infinite" speed.

Now my question is, is this allowed by relativity?

No. There is no such thing as an infinitely rigid rod in relativity.

 

[janakiraman]

Well i do know there is no such body, but why should u need mechanical waves? it is just a mass imbalance that happens in a fulcrum, why do u need mechanical waves to transfer it?

 

[HallsofIvy]

Precisely because there is no such thing as a perfectly rigid body. When you "move" the end of the rod near the earth, you are bending the rod. It takes time for that "bend" to move up the rod.

 

[russ_watters]

Well i do know there is no such body, but why should u need mechanical waves? it is just a mass imbalance that happens in a fulcrum, why do u need mechanical waves to transfer it?

It is a mechanical wave because moving it is a mechanical motion and the rod is basically a collection of springs.

 

[Doc Al]

Well i do know there is no such body, but why should u need mechanical waves? it is just a mass imbalance that happens in a fulcrum, why do u need mechanical waves to transfer it?

A lever is a mechanical device. The only way that one end of the rod "knows" what you did at the other end is through a change in mechanical stress transmitted through the rod.

 

[janakiraman]

Well i think in relativity it is not about the feasibility otherwise we can't imagine of traveling at the speed of light?. What if you have a rigid body of such a long length?

I think Doc Al is not getting my query. Where does the concept of mechanical stress comes from while just moving the rigid body? you just disturb the C.G of the body by moving one end and the other end immediately moves to compensate that in order to bring the body back to equilibrium

 

[George Jones]

I think Doc Al is not getting my query.

Doc Al is getting it.

The speed of sound in a body is always less than the speed of light. If you poke one end of a rod, information about the poke travels down the rod as a compression wave at something like the speed sound (for the rod material), so someone/something at another part of the rod won't know about the poke until the compression wave reaches that point.

 

[Doc Al]

I think Doc Al is not getting my query. Where does the concept of mechanical stress comes from while just moving the rigid body? you just disturb the C.G of the body by moving one end and the other end immediately moves to compensate that in order to bring the body back to equilibrium

On the contrary, I think I know exactly what you are asking about. You want to insist that if you push on one end of a "rigid" body, the other end immediately responds. Sorry, things just don't work that way.

Note that this is quite different than simply imagining a long rigid body traveling past you at some high speed, as is often done in relativity thought experiments. In such a case there's no issue of any signal or mechanical stress being transmitted through the object, since the entire object is already moving at uniform speed.

 

[russ_watters]

janakiraman, please note: this exact question is asked here a lot. Perhaps once a week. We understand perfectly well what you mean - we probably understand your thought process better than you do!

Well i think in relativity it is not about the feasibility otherwise we can't imagine of traveling at the speed of light?.

Relativity does not involve traveling at the speed of light, in imagination or in reality. In fact, it says you can't travel at the speed of light.

 

[atyy]

What is a rigid rod? A rigid rod is made of atoms bound by electromagnetic forces (among other things). What is the electromagnetic force? It is the exchange of photons. So your rigid rod is made of light, that's why your rigid rod cannot propagate information faster than light.

 

[atyy]

You can have a perfectly rigid rod in relativity. The way you are thinking about it, the rod won't be rigid, because you move one end, and then you use the inter-atomic forces (made of photons) to transfer that movement down the rod.

So, for a rod to move perfectly rigidly the way you want, you need lots of experimentalists to meet and synchronize their watches, then ship one experimentalist to every point of the rod, and have them push the rod all at the same time. Then the rod will move rigidly. But information is not transferred faster than the speed of light, because the time at which the experimentalists met to synchronize their watches was when when information started moving up the rod.

 

[jtbell]

Then the rod will move rigidly.

But only in the inertial reference frame in which the experimenters' watches were synchronized. In other inertial reference frames, the rod is stretched or compressed, because in those frames the experimenters don't start pushing the rod simultaneously.

 

[Fredrik]

So, for a rod to move perfectly rigidly the way you want, you need lots of experimentalists to meet and synchronize their watches, then ship one experimentalist to every point of the rod, and have them push the rod all at the same time. Then the rod will move rigidly.

I wouldn't call this rigid motion. If you give every atom a push at the same time in the frame where the rod is initially at rest, you're not pushing at the same time in the frame where the rod is at rest after the push. So it's at best "rigid motion in this particular frame".

Note also that after the push the rod will have a non-zero velocity in the frame where it was at rest before the push, so now it's Lorentz contracted, but it's not shorter because you have forced it to remain the same length. So what you have done is actually to forcefully stretch the rod by the exact amount you need to compensate for the Lorentz contraction.

Edit: #¤%& I'm too slow.

Edit 2: I should probably have mentioned that (for simplicity) I'm considering a rod that's being pushed in its own direction, not "turned" as in the OP's example. Similar comments would of course hold in that case too, but they would be more complicated.