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DanielLC comments on What are your contrarian views? - Less Wrong
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In the normal example, where the ladder is straight and moving forward, it has only one reference frame. Strictly speaking, each rung has a different reference frame, but they differ only by translation.
From what I understand, you modified it to a circular ladder spinning in a circular garage. In this case, each rung is moving in a different direction, and therefore at a different velocity. Thus, each rung has its own reference frame.
ah, I meant to glue the end and start together without curved shape/motion. But I guess that is physically unrealisable and potentially more distracting than explanatory.
Actually that's not a big deal. Technically you need general relativity to do that, but it's just a quotient space on special relativity. In any case, it works out exactly the same as an infinite series of ladders and garages.
There is one thing you have to be careful about. From the rest frame, the universe could be described as repeating itself every, say, ten feet. But from the point of view of the ladder, it's repeating itself every five feet and 8.8 nanoseconds. That is, if you move five feet, you'll be in the same place, but your clock will be off by 8.8 nanoseconds.
Actually from the point of view of the ladder the universe still repeats at every ten feet. It is just that from it's point of view it takes the space of two carages at any one instant.Both the garage and ladder are in a state of rest and show equally good times. Yes they read different but doesn't mean they are in error.
I am not sure whether it would see other instances of itself. I only spesified a spatial gluing and not that the garage be split into timeslices. I guess that the change of the point of view has changed some of that gluing to be from future to past. For if the ladder would be too long the frontend would not crash to the same ladder time backend but to a future one. (ignoring the problem of how you would try to slide the ladder into too small a hole in the first place)
No, it does not. I think I messed up before and it's actually 20 feet and 8.8 nanoseconds. From the the point of view of the garage, the coordinates (0 ft, 0 ns) and (10 ft, 0 ns) correspond to the same event. From the point of view of the ladder, the coordinates became (0 ft, 0 ns) and (20 ft, 8.8 ns). They still have to be the same event.
The universe is definitely repeating itself to be off by a certain time, and the distance it is off by is not ten feet.
The ladder sees the carage length contract. That is less than 10 feet. The ladder doesn't see itself contract that puts the limit on the repeating of the universe.
Are you sure the ladder point equivalences are not (0 ft, 0ns) and (20 ft, -8.8ns)?
It depends on which direction it's moving. I didn't bother to check the sign.
Thinking about it now, if it's going in the positive direction, then it should be (20 ft, -8.8ns). You are correct.