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Suppose a gondala lift, which is a continuously circulating loop of steel cable strung between two stations (bull-wheels), is gradually accelerated from normal speed to relativistic speed, v= 0.9 c. Does the steel cable actually contract to half its length, and does it really not fit anymore between the stations?

Edit, in response to a comment: the cable is accelerated to .9c in such a way that at every moment, every part of the cable has the same speed as every other part, in the reference frame of an observer on the ground. I am assuming an ideal cable composed of a substance that cannot stretch (in its rest frame), but it can break. The circulating cable consists of an upward moving half, and a downward moving half. Relativity says both halves are subject to length contraction, so does the cable still fit between the stations?

Basically I just want to know whether relativistic length contraction is real in the sense that it will break the cable.

jkien
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1 Answers1

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If the cable is accelerated to .9c in such a way that at every moment, every part of the cable has the same speed as every other part, then (quite obviously) the cable cannot change length. [All of this is from, say, the reference frame of an observer on the ground].

[If the cable had been accelerated in such a way that at some moments, some parts are moving faster than others, then (quite obviously) its length could have changed.]

Of course an observer riding on the cable at .9c and an observer on the ground will have different descriptions of the history and therefore might disagree about the length of the cable. (They might also disagree about whether the distance between points A and B on the cable is equal to the distance between points C and D.)

As to whether length contraction is "real", of course it is. Take your scenario, where, in the ground frame, every part of the cable has the same speed as every other part at every moment during the acceleration. Consider two observers $A$ and $B$ riding on the cable, initially 1 meter apart. After the cable is up to speed, you, on the ground, will say that they're still 1 meter apart. They, however, will say that they are now about 2.3 meters apart. So the length you measure is contracted relative to the length they measure.

If the cable is incapable of stretching in any frame, then the increased distance between $A$ and $B$ means the cable has to snap. I would be disinclined to characterize this as "due to length contraction", because in the ground frame, the length of the cable never changes. From $A$'s viewpoint, the cable snaps because it expands, not because it contracts. From the ground viewpoint, the snap is presumably caused (in some complicated way) by the forces that create the acceleration. Others might prefer a different description, but this comes down to a dispute over word choices, not physics.

WillO
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