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Comment by philwelch | Hacker News Reader

That sounds somewhat plausible to me because it fulfills the criterion of something that would mess up our observations of gravitational force but nothing else. Is the n-body problem really so intractable we can't even handwave our way to an approximate answer that accounts for this stuff?

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Everyone has thought "maybe it's just a bad gravity equation?" at some point. It's a fun idea, but it's contrary to observation.

https://en.wikipedia.org/wiki/Bullet_Cluster

Oof, a gravitational lensing based result at 8 sigma... so much for this fun little theory

>> gravitational lensing based result

What's wrong with basing your results on gravitational lensing? Is it related somehow to the complexity of inferring on how much the images are wrapped by gravitational lensing?

nothing, I'm talking about OP's theory. A gravitational lensing based result is particularly strong due to it being model independent. OP's theory cannot account for lensing inferred CoM differing from the baryonic CoM in the bullet cluster.

This always gets trotted out, but it isn't ironclad proof of anything. Everything about the Bullet Cluster is conjecture based on secondary observations. They're not measuring "mass", they're measuring light, from which they're inferring mass. The galaxy collision is an unusual case, being at relatively high velocity, so the models may not even cover it well.

They're also assuming that the majority of the mass is in the gas, not the stars or invisible brown dwarvf stars or even black holes.

It's layers of assumptions a mile deep being used as irrefutable proof.

I'm not sure what you mean. The n-body problem has no analytical solution in general. You have to simulate. The author is suggesting that assumptions you make (such as representing the earth moon system as a point mass at their CoM) in order to make simulation feasible might lead to a catastrophic divergence from reality over time.

This is all a consequence of n-body dynamics being chaotic [1]

https://en.wikipedia.org/wiki/Chaos_theory

I don't know a lot about physics, but I do know a little bit about computer science, and it seems to me that--barring some crazy breakthrough in computation--any simulation accurate enough to overcome the chaotic nature of this problem may very well be fundamentally impossible. That in itself would be a pretty fascinating result.

The problem isn't the fidelity of the simulation persay, it's that chaotic systems are quite literally infinitely sensitive to initial conditions.

Sure; the possible result that the physical universe is fundamentally uncomputable is the result I find interesting.

That is _not_ the result though. This has nothing to do with computability. It's about the behavior of a certain pervasive class of dynamical systems.

Okay, I’m missing something then.

Meh. The axiom of choice is well documented.

Each initial set of conditions would create a unquie system.

Look at Banach–Tarski paradox

What does this have to do with the axiom of choice?

You implied the issue is the infinite set of initial conditions.

All systems are based off the initial set of conditions. The axiom of choice.

The issue is the degrees of freedom introduced with more dimensions...

N-body we can do, for example Illustris Project. To address the concern of this post, one would need non-linear general relativity simulation. That's more challenging.

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