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Comment by samsartor | Hacker News Reader

https://en.wikipedia.org/wiki/Tests_of_general_relativity#Pe... is the example I learned in school. You don't need to be around a black hole for GR to suddenly switch on.

Newtonian gravity is an approximation. A perfectly acceptable one in many contexts, but still measurably incorrect.

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Nobody said that general relativity is "switched on" around black holes.

But ok, let me put it this way: outside of extreme energy/mass environments, gravity is described by Newton's law of gravitation with very high precision. If you look very hard, you may notice differences on the order of 10e-MANY. But for all intents and purposes, gravity is Newtonian in 99.99999% of the universe.

that's like saying the visible mass of the universe is 99% hydrogen and helium, so we don't need to learn about chemistry.

So you're saying we should model galaxies down to the level of individual protons? Lol.

Galactic dynamics is governed by gravity, which is Newtonian at those scales.

No I did not say that.

Ok, then how does your chemistry comment have anything to do with the motion of galaxies? Reminder: you're commenting on an article about MOND, which is a theory that stems from trying to explain the motion of galaxies.

> outside of extreme energy/mass environments, gravity is described by Newton's law of gravitation with very high precision. If you look very hard, you may notice differences on the order of 10e-MANY. But for all intents and purposes, gravity is Newtonian in 99.99999% of the universe.

I meant it in the sense that "most of the cosmos runs on Newtonian gravity, therefore we can ignore GR" is similar to "most of the visible matter in the cosmos is hydrogen/helium, so we can ignore chemistry".

The interesting part is in the 0.0000001% that isn't like the others.

Not for all intents and purposes.

If we are asking whether MOND is useful, then the answer is probably yes. You might use it for simulations of galaxy formation where Newtonian gravity is considered a reasonable approximation today. But MOND is not a correct model of the universe. There is no place in the universe that Newtonian gravity applies, only places where the error is an acceptable trade-off for simpler calculation.

By the same logic, there's no place in the universe that general relativity applies either, since it breaks down at the quantum level. There's no place in the universe where any theory other than the one true grand unified theory applies, because everything else is just an approximation. At which point we're just arguing about semantics, and I don't see a reason for continuing it on my part.

There are vastly different scales where the approximation is correct for newton vs general relativity. Perhaps you can define the scales that you are calling relevant so we understand what you mean.

The scale of galaxies? Which the original article is about? I feel like I need to spell out everything, but ok:

The article is about modified Newtonian dynamics (MOND), which is a theory that modifies Newtonian gravitation to fix some observed differences in galaxies' motion, without invoking dark matter. The original commenter then proclaims "haha, MOND cannot be right, because we know that Newtonian gravity is incorrect". Yeah, no shit Sherlock; it is "incorrect" because it is just a limiting case of general relativity. But that's completely besides the whole point of MOND, which tries to "fix" gravity at galactic scales, which is a Newtonian regime even with general relativity. MOND is trying to tweak the Newtonian formula at those extreme distances, and if it works, then maybe it can be worked out to be a limiting case of a "modified general relativity", just as Newtonian gravity is a limiting case of GR. Got it?

The inaccuracy of the Newtonian theory of gravity is large enough that it was already noticed by astronomers in the mid-1800s.

So spacetime (interactions between mass, space, and time) are required for any sort of precision explanation. If "extreme" means planet size masses, I guess, but I generally consider our solar system pretty normal. However we cannot explain the planetary motion of mercury without relativity, so define your extreme.

But sure, newton is good enough to handle most ground based scenarios where we only care about forces at low precision.

My first thought was that we only know Cavendish's constant to a little over 4 significant figures, so how could this be right? The relativistic effects at Earth's surface would change this by only ~10^-8, so I think the challenge in refining the Cavendish gravitic constant lie elsewhere.

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