A follow up question concerning the speed as to which a very long pole would move between two stars!?

Question

Some time ago I asked if there was a long pole between 2 stars, and somehow I managed to pull on one end, would someone on the other star, say 3 light years away, feel it pull at the same time? Or would they have to wait a few years?
Someone said no because of 'rigidity' and the speed at which waves of atoms pull on each other. Nothing pulls instantaneously.
Ok, therefore if you was in the middle of the two stars and you was pulling the pole backwards and forwards from the middle, the pole atoms would surely be compressing on one side of your hand, and expanding on the other side (before the pole is seen to move). Is there a formulae to work out how far the atoms in a pole (for example) would compress or expand before there is movement? Putting it another way, suppose you was pushing or pulling a 20cm long pencil (say in a vacuum without gravity to remove effects of resistance), whats the formuale to work out how long it would take for it to move, after the initial push or pull?

Answer 1

The formula is statistical quantum electrodynamics. I don't wan to do the math bit. So think of it like this. All solids (like your pencil or pole) are collections of molecules held together by various types of bonds (molecular, covalent, ionic, metallic). It is easy to visualize your pole as a crystalline structure of molecules. When you push on one end, the structure distributes the force by adjusting bond angles. Same thing if you push on the pencil, by the way. The impulse of your forcing will create a front that travels through the solid. This front is roughly equivalent to acoustic wave s in the same media. Now, what is interesting, if you had a slight electrical charge (vacuum is a good insulator, so the chance of you having a charge is pretty good) and pushed the pole, and the pole conducted electricity, a electrical signal would be sent off along the pole. This would travel much faster, some large fraction of the speed of light. But, resistance will prevent it from being detected at the other end.

Look at the Nevada test sight declassified videos of underground nuclear tests. You can see the propagation of the shock wave in rock. As visualized, the time it would take for the person at the other star to feel your push would be (for steel): 3 lyr = 2.84e16 m, divide by 5960 m/s = 4.76e12 s, divide by 3.15e7 s/yr and you end up with 150,000 yr before your push is felt at the other end.

Answer 2

You would need two things:

Young's modulus describes the pole or pencils elasticity; how far it will expand or contract in response to a force. It's equal to:

Y= (F/A)/(dL/L)

where F is Force, A is cross sectional area, dL is the change in length, and L is the total length.

Typically, Young's modulus for a given material is looked up in a table and either the Force or the change in length is solved for.

The speed of the reaction should match the speed of sound? The speed of sound in your pole or pencil is equal to:

v= sqrt (Y/p)

where Y is Young's modulus and p is the density of the pole or pencil (closest I could come to the letter rho).

Answer 3

The speed of sound through the material would be a good estimate, though there would be internal reflections and such that would slow it down. Also you could make a shock wave go through, which by definition is a wave that moves faster then the speed of sound in the medium, though it would quickly slow down to the speed of sound.