Pushing Pole: When Will Opposite End Move?

[cdm1a23]

If you have a pole, short or long, and you push it, doesn't the opposite end of the pole begin to move faster than the time the speed of light would take to travel the distance of the pole?

Assuming there is very little (none if possible?) compression in the pole, and it was floating in space, and it was 186000 miles long, and I push on one side of it, when does the other side move?

 

[cdm1a23]

Meant to put this in General Relativity... Please move if possible.

Thanks

 

[James R]

You need to ask: how does the far end of the pole "know" about the push at the near end? Answer: the push is transferred along the pole as a sound wave. Sound travels a lot slower in the pole than the speed of light, and the far end won't move until the sound wave has had time to propagate along the pole.

Completely incompressible objects are prohibited by relativity, since in that case the far end of the pole would move "instantly", potentially violating causation in some reference frame.

 

[Pengwuino]

I believe the problem lies in the fact that there is no such thing as a incompressible object since objects transmit movement at the speed of sound in the object.

 

[Physics Monkey]

Think about the microscopic situation. The pole is just a collection of atoms held together by electromagnetic forces. Since electromagnetic influences can only travel at the speed of light, the end of the pole certainly can't feel the push until the electromagnetic field has had time to adjust. The ultimate limit is therefore c, and as James R and Pengwuino indicated, the practical limit is usually a lot less than that.

 

[russ_watters]

Actually, since the atoms have mass, they are governed by f=ma. Electrical impulses may move at the speed of light, but each atom needs to physically move the next one to keep the energy transfer going. That's why the limit is the speed of sound, not light.

 

[Severian596]

Good thought though, cdm1a23. Without asking these kinds of questions we'd forget to keep in mind the differences between our impressions of reality (a rigid pole) and the reality...of reality (a "rigid" pole that moves at the speed of a compression wave).

 

[Physics Monkey]

russ,

I agree with you in most practical cases, but technically the earliest that the atoms at the far end of the pole can know about the push is still governed by the speed of light. The main effect of the push is, of course, to generate a mechanical disturbance which propagates at the speed of sound. However, accelerating those charges at one end of the pole also produces some electromagnetic radiation that travels much faster. The atoms at the far end of the pole will feel this radiation first and thus "know" about the push in a time governed by the speed of light and not the speed of sound. I freely admit that this effect is tiny tiny for a normal size pole, but it is technically there.

The point of my comment was simply that you don't need to know anything about the material except that it is electromagnetically bound to see that effects of the push can't travel faster than light.

 

[cdm1a23]

Thanks everyone for the responses... that's really cool how the push "travels" through the object, but the responses have led me to another question...

What if we shrink everything down, and say what is the amount of time it takes for a push on one side of an atom to move the other side?

Or what about the time it takes for a proton? Or anything smaller? Basically as you take this thing down to the smallest bit of matter, is there anything that is incompressible where the opposite side moves at the same time as the side being pushed? Or is that when things get "1 dimensional" LOL

Thanks again for any replies!

 

[pervect]

Well, you can ask what the electric field of a moving "point charge" looks like. The non-technical answer is that it gets "squished" (Lorentz contracted). The charge may be pointlike, but the field around it gets Lorentz contracted so that it is no longer spherically symmetrical when viewed from a moving frame.

http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_15.pdf
http://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_14.pdf

have more details.