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Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

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Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#51

Post by pizza »

dawnofdusk wrote: post #20
itsthecourier wrote: post #3

Earlier quoted context omitted.

may you please elaborate on why it is important, why hasn't been solved before and what new applications may you imagine with it, please?

The short answers: 1. It answers how macroscopic equations of e.g., fluid dynamics are compatible with Newton's law, when they single out an arrow of time while Newton's laws do not. 2. It was solved in the 1800s if you made an unjustified technical assumption called molecular chaos ( https://en.wikipedia.org/wiki/Molecular_chaos ). This work is about whether you can rigorously prove that molecular chaos actually doe…

> 3. There are no applications outside of potentially other pure math research.

I would feel remiss not to say: such statements rarely hold

Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#52

Post by MathMonkeyMan »

LudwigNagasena wrote: post #49
MathMonkeyMan wrote: post #47

Earlier quoted context omitted.

Even three bodies under newtonian gravity can lead to chaotic behavior. The neat part (assuming that the result is valid) is that precisely the equations of fluid dynamics result from their billiard ball models in the limit of many balls and frequent collisions.

But even millions of bodies under Newtonian gravity lead to reversible behaviour unlike Navier-Stokes.

The Navier-Stokes equations are a set of differential equations. The functions that the equations act upon are functions of time (and space), so the system is perfectly reversible.

It's just hard to figure out what the functions are for a set of boundary conditions.

Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#53

Post by adornKey »

edwardbernays wrote: post #35
bawolff wrote: post #22

Earlier quoted context omitted.

> Professor Dave's videos on how Sabine Hossenfelder is actively contributing to an atmosphere of anti-intellectualism I feel like the core of intellectualism is accepting criticism, including criticism you disagree with. I find some of Sabine's videos to be a bit click-baity, but they are usually logically coherent, even the ones that aren't convincing. She's not just a crazy person yelling at the sky. Science is no…

It's ok to have opinions. It's ok to have criticisms. Claiming that the whole of academia is failing is not a measured criticism. Claiming that the whole of physics academia is failing is not a measured criticism. Claiming that "all of science is bullshit" (which she does, in those exact words) is not a measured criticism.

Maybe it's not measured criticism, but that doesn't mean that something is true or false. Today there are serious problems with academia and criticism in general. Also Cancel-Culture nowadays is big.

I know enough good scientists that don't work in academia today. And I've seen a clan of religious nuts (like flat-earthers) working in bio-science academia. If people claim that academia nowadays is worth something I'd add a big "citation needed"...

For physics maybe there is some hope. I still know some good guys working there... But there is e.g. atmosphere physics... if you look deeply you'll find more failure there than non failure.. The rot for sure has already started...

Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#54

Post by Twisol »

bawolff wrote: post #42
Twisol wrote: post #27

Earlier quoted context omitted.

Your second paragraph is a much more thoughtful critique, and posting that below the original answer would focus the subsequent conversation on those points. The issue here isn't whether the comment was AI-generated; it's how we carry the conversation forward even if we suspect that it is. (For the record, if I had attempted to answer the earlier question, I probably would have laid out a similar narrative. The asker…

To be clear, im not the person who made the original ai accusation. I agree that just yelling its AI, and running away is super rude and not very constructive.

I know it wasn't you :) Sorry if I came across that way.

Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#55

Post by falcor84 »

bawolff wrote: post #23
andyfilms1 wrote: post #9

Earlier quoted context omitted.

Interesting, her videos have never struck me as contrarian for the sake of it, she seems genuinely frustrated at a lack of substantial progress in physics and the plethora of garbage papers. Though I imagine it must be annoying to be a physicist and have someone constantly telling you you're not good enough, but that itself is kind of part of the scientific process too.

My biggest complaint is sometimes it seems like she will take some low quality paper and just dunk on it. This feels a bit click-baity/strawman-y if nobody was being convinced by the paper in the first place [I am not a physicist so probably can't really evaluate the whole thing neutrally]

What's the downside of that? Shouldn't a bit of public criticality help raise the publication standards?

Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#56

Post by bawolff »

falcor84 wrote: post #55
bawolff wrote: post #23

Earlier quoted context omitted.

