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Comment by _0w8t | Hacker News Reader

What is puzzling about MOND and to lesser extent about Dark Matter is that both uses violation of Newton mechanics to justify themselves when we know that Newtonian mechanics is wrong. The problem is that we cannot yet model behavior of galaxies using just General Relativity. Typically models assumes Newtonian physics with minimal accounting for relativity. However there is no sound proof that it is a valid approximation. The General Relativity is extremely non-linear and even small contribution may lead to very big consequences.

We cannot yet rule out that there are no problems with dynamic of galaxies. It can be that we model them using wrong approximations.

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There is something that always puzzles me and I would like if something could illuminate me. How are those kind of massive scale astrophysical calculations made? Do they take into account every visible mass aggregate in the galaxy and simulate them, or just apply cinematic at scale assuming the galaxy centre is a point of certain mass?

I have played a little with N body simulations and I can't but be amazed about how numerically unstable physical simulations are, and how much the result can change depending on trivial simplifications.

I'm not much of an expert on the topic, but have also played with writing N-body simulations. At some point, obviously N^2 is unfeasible, so most simulations seem to use some approximation, such as the Barnes-Hut approach [1]. That approach divides the simulation space into an octtree. One can then use said octtree to approximate the force of distant quadrants by simply using the center of mass of an entire region. Due to the rate at which gravity drops off over large distances, it's "accurate enough", and fortunately the majority of "N" is "distant".

A good (but pretty shallow) overview exists on Wikipedia about other approaches [2] (under "Calculation optimizations").

[1] https://en.wikipedia.org/wiki/Barnes%E2%80%93Hut_simulation

[2] https://en.wikipedia.org/wiki/N-body_simulation

EDIT: It's occurred to me that you were referring more to stability of the simulation, rather than what optimisations are used. I have less information to offer on that part, and I agree that it would be a huge problem, if complete accuracy was desired. I suspect, however, that in the kinds of simulations we're talking about, it's more about a general result such as "the whole galaxy should be divergent", not whether a single star went left or right when interacting with a black hole.

You may be interested in this paper: http://dl.acm.org/citation.cfm?doid=3028256.3015569

Actually in a lot of new HPC codes for doing physical simulation we are now starting to incorporate Uncertainty Quantification (UQ)[1] directly into the code such that we can determine where the instabilities and bifurcation points exist in non-linear systems. UQ is really expensive to compute, but it at least allows us to know when our simulations are accurate or are sensitive to perturbations.

[1] https://en.wikipedia.org/wiki/Uncertainty_quantification

Here is a paper that discusses a possibility that the General Relativity alone can be enough to explain the observed dynamics of galaxies:

https://arxiv.org/abs/0712.0019

From the paper:

we are witnessing here the power of the nonlinearities inherent in general relativity in the context of weak gravity to effect very significant changes relative to the results expected on the basis of Newtonian theory. It suggests that hitherto unexplained astrophysical phenomena be re-considered on the basis of the application of general relativity to weak-field gravity.

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