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Let's say there's an object on Mars, I stand on Earth, and hold a non-elastic, unbreakable rope (or an iron bar or something) tied to the object on Mars. And I try to tug it. The tug cannot travel over the speed of light, right? So if I'm tugging the object from Earth, does the rope just keep prolonging until "the tug" reaches the object?

Would the answer different from my point as an observer on Earth to a third-party observer watching from the middle point of the rope?

Or is there just no other acceptable answer than "the rope would snap"?

Štěpán Bartoš
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The rope or steel bar or whatever will stretch. If, at any point, in order to keep the ends fixed to their respective places, any part of the rope would have to move faster than the speed of light, then the rope will break.

Here are a couple more examples.

Suppose a very long train moves off from a platform. Say the front accelerates to some speed $v$. The back will also accelerate and if the train keeps the same proper length then in the original reference frame it will contract. Therefore the back has to travel faster, on average, than the front, in order to keep up. You can easily find a case where this means the back will have to travel faster than $c$. In that case what happens in fact is that the train breaks into two or more pieces.

An other example is a pair of rockets which take off at the same moment in some inertial frame, with a rope extending between them. If the rockets have the same proper acceleration (maintained by some powerful rocket motor) then the rope comes into tension, stretches (in its own rest frame), and eventually breaks.

Andrew Steane
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  • Mr. Physics Professor from Oxford immediately answering a curious question of a physics-uneducated IT manager from Czech rep. This platform is awesome. Thank you, Andrew! – Štěpán Bartoš Jan 31 '24 at 11:55