Nice to be validated. 
I agree with the rest of your post.
Blast, you beat me too it! :mad:
Although I can take consolation that flex727 beat you to it in post #16. 
Wait a minute. I thought that he was able to jog simply because his inertia kept pressing him to the floor and he could thus maintain traction and therefore his motion. I didn’t think the jogging ring was spinning or that it was necessary that it was spinning. I don’t know how he got started running in the first place, though.
Yeah, it’s more accurate to say that an acceleration is indistinguishable from a constant gravitational field. The elevator on the surface of the Earth is just a convenient real-world example that approximates a constant gravitational field (since if the elevator is small enough there isn’t going to be much difference in the field from one point to another).
I think the real point of the analogy is to illustrate the equivalence principle. Everything experiences the same acceleration due to gravity, since the gravitational force on an object is proportionate to its mass. This is why we can’t distinguish a constant gravitational field from a constant acceleration (whereas we could distinguish an acceleration from, say, an electric field, as electric fields accelerate particles by different amounts depending on their charge to mass ratio).
Nope, the bridge chamber of the Discovery is definitely spinning, to produce artificial gravity for those inside. You can see there are consoles and chairs all around it, oriented with “up” toward the axis, and “down” toward the outside of the ring. Also, at one point while the jogging astronaut (Poole?) is making his rounds, you can see the other astronaut sitting at a console in the background. He appears nearly upside-down, so to speak.
Of course we’re talking about a fictional ship here, so who’s to say? Actually, this special effect was deliberately planned. The bridge was a big circular set mounted on an axis so that it could rotate. The jogging actor stayed at the bottom, more or less jogging “in place” while the set rotated under him. The other actor was strapped in so that he wouldn’t fall out of his chair.
The “inertia” idea you propose wouldn’t work. If the chamber weren’t spinning, everything would be weightless. The would-be jogger’s first step would just send him on a straight line collision into the axis gangway, or maybe more likely into a patch of the floor on the other side.
Just to be nit picky, the equivalence principle only applies if you’re a dimensionless point. If you have any extension at all you’ll be subject to tidal gravity near a gravitating mass, but not in an elevator.
BTW if you are a dimensionless point you’ll find it’s very difficult to get a date.
>Wait a minute. I thought that he was able to jog simply because his inertia kept pressing him to the floor and he could thus maintain traction and therefore his motion. I didn’t think the jogging ring was spinning or that it was necessary that it was spinning. I don’t know how he got started running in the first place, though.
Interesting. He’s got traction because his inertia keeps pressing him to the floor, but the inertia we are talking about depends on his distance from the center of the ring, and his revolutional speed, in an absolute sense. That is, define an inertial reference frame in which the center of the ring is stationary, and watch him jog, and see how fast he runs his circle. For his traction, it doesn’t matter how fast the ring spins, or how fast he goes relative to the ring, only how fast he circles with respect to inertial space. If he wants to feel heavier, he ought to jog along with the ring, and if he wants to feel lighter, he should jog in the opposite direction. If the ring spins at jogging speed, he can get himself floating by jogging countercurrent and then pulling his feet up.
Now that you’ve jogged my memory, I do remember the scene as you describe it.
But with my original proposition, while it does seem the runner would have difficulty starting out, wouldn’t it work if we had the correct ring diameter given a runner’s expected speed?
(my bold) Do we know this to be the case? It’s true for a spherically symmetric mass distribution, but I could imagine a constant gravitational field over a finite volume being made with the right mass distribution.
>I could imagine a constant gravitational field over a finite volume being made with the right mass distribution.
I’m trying to picture this, for example as a Dirichlet problem, and finding it very hard to imagine, except in the case that the mass distribution surrounds the space (you’re inside a hollow earth). But I also can’t think of a proof against it.
I can imagine that you could achieve a field that is arbitrarily close to flat, but never perfectly flat (sort of like approaching absolute zero).
Possibly to get exactly zero would require a non-zero mass distribution throughout space. To get to any arbitrary accuracy may only require a finite-sized distribution.
