7 ms·
Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
- whatshisface 1y agoThis is the larger part of the work: https://arxiv.org/abs/2408.07818 https://arxiv.org/abs/2408.07818
- itsthecourier 1y agomay you please elaborate on why it is important, why hasn't been solved before and what new applications may you imagine with it, please?
- makk 1y agoExplained for the layperson in the video cited here: https://news.ycombinator.com/item?id=44439593 https://news.ycombinator.com/item?id=44439593
- bravesoul2 1y agoThat video s very light and doesn't explains at what point (or intuitively) where the arrow of time comes in.
- killjoywashere 1y agoDavid Hilbert was one of the greatest mathematicians of all time. Many of the leaders of the Manhattan Project learned the mathematics of physics from him. But he was famous long before then. In 1900 he gave an invited lecture where he listed several outstanding problems in mathematics the solution of any one of which would change not only the career of the person who solved the problem, but possibly life on Earth. Many have stood like mountains in the distance, rising above the clouds, for generations. The sixth problem was an axiomatic derivation of the laws of physics. While the standard model of physics describes the quantum realm and gravity, in theory, the messy soup one step up, fluid dynamics, is far from a solved problem. High resolution simulations of fluid dynamics consume vast amounts of supercomputer time and are critical for problems ranging from turbulence, to weather, nuclear explosions, and the origins of the universe. This team seems a bit like Shelby and Miles trying to build a Ford that would win the 24 hours of LeMans. The race isn’t over, but Ken Miles has beat his own lap record in the same race, twice. Might want to tune in for the rest.
- bawolff 1y agoThis kind of misses the point. The problem isn't interesting because its on hilbert's list; its on hilbert's list because it is interesting. This is not my field, but i also don't think this would help with computational resources needed for high resolution modelling as you are implying. At least not by itself.
- quantadev 1y ago[flagged]
- fiction1 1y agoyes, and advertising the new f1 movie.
- gnubison 1y ago> the solution of any one of which would change not only the career of the person who solved the problem, but possibly life on Earth. Many have stood like mountains in the distance, rising above the clouds, for generations. Whether or not this is AI, this comment is not true. An axiomatic derivation of a formula doesn’t change how it’s used. We knew the formulas were experimentally correct, it’s just that now mathematicians can rest easy about whether they were theoretically correct. Although it’s interesting, it doesn’t change or create any new applications.
- dawnofdusk 1y agoThe 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 https://en.wikipedia.org/wiki/Molecular_chaos). This work is about whether you can rigorously prove that molecular chaos actually does happen. 3. There are no applications outside of potentially other pure math research. For a physics/engineering perspective the whole theory was fine by assuming molecular chaos.
- pizza 1y ago> 3. There are no applications outside of potentially other pure math research. I would feel remiss not to say: such statements rarely hold
- franktankbank 1y agoThat's high praise!
- jerf 1y agoIn this case, what the research says is that the approximations we have already been using for a long time are correct. "You're already right, keep doing what you're doing!" is not generally something people consider a "practical application".
- IdealeZahlen 1y agoSabine Hossenfelder's video on this: https://youtu.be/mxWJJl44UEQ https://youtu.be/mxWJJl44UEQ
- Xmd5a 1y agohttps://news.ycombinator.com/item?id=44442123 https://news.ycombinator.com/item?id=44442123
- Ygg2 1y agoI found https://www.quantamagazine.org/epic-effort-to-ground-physics-in-math-opens-up-the-secrets-of-time-20250611/ https://www.quantamagazine.org/epic-effort-to-ground-physics... much more informative. Sometimes you can't digest everything in 10min.
- baxtr 1y agoIn my perception Sabine’s quality degraded over the last year or so. Maybe it’s also the topics she covers. I’m not sure why she is getting into fantasies of AGI for example. I liked the skeptical version of her better.
- jakeinspace 1y agoAgreed, she's pumping out too many videos I think. Perhaps she's succumbed a bit to the temptation of cashing in on a reputation, ironically one built on taking down grifters.
