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army1987 comments on What are your contrarian views? - Less Wrong
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Each piece of the ring is longer as measured by an inertial observer comoving with it than as measured by a stationary one (i.e. one comoving with the centre of the ring). But note that there's no inertial observer that's comoving with all pieces of the ring at the same time, and if you add the length of each piece as measured by an observer comoving with it what you're measuring is not a closed curve, it's a helix in spacetime. (I will draw a diagram when I have time if I remember to.)
The inertial observer in the centre of the carousel measures those torus segments when they are stationary.
Then, after a million years of a small acceleration of the torus and NOT the central observer, the observer should see segments contracted.
Right?
During the million years of small acceleration, the torus will have to stretch (i.e. each atom's distance from its neighbours, as measured in its own instantaneous inertial frame will increase) and/or break.
Specifying that you do it very slowly doesn't change anything -- suppose you and I are holding the two ends of a rope on the Arctic Circle, and we go south to the Equator each along a meridian; in order for us to do that, the rope will have to stretch or break even if we walk one millimetre per century.
I don't see any reason this very big torus should break.
Forces are really tiny, for R is 10^21 m and velocity is about 10^8 m/s. That gives you 10^-5 N per kg of centrifugal force. Which can be counterbalanced by a small (radioactive) rocket or something on every meter.
Almost any other relativistic device from literature would easily break long before this one.
If breaking was a problem.
It's not the centrifugal force that's the problem. It's the force you are using to get the ring to start rotating.
Both forces are of the same magnitude! That's why we are waiting 10000000 years to get to a substantial speed.
If one is so afraid that forces even of that magnitude will somehow destroy the thing, one must dismiss all other experiments as well.
Ehrenfest was right, back in 1908. AFAIK he remained unconvinced by Einstein and others. It's a real paradox. Maybe I like it that much, because I came to the same conclusion long ago, without even knowing for Ehrenfest.
The question of the OP was about contrarian views. I gave 10 (even though I have about 100 of them). The 10th was about Relativity and I don't really expect someone would convert here. But it's possible.
Yes, and over 10000000 the forces can build up. Consider army's example of the stretching rope. Suppose I applied force to one end of a rope sufficient that over the course of 10000000 years it would double in length. You agree that the rope will either break or the bonds in the rope will prevent the rope from stretching?
The same thing happens with the rotation. As you rotate the object faster the bonds between the atoms are stretched by space dilation. This produces a restoring force which opposes the rotation. Either forces accelerating the rotation are sufficient to overcome this, which causes the bonds to break, or they aren't in which case the object's rotation speed will stop increasing.
(or stretch)
In the case of the ring there's another possibility.
Irrelevant. How many tiny forces are inside a street car? They don't just "build up".
Nonsense.
No one's saying that forces "just build up" by virtue of applying for a long time. Azathoth123 is saying that in this particular case, when these particular forces act for a long time they produce a gradually accumulating change (the rotation of the ring) and that as that change increases, so do its consequences.
I understand. But imagine, that only 1 m of rope is accelerated this way. No "forces buildup" will happen.
As will not happen if we have rope around the galaxy.
Can you see why the rope in my example would break or stretch, even if we're moving it very very slowly?
Your example isn't relevant for this discussion.
Why not?
Look!
Not every relativistic projectile will be broken. And every projectile is relativistic, more or less.
Trying to escape from the Ehrenfest's paradox with saying - this starship breaks anyway - has a long tradition. Max Born invented that "exit".
Even if one advocates the breaking down of any torus which is moving/rotating relative to a stationary observer, he must explain why it breaks. And to explain the asymmetry created with this breakdown. Which internal/external forces caused it?
Resolving MM paradox with the Relativity created another trouble. Back to the drawing board!
Pretending that all is well is a regrettable attitude.
Why wouldn't that also apply to my rope example?
We, at this problem, don't care for a "comoving" inertial observer. We care for the stationary observer in the center, who first see stationary and then rotating torus, which should contract. But only in the direction of moving.