Problem for special relativity geniuses?

Question

Identical rockets A and B are 1 mile apart, tethered by a taut slender steel cable in outer space. A green light signal arriving from a distance perpendicular to the cable says "go!", and both rockets accelerate at identical rates. The rockets A and B and cable soon approach a fraction of the speed of light. Does the cable break, or not? Explain your reasoning.

Answer 1

This is a variation of the famous "Bell's Spaceship Paradox". There is a pretty good explanation on Wikipedia. The short answer is: If the two rockets undergo the same "proper" acceleration (as measured by each respective ship's crew), the cable will break. If the cable is too strong to break, it will prevent the rocket in front from accelerating at the same proper rate as the rear rocket.

The reason for this is that if these two rockets each accelerate at 1G (as measured by the crews), they will get farther and farther apart. See the link below for more detail.

Answer 2

Barring an asteroid collision or some other unintended event, the cable should be just fine.
Assuming the rockets fire "simultaneously" in relation to each other - i.e. the signal is received by both rockets at the same time, relative to both rockets.
Both rockets will accelerate at the same rate and, although their clocks will slow and the distance will dilate, their tether will under go the same phenomenon and everything should remain intact.

Answer 3

I don't see why the rope would break if the rockets both start moving at the same time.....