How can Earth accelerate toward US and China with no expanding?

Question

In this video it's explained that there is no gravity force, it's all acceleration: Earth moving toward us, but how that's possible without expanding (toward people standing on the opposite sites of the planet) isn't clear (formula's magic doesn't clarify this).

Also this guy disagree and I understand him.

The question in the title is a duplicate of this one, but the question in the body about the YouTube videos may not be. — benrg, Oct 20 '20 at 20:48
Does this answer your question? Why doesn't planet Earth expand if I accelerate upwards when standing on its surface? — Claudio Saspinski, Oct 20 '20 at 23:19
If you and your rulers are expanding at the same rate as Earth, then how would you tell the difference from no expansion? — George Robinson, Oct 21 '20 at 00:35
The acceleration involves the time direction. The direction of the time unit vector in spacetime is changing, and this is like centripetal acceleration in Newtonian physics, except that the radius of curvature involved is on the order of light years. — Chet Miller, Oct 21 '20 at 02:12

score 2 · Accepted Answer · answered Oct 20 '20 at 21:33

It wouldn't be possible for opposite sides of the Earth to perpetually accelerate away from each other while the distance between them stays constant if spacetime were flat, but it is possible when spacetime is curved. See this answer for an analogy: two people walking on opposite sides of the equator have to constantly veer away from each other to stay the same distance apart.

I watched the second video (by "Desertphile"), including the clips from the video that he was responding to.

The only clear mistake that I noticed in the original video is the claim at around 1:23 that "the force of gravity is actually upward". The upward force is called the normal force and is due to a combination of electromagnetism and the Pauli exclusion principle, not gravity. You can say that gravity is a force or not. If it is a force, then it's a downward force that counters the normal force. If it isn't a force, then nothing counters the normal force and you perpetually accelerate upward when standing on the Earth. Both of these descriptions are fine, but in neither of them is the normal force the force of gravity.

On the other hand, virtually everything that Desertphile says is wrong and it's clear that he doesn't understand general relativity or the first video at all. It's possible that he mistook it for a flat-Earther video. I don't think he even understands Newtonian physics given that he claims that the acceleration in circular motion is away from the center (starting around 5:16).

(Oh, there's another mistake in the original video: they misspell "centripetal" as "centripedal" at least twice at around 5:11. Honestly, both videos seem pretty bad and I'm not sure you should be trying to learn general relativity from random YouTube channels.)

Thanks a lot. There could be a useful addition which explains how exactly the curvature does it (the most interesting)? — R S, Oct 20 '20 at 22:23
@RS It’s not easy to explain spacetime curvature exactly. For example, just to specify the curvature in general takes 20 numbers at every point. Any non-mathematical explanation you get is going to be a great simplification, and most of these simplifications (like the “fabric of spacetime”) are extremely misleading. — G. Smith, Oct 21 '20 at 04:45

How can Earth accelerate toward US and China with no expanding?

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