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JGWeissman comments on Open Thread: April 2010 - Less Wrong
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Your feet are in an accelerating reference frame, being pulled towards the planet faster than your head. One way to look at it is that the acceleration of your feet cancels out a gravitational field stronger than that experienced by your head.
But I've ruled that explanation out from this perspective. My feet are defined to be at rest, and everything else is moving relative to them. Relativity says I can do that.
Relavtivity says that there are no observable consequences from imposing a uniform gravitational field on the entire universe. So, imagine that we turn on a uniform gravitational field that exactly cancels the gravitational field of the planet at your feet. Then you can use an inertial (non accelerating) frame centered at your feet. The planet, due to the uniform field, accelerates towards you. Your head experiences the gravitational pull of the planet, plus the uniform field. At the location of your head the uniform field is slightly stronger than is needed to cancel the planet's gravity, so your head feels a slight pull in the opposite direction, away from your feet.
An important principle here is that you have to apply the same transformation that lets you say your feet are at rest to the rest of the universe.