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Needles to say I am a visitor here. I do not belong to the science world;)

But I have read both of these things before:

  1. Apple falls to the ground because curved spacetime pushes it there (same force as keeps moon in orbit)
  2. Apple 'falls' to ground because the ground is rushing up to meet the apple (which is actually suspended in space) because of Earth's acceleration through space.

I don't think these can both be true. I'd appreciate any clarification - thank you.

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you'll have to elaborate way, way better why you think these 'can't both be true' –  lurscher Oct 3 '11 at 16:41
    
With my extremely limited knowledge about this, I would see the earth accelrating through space and the curved spacetime around earth as 2 unrelated things; I'd think that one or the other is responsible for the apple, not a mixture. –  Joe Oct 3 '11 at 16:45
    
both are accelerating toward each other - earth acceleration toward the apple is by at least 20 or 30 orders of magnitude too small to be measurable - give it or take 5 orders of magnitude –  lurscher Oct 3 '11 at 17:09
    
Consider what would happen on the 'trailing' side of a planet, in the case of explanation #2. Apples, people and pretty much everything else would not have an easy time of it. –  Richard Terrett Oct 4 '11 at 1:34
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2 Answers

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The difficulty here is one of definitions.

  • In the pre-Einstein-ian view there is a privileged frame (typically taken as that of the "fixed" stars), and whichever body is experiencing the smallest acceleration with respect to that frame (which is to say the Earth by a large margin) would have a stronger claim to being "still" Thus the apple accelerates and the ground is still.
  • In general relativity it is inertia frames that are special, and you can tell if you are in one by setting a test mass next to and letting go of it. If it stays there you are in an inertia frame. In that view, the apple is still and the ground comes rushing up to it. Note that the Earth as a whole is free falling and is therefore in an inertial frame, but object on the surface are not.

At the kinds of energies that apply to falling apples on Earth you can do physics correctly in either view. We teach the former in physics 101, but the latter has a pretty strong claim to being more fundamental.

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Number 1 is correct. Number 2 is incorrect. The apple has the same velocity as the Earth since it grew on earth. Also, if the earth were moving into the apple you wouldn't see the apple accelerating unless the Earth is constantly linearly accelerating at 9.8m/s^2, which is impossible.

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Err...number 2 is a rather imprecise and pop-sci way of stating the general relativistic view. Neglecting air resistance the falling apple is in free fall which is to say an inertial frame, while the observer standing on the ground is not. –  dmckee Oct 3 '11 at 17:11
    
Thanks all! I am glad I stopped by here before trying to win any bar bets with #2! –  Joe Oct 3 '11 at 17:39
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@Joe: hold on, you might be getting some different responses from others and I wouldn't want you to run off without getting the full story. –  David Z Oct 3 '11 at 18:08
    
Excellent, always ready to listen ;) –  Joe Oct 3 '11 at 18:42
    
@dmckee I see what you're saying regarding free fall, but it's definitely the apple undergoing noticeable acceleration, not the Earth. The #2 in the original post specifically says the Earth's acceleration through space –  Brian Gordon Oct 5 '11 at 0:31
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