Faster than light paradox

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My friends had asked me a question which I thought was rather troubling and provoking. The problem is that is actually seems to violate the law that states that nothing travels faster than the speed of light. Their question was:

Suppose two planets (planet A and planet B) which are one thousand light years apart to be connected with a strong cable. Then the living beings on planet A tugs at the end of the cable. Now the problem is: Would the life forms on planet B, which is the other side of the cable, feel the pull instantly even when the two planets are a thousand light years apart?
 
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physicskid said:
My friends had asked me a question which I thought was rather troubling and provoking. The problem is that is actually seems to violate the law that states that nothing travels faster than the speed of light. Their question was:

Suppose two planets (planet A and planet B) which are one thousand light years apart to be connected with a strong cable. Then the living beings on planet A tugs at the end of the cable. Now the problem is: Would the life forms on planet B, which is the other side of the cable, feel the pull instantly even when the two planets are a thousand light years apart?
No. You're assuming that the cable is rigid. In special relativity nothing is rigid. Think of the cable as an elastic band. The tug on the cable propagates down the length of the cable at a finite speed which is always less than the speed of light.

Pete
 
The cable is indeed elastic and if the elasticity modulus is E in Newton (kg*m/s²), and the linear density Lambda (kg/m), the wave propagation speed isequal to:

c = sqrt(E/Lambda)

Which will be quite a bit lower than the lightspeed. Typically in the order of several hundred to thousand meters per second.
 

russ_watters

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pmb_phy said:
The tug on the cable propagates down the length of the cable at a finite speed...
A.K.A "the speed of sound."

Relativity or not, there is no such thing as a perfectly rigid substance (yes, even a rock has elasticity).

Whether it was set up on purpose or not, this is a common trap people fall into where they try to evaluate the implications for physical reality of something that can't be physically real. Ie, start with impossible assumptions and you can draw any conclusions you want.
 
also you are saying that the tug would be felt immediately - not that they would see it immediately - this has nothing to do with light speed
 

selfAdjoint

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europium said:
also you are saying that the tug would be felt immediately - not that they would see it immediately - this has nothing to do with light speed

It isn't just seeing. Although we talk about "the speed of light" and that one inertial frame "sees" the dilation in the other, it is really causation that can not be communicated faster than light. Faster than c that is, where c is the conversion factor between time and space (so many length units for each time unit).
 
What? Even a rock is elastic? Hell, I did not know that.

Anyway, thanks for everyone's replies so that I am now able to prove to my friend who is the real physics expert!
 
physicskid said:
What? Even a rock is elastic?
If rock wouldn't be elastic, how do you think you would get earthquake waves?
 

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