- schuyler2d 1y agoAgree in general -- I think the tiktok/shorts wave is biasing strongly for shorter video and then the time format kills any followup/2nd iteration-explanation But this one was pretty good.
- naasking 1y agoAs far as I've seen, her position is only that AGI is pretty much inevitable. What's so fantastical about that?
- edwardbernays 1y ago[flagged]
- IdealeZahlen 1y agoShe certainly fell into the rage bait trap, and I don't really like her these days, but this video seems fine - no ranting, just a nice piece of science communication.
- maegul 1y agoRings true for my impression too. In the end, she’s a YouTuber now, for better or worse, but still puts out what look like thoughtful and informative enough videos, whatever personal vendettas she holds grudges over. I suspect for many who’ve touched the academic system, a popular voice that isn’t anti-intellectual or anti-expertise (or out to trumpet their personal theory), but critical of the status quo, would be viewed as a net positive.
- Xmd5a 1y ago[flagged]
- kgwgk 1y ago> [Quantum Cognition] is a real field with dozen of collaborators and even a textbook. Flat Earth is also a real field, with conferences with hundreds of attendees.
- Xmd5a 1y agoHave you visited Busemeyer's website ? Here's the textbook he wrote, 2nd edition https://www.cambridge.org/us/universitypress/subjects/psychology/cognition/quantum-models-cognition-and-decision-principles-and-applications-2nd-edition?format=PB https://www.cambridge.org/us/universitypress/subjects/psycho... Looks totally respectable. Why do you feel the need to ridicule it?
- 1y ago
- quantadev 1y ago[flagged]
- Twisol 1y agoNot enough em-dashes for it to be AI. (Less jokingly, nothing strikes me as particularly AI about the comment, not to mention its author addressed the question perfectly adequately. Your comment comes off as a spurious dismissal.)
- quantadev 1y ago[flagged]
- deleted 1y ago[deleted]
- Mtinie 1y agoBut you cannot prove it. So what value did your comment bring? The readership of this site should always question if a comment is in good faith, legitimate, and accurate. Your commentary may only be one of those.
- quantadev 1y ago> But you cannot... Prove it. Prove I cannot.
- Mtinie 1y agoThat’s your responsibility. I did not state that it was 100% created by AI. You did, so back it up since you obviously know things the rest of us don’t. Without proof I can only assume you 100% made up your argument.
- quantadev 1y ago100% refers to my level of certainty, as a probability. You can think of it purely as a Quantum Mechanical Wave if that helps any.
- ngriffiths 1y agoJohn Baez wrote a Mastodon thread on this paper here: https://mathstodon.xyz/@johncarlosbaez/114618637031193532 https://mathstodon.xyz/@johncarlosbaez/114618637031193532 He references a posted comment by Shan Gao[^1] and writes that the problem still seems open, even if this is some good work. [^1]: https://arxiv.org/abs/2504.06297 https://arxiv.org/abs/2504.06297
- perching_aix 1y agoShan Gao's review on this is really nice and accessible, thanks.
- LudwigNagasena 1y agoSo where and how does a jump from nice symmetric reversible equations to turbulent irreversibility happen?
- MathMonkeyMan 1y agoEven 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.
- LudwigNagasena 1y agoBut even millions of bodies under Newtonian gravity lead to reversible behaviour unlike Navier-Stokes.
- MathMonkeyMan 1y agoThe 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.
- bubblyworld 1y agoThis 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.
- rnhmjoj 1y agoCan someone explain what's groundbreaking about this? Maybe it's not done so very rigorously, but pretty much every plasma physics textbook will contain a derivation of Boltzmann equation, including some form of collisional operator, starting from Liouville's theorem[1] and then derive a system of fluid equations [2] by computing the moments of Boltzmann equation. [1]: https://en.wikipedia.org/wiki/Liouville%27s_theorem_(Hamiltonian) https://en.wikipedia.org/wiki/Liouville%27s_theorem_(Hamilto... [2]: https://en.wikipedia.org/wiki/BBGKY_hierarchy https://en.wikipedia.org/wiki/BBGKY_hierarchy
- Iwan-Zotow 1y agoNot only plasma