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This is an intuition check. Maybe I'm starting to get it, or maybe I'm not.

I apologize ahead for my potential ignorance and naivety, but I've been trying to curve the space in my head around special and general relativity, and I'm just a layman with poor comprehension of Einstein's equations.

When I read about how Einstein pondered on the way a force apparently acts upon a falling object, without the object "feeling" any force during its fall, leading him to the idea that spacetime got curved, it made me think about inertial reference frames in a way I haven't thought about them before.

In my (potentially wrong) mind, it seems like people around the globe should sit in a variety of inertial reference frames due to being drawn towards the Earth's centre of mass between them all.

If so, is it sort of correctly intuited that when Alice - who had always lived halfway around the globe from Bob - one day magically teleported herself halfway around the globe into a stable upright stance on the ground next to Bob, it turned out that she had always aged minuscully slower than Bob, because Bob's and Alice's frames were initially different, but then Alice altered her frame by Earth's gravity × 2 to join Bob's inertial reference frame?


Edit: Alice and Bob are at the exact same height. From the first answer, it appears that my intuition is completely wrong. If GR is a generalization of SR, I would have thought that an SR scenario could be described in GR. If GR doesn't have a link between relative motion and gravity/acceleration, then I don't understand how it is a generalization.

To be as clear as I know how to: I thought that the force acting upon Alice and Bob at the same height gave them inertial reference frames that were opposite to each other seen from the POV of the Earth's centre of mass.

I can understand the difference between being accelerated and being at rest while technically moving relative to someone else, but I thought I had to see a link between GR and SR, and I just can't without resorting to this confused and mad misapplication of inertial reference frames.


In conclusion, I suppose I may need to study Einstein's equations before I can hope to develop an accurate intuition.

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A person standing on the Earth's surface is in an accelerated frame, not a rest frame. He is, effectively, accelerating at 1 g, or about 32 ft/sec^2. So nobody on the Earth is in a rest frame.

Time dilation has two forms: special relativitistic and gravitational. If Bob and Alice are at the same distance from the earth's center but on opposite sides of the Earth, and are standing on the earth's surface, then they are indeed moving relative to each other; and Bob will say that Alice's clock is running a bit slow due to their relative motion. But Alice will say that Bob's clock is running slow. The situation is symmetrical.

Magical teleportation breaks the rules. If we limit ourselves to real, physical motion, answers to this kind of question can be calculated.

If Bob and Alice are at different distances from the Earth's center, so that they are at different heights in the Earth's gravitational potential, then whoever is higher will say that the other's clock is running slow, and whoever is lower will say that the other's clock is running fast. If Alice starts out next to Bob on a mountaintop, then travels to the other side of the earth and descends to the bottom of the sea, she will age very slightly slower than Bob. When she returns to the mountaintop, Bob will indeed notice that Alice has aged a bit less than he has.

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  • $\begingroup$ Ok thanks. So since you ignored my notion that it matters that Bob's and Alice's frames have opposite direction to each other with regard to the Earth's centre of mass, I take it my intuition was wrong. See, I just thought that GR was called General because it was a generalization of SR. If it is, then I still don't understand anything. Back to square 1. I used magical teleportation to check if it is the change of inertial reference frame of one to the other's that resolves a twin paradox, so I assumed A and B are initially time dilated wrt. each other even at the same height. $\endgroup$ – Fisk42 Aug 15 '18 at 6:03
  • $\begingroup$ There is no differential time dilation due to relative motion for any pair of clocks on the same circular orbit, diameter of the orbit can be infinitely large. If two clocks are on the same orbit and in the same gravitational potential they will always tick at the same rate wrt each other. To resolve twin paradox just don't change frames and the paradox naturally disappears. $\endgroup$ – Albert Aug 15 '18 at 8:01
  • $\begingroup$ Ok. I think I need to play with the math at least to get it. I thought changing the inertial frame of reference was the whole point of the scenario. The way I understand, the paradox is resolved by taking physical changes of reference frame into account. But of course there's no paradox if no one changes frame, but that's beside the point, isn't it? $\endgroup$ – Fisk42 Aug 15 '18 at 9:58

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