My biggest complaint is sometimes it seems like she will take some low quality paper and just dunk on it. This feels a bit click-baity/strawman-y if nobody was being convinced by the paper in the first place [I am not a physicist so probably can't really evaluate the whole thing neutrally]

What's the downside of that? Shouldn't a bit of public criticality help raise the publication standards?

Attacking your opponent's weakest argument is easy. Attacking their strong arguments is what takes skill.

If the paper is getting a lot of press that is one thing, but if its languishing in obscurity, it just feels a bit self-indulgant

Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#57

Post by falcor84 »

bawolff wrote: post #56
falcor84 wrote: post #55

Earlier quoted context omitted.

What's the downside of that? Shouldn't a bit of public criticality help raise the publication standards?

Attacking your opponent's weakest argument is easy. Attacking their strong arguments is what takes skill. If the paper is getting a lot of press that is one thing, but if its languishing in obscurity, it just feels a bit self-indulgant

It sounds like you're saying that her opponents are the entirety of physics researchers in academia. But isn't it that her opponents are those particular researchers that are publishing poor work, and that she's attacking the strongest arguments of those? Or am I missing something?

And I don't accept the "languishing in obscurity" argument - if a published work is poor, we should still critique it (by publishing a letter to the editorial, or any other manner), rather than just let it pollute the space. There have been many cases of obscure works being picked up decades hence, and especially now with AI "deep research", it's easier and easier for bad work to slip in - so I believe that science communicators should do what they can to add the appropriate commentary to such works. And if it seems like "easy" work, then all the better.

Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#58

Post by bubblyworld »

MathMonkeyMan wrote: post #52
LudwigNagasena wrote: post #49

Earlier quoted context omitted.

But even millions of bodies under Newtonian gravity lead to reversible behaviour unlike Navier-Stokes.

The Navier-Stokes equations are a set of differential equations. The functions that the equations act upon are functions of time (and space), so the system is perfectly reversible. It's just hard to figure out what the functions are for a set of boundary conditions.

This is not quite right. Time-reversibility means that solutions to your differential equation are invariant under the transformation x(t) -> x(-t). It's pretty easy to verify that is the case for simple differential equations like Newton's law:

F = mx''(t) = mx''(-t) since d/dt x(-t) = -x'(-t), and d/dt (-x'(-t)) = x''(-t)

Navier-Stokes is only time-reversible if you ignore viscosity, because viscosity is velocity-dependent and you can already see signs of that being a problem in the derivation above (velocity pops out a minus sign under time reversal). From my reading the OP managed to derive viscous flow too, so there really is a break in time-symmetry happening somewhere.

Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#59

Post by bubblyworld »

LudwigNagasena wrote: post #18

So where and how does a jump from nice symmetric reversible equations to turbulent irreversibility happen?

I've been puzzling about this as well. The best answer I have (as an interested maths geek, not a physicist, caveat lector) is that it sneaks in under the assumption of "molecular chaos", i.e. that interactions of particles are statistically independent of any of their prior interactions. That basically defines an arrow of time right from the get-go, since "prior" is just a choice of direction. It also means that the underlying dynamics is not strictly speaking Newtonian any more (statistically, anyway).

Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory

#60

Post by MathMonkeyMan »

bubblyworld wrote: post #58
MathMonkeyMan wrote: post #52

Earlier quoted context omitted.

The Navier-Stokes equations are a set of differential equations. The functions that the equations act upon are functions of time (and space), so the system is perfectly reversible. It's just hard to figure out what the functions are for a set of boundary conditions.

This is not quite right. Time-reversibility means that solutions to your differential equation are invariant under the transformation x(t) -> x(-t). It's pretty easy to verify that is the case for simple differential equations like Newton's law: F = mx''(t) = mx''(-t) since d/dt x(-t) = -x'(-t), and d/dt (-x'(-t)) = x''(-t) Navier-Stokes is only time-reversible if you ignore viscosity, because viscosity is velocity-d…

Now I get it, thanks for the explanation.

I wonder if "t -> -t" is lost in the Boltzmann step or in the hydrodynamic step.

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