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If freely-falling frames are the local inertial frames according to GR, then is the surface of earth "really" expanding outward at a every point on the surface, locally? What does this mean?

PhyEnthusiast
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  • I think this is a fascinating question and it was one of the high points in my (physics) life when I realised I knew the answer. See the linked question where I discuss it in some detail. – John Rennie Feb 04 '18 at 05:40
  • Great qn!! I thought the same too. – QuIcKmAtHs Feb 04 '18 at 05:52
  • @XcoderX was it you voted to reopen? While I think it's a great question (and I upvoted it) it is definitely a duplicate of the question I linked. – John Rennie Feb 04 '18 at 06:32
  • @JohnRennie After going through all that, not able to understand half the math, what I understand is that the answer to my question is "Yes" ?? – PhyEnthusiast Feb 04 '18 at 08:24
  • Sort of. If you're standing on the surface of the Earth then relative to an observer at infinity you are accelerating in time - sort of. It's the movement along the time axis that causes the gravitational force. – John Rennie Feb 04 '18 at 08:27
  • @JohnRennie no it wasn’t me – QuIcKmAtHs Feb 04 '18 at 08:32
  • @JohnRennie It's kinda weird that while stationary on Earth, I am accelerating "in time", while acceleration itself is related to change in positions over time – PhyEnthusiast Feb 04 '18 at 08:56
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    Wrong! Coordinate acceleration is change in position with time, but coordinate acceleration is a three vector and not covariant. The acceleration in GR is four acceleration. This includes a term $dt/d\tau$, where $\tau$ is proper time. – John Rennie Feb 04 '18 at 09:01
  • @JohnRennie Ok, I was just saying. – PhyEnthusiast Feb 04 '18 at 09:02
  • I wasn't trying to be critical. I think this is a really good question and I upvoted you for spotting that the question existed, even though it is a question that has been asked and answered before. The problem is that it isn't possible to give more than a caricature of an answer unless you're willing to get down and dirty with the maths. – John Rennie Feb 04 '18 at 09:09
  • @JohnRennie So, the surface of the Earth is accelerated "in time" with respect to an inertial frame. But, the freely-falling frames are accelerated "in space" with respect to the Earth. How does that work? – PhyEnthusiast Feb 04 '18 at 09:14

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