For a first cut, consider a mass of 1M at one unit from the elevator, and a mass of 8M two units away in the opposite direction. The lowest order tidal forces cancel at that point, but not the attraction towards the larger mass. (I recall working through this, but I just now only verified it in the direction through the masses.) So you’re closer to constant over a finite volume.
On preview:
Then you just wave your arms, mutter Heisenberg uncertainty something, and you’re good.
Well, thanks for treating me like an idiot, but I don’t think you understood the question. MikeS has it right; the problem is called Newton’s Bucket, and it’s not as easily dismissed as you seem to think:
First, I’m sorry if I sounded condescending. It certainly wasn’t my intent, and on rereading my own post I’m not sure why you think so. I was just responding to the question as written, and obviously have no knowledge of your background (I haven’t seen a post by you before) or the context that drove the question. The board is filled with questions about physics from people with no physics background at all to those who are quite knowldgeable. I could only go by the OP in isolation and I interpreted it as a question about classical physics, as several other posters did also.
Secondly, neither did I intend to say anything dismissive.
Had you provided your cite in the OP, or at least some hint at why you drew the conclusion that you stated starting with “It seems like…,” I would have I would have understood more clearly what you were getting at, and would have stepped aside to let those familiar with Mach’s principle discuss further.
I think I once heard someone say that angular velocity is a fundamental property of matter, like mass or energy. This would seem to solve the whole Newton’s Bucket problem. Is this true?
Well it’s true that quantum particles have both intrinsic and orbital angular momentum, but these vectors are normally randomly aligned and therefore have no net AM.
In the Einstein De Haas experiment a magnetic field is imposed on a suspended iron cylinder; This imposed B field then causes the intrinsic spin vectors to align and the cylinder to spin.
I suppose you could put some water in the cylinder, but this still wouldn’t explain why the fluid piles up at the edges of the pail. So, no, this doesn’t solve the problem.
Way out of my league, but is there any analogy here with the impossibility of suspending a stationary object in a stationary magnetic field? (Mathematically speaking…)
Cool, a relativity thread just in time for me to come back from vacation! Thanks, guys.
Several points:
First, the textbook way to make a uniform field (electric or gravitational) is to have your source uniformly distributed across an infinite plane. Infinite planes of mass are of course hard to come by, but one can get a pretty good approximation by making your mass much wider than the distance of your experiment away from it. It is actually possible to create a region of truly uniform field with a finite mass distribution (at least, with Newtonian gravity: I’m not entirely certain of the relativistic answer), but your constant region needs to be completely enclosed by mass.
Second, quoth Bytegeist:
Others have already addressed the distinction between centripetal force (which is just a description of what some force originating from perfectly normal sources is doing) from centrifugal force (which is a way that a force, or something that looks a lot like one, can originate without a source, due to one’s reference frame). I’ll just add that centrifugal force, according to Einstein, is exactly as real as gravity. You can, if you like, argue that there’s some sense in which the centrifugal force isn’t really “real”, but if you do so, then you’re also forced to argue that the gravitational force isn’t really “real”, either.
Finally, back to the OP:
Even assuming that centrifugal force does depend on the presence of other matter in the Universe (I don’t think that can actually be ruled out by experiment), there’s still no problem here. Even if the universe you popped out into was empty, it’s not any more. When you started your ship spinning, you gave it angular momentum, which means that you also had to give something else an equal and opposite angular momentum. Maybe you spun a flywheel the other way, in which case your ship is now rotating relative to that flywheel. Or maybe you started your ship spinning by firing up your rocket motor, in which case you’re now rotating relative to your rocket fumes. No matter how you did it, you’re going to end up with something else in the universe which is not rotating the same way as you.
Does that work?
Say I got a wagon-wheel style space station (not a small moon) rotating at X feet per second. If I run the same X-feet per second counter to the rotation and jump, what happens?
What happens as the rotating air hits me and I slow due to friction?