Angular Momentum Question

Sep 28, 2012 Posted Under: physics

It seems to me all momentum is angular momentum.  An ice skater pulling in her arms will rotate faster, and conversely, extending her arms will slow her rotation.  If her arms are extended to the radius of the planet, her rate of spin will slow to unnoticeable (to us), seeming instead to go in a straight line.

If as Einstein concluded, gravity and acceleration are indistinguishable, the spacetime curvature shown as gravity ought also to be observed as we shorten the arms of the ice skater from 4000 miles to 1 meter.  She spins faster, and has a correspondingly more curved signature in her local spacetime.

So why aren’t other things close to her “sucked in” to her much more curved spacetime?

P.S. It appears my intuition of the matter is correct, but did not scale appropriately.  Further research shows

In 1918 Joseph Lense and Hans Thirring obtained approximate solutions of the equations of general relativity for rotating bodies. Their results show that a massive rotating body drags space-time round with it. This is now called ‘frame dragging’ or the ‘Lense-Thirring effect’.

Frame dragging has recently been verified experimentally. This involved using the rotating earth as the massive body and putting a satellite into orbit with a gyroscope which kept it pointing in a fixed direction. Although the Earth has only a tiny frame dragging effect it was possible to detect the extremely small precession of the gyroscope which was caused. A report of the experiment is at the NASA web-site

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