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If you had a glass ball filled with water, completely sealed and containing a fish, could the fish move the ball?

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Yes it could! ;-) for example it may jump outside the ball and push it by means of its tail. More seriously - yes it could even waving portions of the water without going outside the ball. – kakaz Apr 26 '11 at 11:40
Yes, the famous Harungus Muenchhausii can do that. – Georg Apr 26 '11 at 11:53
Unless you assume that the density of the fish is exactly the same as the density of water, this is no different from a hamster in a sealed ball? – Peter Shor Apr 26 '11 at 13:30
Since fish float, that's not such an unreasonable assumption! – Andrew Apr 26 '11 at 14:12
Exactly, @Peter Shor, that's the right analogy. Bjorn writes a similar thing below - the fish may distribute the angular momentum to take a part, and force the remainder of the ball to rotate in the opposite way - and in this case, it resembles your hamster. Also, the center-of-mass remains at the same spot, so even without a rotation, if the fish heavier than water moves in one side, the water and glass goes in the opposite. Except that a floating fish is optimized so that it is as heavy as water in average, otherwise it wouldn't float, Peter. ;-) – Luboš Motl Apr 26 '11 at 14:32
up vote 5 down vote accepted

Yes, with gravity and a generous definition of "moving".. it would be the same principle as the toys where you can control a sphere using a radio control (or using your iphone). The fish swims along the edge and gravity pulls it back down, which starts a rotation of the water and by friction to the sphere starts the rolling motion of the sphere on the ground or other surface. Obviously the water/sphere friction will probably be miniscule, but at least it is possible in theory :)

A follow-up question would of course be if it's possible to move a hermetically sealed sphere freefloating in vacuum and without gravity or any other appreciable fields intersecting it. If you solve this, I'm pretty sure NASA will want to talk to you (or the fish)!

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Yes, the fish could (theoretically at least) move the ball.

A quick way to visualize why this is so is to imagine yourself sealed in a 7-foot diameter ball of air. You could easily move the ball by walking in the direction you wanted it to go. Of course you would have a much easier time of it, since your density is much higher relative to the surrounding fluid (air). The fish's density is much closer to the surrounding fluid (water), so it would have a harder time of it.

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Yes, the fish can move the sealed ball, but the centre centre of mass of the fish and the ball will not move.

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In vacuum; with gravity and on a table, rolling is possible. – mbq Apr 28 '11 at 10:40

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