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Similar to this question: How does general relativity explain tides?

But I’m specifically interested in if General Theory of Relativity would predict that bending spacetime means the water and land on earth bend together as the below authors suggest.

“According to the General Theory of Relativity, mass do not interact gravitational [sic] with each other by the gravity force, but because they bend the space. If, according to the General Theory of Relativity, gravity manifests itself as a curvature of space, then it is difficult to explain tides and outflows. At tides and outflows, the differences in water levels reach several meters. It follows that the changes in curvature of space, postulated by GTR, caused by variable gravitation of the Moon are very large. The problem is why tides and outflows are very clear, while the deformations of mainland are invisible. If the mass of Moon bends the space, it is the same when that space is filled with water and when it is filled with the mainland. Therefore, sea water should be deformed in the same way as the mainland. The banks should rise in the same way as the water. Then, of course, tides and outflows would be invisible. However, because they are visible, it follows that the mass of Moon does not distort space, but rather the matter. The water is malleable, and therefore it deforms more than stiff rocks. This proves that the assumption of GTR, that gravity is a curvature of space, is incorrect.”

(PDF) Gravitational Waves in Newton’s Gravitation and Criticism of Gravitational Waves Resulting from the General Theory of Relativity (LIGO). Available from: https://www.researchgate.net/publication/326034030_Gravitational_Waves_in_Newton's_Gravitation_and_Criticism_of_Gravitational_Waves_Resulting_from_the_General_Theory_of_Relativity_LIGO [accessed Feb 20 2023].

What, if anything, is wrong with this assessment? Would the bending of spacetime make the tides invisible?

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    $\begingroup$ General Relativity has made accurate predictions in a huge variety of applications over 100 years, including some of the most precise measurements ever made by human beings – gravitational wave detection. So unless your reference shows experimental data in conflict with GR, or outlines a different theory which also explains all the observations made in the last 100 years, it saves time to dismiss it as quackery. This reference appears to rely on conceptual arguments of what "space curvature" means instead of math. $\endgroup$
    – RC_23
    Feb 21, 2023 at 14:05
  • $\begingroup$ I find your rationale unconvincing. $\endgroup$ Feb 22, 2023 at 0:32
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    $\begingroup$ "The problem is why tides and outflows are very clear, while the deformations of mainland are invisible" – this happens because solids have shear strength to resist shear deformation, while liquids do not. This is the same difference as when you hang a solid rod halfway off the edge of a table, it deforms slightly due to its weight, but stays. While a long balloon filled with water hung off a table will fall limp, and not even keep its shape at all if not for the balloon. $\endgroup$
    – RC_23
    Feb 22, 2023 at 1:01
  • $\begingroup$ That makes sense to me. It’s like what Jacopo said is contained in his other forces term. Thank you. $\endgroup$ Feb 23, 2023 at 21:04

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If the mass of Moon bends the space, it is the same when that space is filled with water and when it is filled with the mainland. Therefore, sea water should be deformed in the same way as the mainland. The banks should rise in the same way as the water. Then, of course, tides and outflows would be invisible.

The "therefore" is incorrect. In the language of Newtonian gravity, tides happen because of a differential gravitational pull between different places on Earth and its center of mass acting as a forcing term for the system of all the bodies of water, whose response function is rather complex. See this excellent SE answer or Theory of tides on Wikipedia.

The different response accounts for the fact that bodies of water move by much more compared to land.

The thing that differs between Newtonian gravity and general relativity is the way the forcing term is handled; in this low-velocity, low-density regime their predictions are almost identical, although the language is different.

In this regime, the Newtonian language is to consider any given particle (molecule of water, say) to have an acceleration due to gravity:

$$ \frac{\text{d}^2 x^i}{\text{d}t^2} = F^i_{\text{grav}} + F^i_{\text{other}} $$

where the $F_{\text{other}}$ term accounts for all non-gravitational forces.

In the language of GR, the main equation is the geodesic one:

$$ \frac{\text{d}^2 x^\mu}{\text{d}s^2} + \Gamma^\mu_{\nu \rho} \frac{\text{d} x^\nu}{\text{d}s} \frac{\text{d} x^\rho}{\text{d}s} = F^\mu_{\text{other}} $$

which in this case reduces to

$$ \frac{\text{d}^2 x^i}{\text{d}t^2} \approx - \Gamma^i_{00} + F^i_{\text{other}} $$

and in particular, again in this approximation, $- \Gamma^i_{00}$ is quite close to the Newtonian expression for the gravitational force $F^i_{\text{grav}}$.

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    $\begingroup$ Great! Thanks, makes sense. $\endgroup$ Feb 22, 2023 at 0:28
  • $\begingroup$ I like how I link to the criticism of general relativity (on topic), and it’s deemed off topic because the person doing the criticism has an off topic theory I never once mentioned. $\endgroup$ Feb 22, 2023 at 0:30
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    $\begingroup$ Eh, I did not vote to close but I think the decision makes sense; the thing is, what I wrote in my answer would be covered in most GR courses, so the reasoning by the authors you quote really does come across as crackpottery, since it aims to "disprove" a very well-tested theory while misunderstanding its basics. I think it's healthy to engage with these ideas from time to time, but the thing you include in the quote "This proves that the assumption of GTR, that gravity is a curvature of space, is incorrect." is for sure an off-topic, non-mainstream theory. $\endgroup$ Feb 22, 2023 at 14:54
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The mistake in this analysis is that water can flow, while rock cannot on a time scale of hours. Thus, the tide is different for water and land. The oceans don't simply deform: they also flow. This makes the ocean tide larger than the body tide, and also shifts it in phase, making it even more apparent.

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  • $\begingroup$ I guess this makes sense to me from my schooling that gravity is a force, but the criticism is why liquid behaves differently when space bends than does solids. I think Jacopo’s answer is on target. Space bends in the same way (causing acceleration) that an applied force would according to Newton’s theory. So the acceleration is the same for water as it is for solids (from the bending of space), but it’s the other forces that are different, in the same way they are different in newtons theory. $\endgroup$ Feb 22, 2023 at 0:37

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