The Speed of Light: If My Arms Were 10 Light Years Long

[Physics1]

If my arms were as long as 10 light years and I waved, wouldn't they be going faster than the speed of light?

 

[rbj]

well the spiral "arms" of stars in the Milky Way galaxy are at least as long as 10 light years. and they be moving. do any component of those arms (the stars) move faster than c?

 

[pmb_phy]

If my arms were as long as 10 light years and I waved, wouldn't they be going faster than the speed of light?

If your arm were perfectly rigid then what you said would be true. However since no part of your arm, which consists of matter, can actually travel at speeds v > c then it follows that your arm is not rigid. It must bend according to the principle of relativity.

Pete

 

[country boy]

If your arm were perfectly rigid then what you said would be true. However since no part of your arm, which consists of matter, can actually travel at speeds v > c then it follows that your arm is not rigid. It must bend according to the principle of relativity.

Pete

However, if the wave was transmitted along your arm at the speed of light, then someone watching from the other end would see the whole arm move at once and might say it looked very rigid.

 

[MeJennifer]

If your arm were perfectly rigid then what you said would be true. However since no part of your arm, which consists of matter, can actually travel at speeds v > c then it follows that your arm is not rigid. It must bend according to the principle of relativity.

Pete

I think there is no problem if we were to assume a, theoretically, perfectly rigid (Born rigid) arm. Of course, the farther out, the closer the arm component will approach c, but it will never reach or surpass c.
For the simple reason that space is hyperbolic.

 

[DyslexicHobo]

From what I know (which is not much), I think that once the ends of your arms approach c, the force required to push them becomes infinite. Therefore as you move your arms, you can exert as much force as you'd like, but you're never surpassing c.

Is this correct?


But because the tips of your arms are experiencing less time, will this give the illusion that (to a stationary observer) his arm is moving faster than c? I really get confused when it comes to this part; I've only read a couple things on GR and still unsure about it.

 

[Mentz114]

From what I know (which is not much), I think that once the ends of your arms approach c, the force required to push them becomes infinite. Therefore as you move your arms, you can exert as much force as you'd like, but you're never surpassing c.

Yes, that's right. It's easier to image the more realistic scenario where you have a thin disc made from a rigid material with a huge radius. When you begin to rotate the center, a wave of shear-strain travels out from the middle like a ripple, at the speed of sound. The outer rim will only catch up after the time taken for sound to travel one radius. No relativistic effects yet.
If you're standing in the middle of the disc, the whole thing is stationary in your frame so eveything will look normal (?). To an observer who is not on the disc, and not moving relative to it's center, the disc will appear to deform
because some parts of it may be moving at relativistic speed in her frame.

But because the tips of your arms are experiencing less time, will this give the illusion that (to a stationary observer) his arm is moving faster than c? I really get confused when it comes to this part; I've only read a couple things on GR and still unsure about it.

We don't need GR for this, SR will do. Sometimes situations arise in astronomy where something appears to be superliminal, but I don't think this is one of them. But I could be wrong.

 

[Kruger]

What's the problem with the following. I mean information can not be faster than c. But let's take a massiv disk with radius r and angular velocity 0. If I start giving it angular velocity from the centre then the outer site must also get speed, but in accordance with special relativity the time needed that the outer site is moving after the centre begun moving is: r/c. But why? I mean the disk is one thing.

 

[MeJennifer]

I mean the disk is one thing.

One has to realize that while the disk could be seen as one thing at a macroscopic level, it is not on a (sub) atomic level.

 

[ZapperZ]

What's the problem with the following. I mean information can not be faster than c. But let's take a massiv disk with radius r and angular velocity 0. If I start giving it angular velocity from the centre then the outer site must also get speed, but in accordance with special relativity the time needed that the outer site is moving after the centre begun moving is: r/c. But why? I mean the disk is one thing.

What you call a "disk" is a solid object in which the atoms and molecules are assembled together via electromagnetic forces, the same type that is used to describe light! So these forces are "cousins" of light and thus, they obey the same speed limit.

Zz.

 

[Mentz114]

I mean the disk is one thing.

If you had a long rigid stick ( about a mile long say) and you poked me in the back with it, it would be several seconds from the time you started pushing, to when I felt the push. The impulse travels through the rod at the speed of sound. This is established by theory and experiment.

[I hadn't seen Zz's post when I wrote this]