Our planet revolves around its axis with a period of roughly 24 hours. But with respect to what? Is there an inertial frame that we can attach at the earth's position with respect to which we can measure the angular velocity unambiguously? And I think we can answer that by looking at the sun and neglecting for a moment the Earth's rotation around the sun. Every time we see the Sun rising we conclude that the Earth has completed a full revolution around it's axis.
Now suppose we ask this question about the Sun's revolution. Is there an inertial system with respect to which we can measure the Sun's total angular momentum? And moving on to larger length scales, what about the Milky way center that the sun rotates around? Does this structure continue and for how many levels?
And when we finally ask the question about the angular momentum of the entire universe (trying to leave out gravity and space-time curvature for a moment, just the usual flat space-time) must we not conclude that the total angular momentum of the universe is plain zero because space is rotating itself with the universe? I mean there is no structure greater than the universe to give us a handle, so what would such a frame depend upon?
Any impressions, thoughts or ideas appreciated!