Because it’s in contact with other rotating air, which is in contact with yet more air, etc., until you reach the solid edge of the cylinder. The coupling wouldn’t be strong, of course, and if the cylinder’s motion changed, it’d take a while for that change to propagate to the center. But given enough time, why wouldn’t it be rotating?
Here’s a picture worth a thousand words.
I guess my instinct is that air in the white area of that image wouldn’t be rotating because I don’t see how the drag from the air moving below would be enough to overcome the inertia in the large middle layer of air. If the tube were filled with water, I guess the whole thing would feel more intuitively correct to me.
BTW answering a question with, “why wouldn’t it do X?” when it’s clear I don’t understand why it would do X is not very helpful. 
Your picture would be better if the blue regions faded out as they moved away from the rim/axis.
The air adjacent to the inner rim is going to couple with ground and have a rotational velocity. That air is going to couple with the air above it and so on and so on. Eventually, if the distance is sufficient, the coupling would become so weak that no meaningful movement would be taking place. The interesting piece is when you go and introduce a central axis, now you have 2 regions (inner and outer) which have to mesh at some distance between rima and axis. Mind you, at that meshing point there might be effectively no movement at all.
Grey: your thinking jives completely with my own. Now I was exaggerating too low when I said a few dozen feet, but eventually the astronaut would just be stuck there and have to be rescued by a helicopter or something.
The drag from the “blue” air on the “white” air may be small, but it’s also continuous… Given enough time, the blue air with accelerate the layer of white air near it, and that layer the next, &c.
The only tangential force that the layer of white air next to layer of blue air feels is the force exerted by the blue air on it. There is nothing that is trying to “keep the air still” that it is acting against. Eventually even the smallest force wins against no force.
you can see this effect if you spin a cup of water. The very outside edge, by friction, will rotate with the cup but the inside will stay stationary.
However, put the cup on a turntable and leave it rotating steadily, the friction from the outer layer will slowly transfer rotational momentum to the inner layers bit by bit. there’s no magic “air grease” between the 10-foot layer and the 20-foot layer, for example. Eventually the whole contents will turn with the cup.
In a giant cylinder, the rotation may not happen or be evident for the very center axis, but a decent distance from the center, it should all be rotating in concert.
A simple experiment if you still own a turntable.
There’s no such thing as ‘overcome inertia’.
A small force has a small effect. Over time, that adds up to a larger effect.
Actually, now that I think about it more, my idea of a weakening in the coupling is based on a progressively diminishing density as you move to the center of the cylinder. But that’s an extension of the behaviour of earth’s atmosphere and not necessarily what you would find in this case.
If it existed, then I can see random walk movement of the molecules being capable of swamping out a weakening coupling at some point.
There could be all sorts of turbulence and smaller scale effects, but in general, and on average, the fluid inside a rotating container is going to rotate along with it.
You will get a density gradient in a rotating habitat. The density profile won’t look the same as on the Earth, but it’ll be roughly similar. Basically, if the floor of the habitat has Earth-normal gravity and air pressure, then the air pressure at any height above the floor will be greater than (but comparable to) the air pressure at that same height above the Earth.
So, if you had a cylinder hundreds of kilometers in radius, then there would be a vacuum (or near-vacuum) region near the center where you could get stranded for a very long time. For anything smaller than that, though, not likely.
Can you elaborate on this statement, Chronos? (This is a whole other discussion, I’m sure, so if it’s too off-topic I’m happy to take it to a new thread.)
What Chronos is referring to is the Unruh effect.
Quickly: an observer in an accelerating frame will observe a bath of thermal photons (the Unruh effect). An inertial observer won’t see the bath.
One weird consequence is that if I watch someone fall into a black hole, I should see them eventually vaporize from the temperature of the radiation. But the observer falling into the black hole doesn’t experience anything abnormal, since they are on an inertial path. So do you get destroyed or not when passing through the event horizon? The answer might be both.
I don’t see how this can be true: for an in-falling observer close to the event horizon or a static observer held close to the horizon, for the most part, the Hawking effect is the same as the Unruh effect, so the static observer will experience a very high temperature and the in-falling observer experiences zero temperature (from the Hawking effect). Neither observer will see the in-falling observer vaporize. There’s admittedly a few complications in that a BH event horizon and the Rindler horizon are globally inequivalent and that the event horizon itself is almost certainly not unaffected by quantum effects.
Well, the best I can do is point you to my source; The Black Hole War by Leonard Susskind. I’m not knowledgeable enough to give you an argument of my own. It’s possible I’m misinterpreting slightly, but I’m pretty sure I have the gist of it right–the solution to the black hole information paradox is that although outside observers watch in-falling observers vaporize and eventually get scrambled across the surface of the black hole, the holographic principle means that this isn’t inconsistent with the in-falling observer experiencing nothing special.
Is this the black hole firewall hypothesis? I’m not sure because that book was published in 2010, but the firewall hypothesis was only first published just over a year ago.
The firewall appears to be an alternate explanation for the problem. However, the Wiki article on it points to black hole complementarity, which is what I’m talking about:
Leonard Susskind[3] proposed a radical resolution to this problem by claiming that the information is both reflected at the event horizon and passes through the event horizon and can’t escape, with the catch being no observer can confirm both stories simultaneously. According to an external observer, the infinite time dilation at the horizon itself makes it appear as if it takes an infinite amount of time to reach the horizon. He also postulated a stretched horizon, which is a membrane hovering about a Planck length outside the event horizon and which is both physical and hot. According to the external observer, infalling information heats up the stretched horizon, which then reradiates it as Hawking radiation, with the entire evolution being unitary. However, according to an infalling observer, nothing special happens at the event horizon itself, and both the observer and the information will hit the singularity. This isn’t to say there are two copies of the information lying about — one at or just outside the horizon, and the other inside the black hole — as that would violate the no cloning theorem. Instead, an observer can only detect the information at the horizon itself, or inside, but never both simultaneously. Complementarity is a feature of the quantum mechanics of noncommuting observables, and Susskind proposed that both stories are complementary in the quantum sense.
Wow, that’s actually pretty elegant. I guess I got out of studying black holes at just the wrong time.
I have read the the holographic principle solves the problem by more or less saying that both observers are correct: the outside observer “sees” the surface area representation while the falling observer continues to experience the 3D “illusion” (I’m not sure exactly what to call it: naming it the 3D Experience makes it sound like it belongs in Las Vegas).
:smack: Of course. Thank you for clarifying. And thanks to all the other page 2 respondents for discussing the holographic principle firewall solution. I’m definitely going to read up more on that.