Thursday, February 1, 2018

general relativity - Apple falls for which of these 2 reasons?


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.



Answer



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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