Shan Gao&#x27;s review on this is really nice and accessible, thanks.

John Baez wrote a Mastodon thread on this paper here:<a href="https:&#x2F;&#x2F;mathstodon.xyz&#x2F;@johncarlosbaez&#x2F;114618637031193532" rel="nofollow">https:&#x2F;&#x2F;mathstodon.xyz&#x2F;@johncarlosbaez&#x2F;114618637031193532</a>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]: <a href="https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;2504.06297" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;2504.06297</a>

The short answers:1. It answers how macroscopic equations of e.g., fluid dynamics are compatible with Newton&#x27;s law, when they single out an arrow of time while Newton&#x27;s laws do not.2. It was solved in the 1800s if you made an unjustified technical assumption called molecular chaos (<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Molecular_chaos" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Molecular_chaos</a>). 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&#x2F;engineering perspective the whole theory was fine by assuming molecular chaos.

David 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.

Explained for the layperson in the video cited here: <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=44439593">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=44439593</a>

may you please elaborate on why it is important, why hasn&#x27;t been solved before and what new applications may you imagine with it, please?

This is the larger part of the work:<a href="https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;2408.07818" rel="nofollow">https:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;2408.07818</a>

Can someone explain what&#x27;s groundbreaking about this? Maybe it&#x27;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&#x27;s theorem[1] and then derive a system of fluid equations [2] by computing the moments of Boltzmann equation.[1]: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Liouville%27s_theorem_(Hamiltonian)" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Liouville%27s_theorem_(Hamilto...</a>[2]: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;BBGKY_hierarchy" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;BBGKY_hierarchy</a>

This has been known for a long time: the irreversibility comes from the assumption that the velocities of particles colliding are uncorrelated, or equivalently, that particles loose the &quot;memory&quot; of their complete trajectory between one collision and another. It&#x27;s called the molecular chaos hypothesis.See <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Molecular_chaos" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Molecular_chaos</a>

It comes about when the deterministic collision process is integrated over all the indistinguishable initial states that could lead into an equivalence class of indistinguishable final states. If you set the collision probability to zero it&#x27;s time reversible even with molecular chaos, and if the particles are highly correlated (like in a polymer) there can still arise an arrow of time when the integral is performed.

I&#x27;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 &quot;molecular chaos&quot;, 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 &quot;prior&quot; is just a choice of direction. It also means that the underlying dynamics is not strictly speaking Newtonian any more (statistically, anyway).

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

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.

In derivations of the Navier Stokes equations from reversible particle models, the former get their irreversibility from some approximation, e.g.
 a transition to a less detailed state and a simpler evolution equation for it is made. Often the actual microstate is replaced by some probabilistic description, such as probability density, or some kind of implied average.

Strictly speaking, naturally on its own, it doesn&#x27;t. Detailed equations remain reversible. Even for very big N, typical isolated classical mechanical systems are reversible. However, typical initial conditions imply transitions to equilibrium, or very long stay in it. The reversed process (ending in Poincare return) will happen eventually, but the time is so incredibly long, it can&#x27;t be verified.

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

Agree in general -- I think the tiktok&#x2F;shorts wave is biasing strongly for shorter video and then the time format kills any followup&#x2F;2nd iteration-explanationBut this one was pretty good.

I don&#x27;t know if it&#x27;s just the persona she plays in these videos, but it&#x27;s so so so creepy and cringe.

As far as I&#x27;ve seen, her position is only that AGI is pretty much inevitable. What&#x27;s so fantastical about that?

Agreed, she&#x27;s pumping out too many videos I think. Perhaps she&#x27;s succumbed a bit to the temptation of cashing in on a reputation, ironically one built on taking down grifters.

In 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.

I found <a href="https:&#x2F;&#x2F;www.quantamagazine.org&#x2F;epic-effort-to-ground-physics-in-math-opens-up-the-secrets-of-time-20250611&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.quantamagazine.org&#x2F;epic-effort-to-ground-physics...</a> much more informative. Sometimes you can&#x27;t digest everything in 10min.

<a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=44442123">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=44442123</a>

Sabine Hossenfelder&#x27;s video on this: <a href="https:&#x2F;&#x2F;youtu.be&#x2F;mxWJJl44UEQ" rel="nofollow">https:&#x2F;&#x2F;youtu.be&#x2F;mxWJJl44UEQ</a>

Rings 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.

She certainly fell into the rage bait trap, and I don&#x27;t really like her these days, but this video seems fine - no ranting, just a nice piece of science communication.

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&#x2F;strawman-y if nobody was being convinced by the paper in the first place[I am not a physicist so probably can&#x27;t really evaluate the whole thing neutrally]

The issue is that many of her videos argue that funding for particle physics should instead go into foundations and interpretations of quantum mechanics, specifically research completely identical to what she works on.This is not helped by the fact that she pushes an interpretation of quantum mechanics viewed as fringe at best. Her takes on modern physics seem typically disingenuous or biased.

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&#x27;re not good enough, but that itself is kind of part of the scientific process too.

IDK why I&#x27;d want to listen to physicists about this result, which is mathematical rather than physical or scientific. John Baez, sure, he&#x27;s in the intersection between math and physics. But physics in the broader sense is an empirical science where truth comes from experiments. This result is the opposite of that.

We detached this comment from <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=44439593">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=44439593</a> and marked it off topic.

It&#x27;s ok to have opinions. It&#x27;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 &quot;all of science is bullshit&quot; (which she does, in those exact words) is not a measured criticism.

&gt; Professor Dave&#x27;s videos on how Sabine Hossenfelder is actively contributing to an atmosphere of anti-intellectualismI feel like the core of intellectualism is accepting criticism, including criticism you disagree with. I find some of Sabine&#x27;s videos to be a bit click-baity, but they are usually logically coherent, even the ones that aren&#x27;t convincing. She&#x27;s not just a crazy person yelling at the sky.Science is not religion. Its ok for people to feel certain research programs are off track. That doesn&#x27;t neccesarily mean they are right, but its ok to have opinions

The challenge is that she’s right on all three of these major points … to some extent. Unfortunately at times she seems eager to fling babies without even encountering bathwater.

You are making her arguments for her. We should not &quot;boil down&quot; the arguments she makes. This is some of the arguments she makes. She does not ground it in particular, measured criticisms, aimed at particular researchers or departments. She does not provide solutions. She uses this broadly sweeping argument as a way to cast judgment on fields of research she is not an expert in. We should evaluate the arguments that she makes, not the arguments we would like her to have made. This includes not just a dispassionate listing of the truth claims she makes, but the specific rhetoric she employs. Is modern science flawed? Absolutely. Should we be saying &quot;scientists are not to be trusted&quot; as a general, categorical statement? No, that&#x27;s laughable, and dangerously anti-intellectual.

Prof. Sabine Hossenfelder is a pretty clear-headed communicator. I&#x27;ve been following her for nearly 20 years, almost since she started writing the Backreaction blog.Her criticisms boil down to:1. Modern science spends perhaps too much time on frivolous research that doesn&#x27;t lead to anything. This very much applies to the theoretical physics and the endless series of attempts at ToE. But it&#x27;s not limited to theoretical physics.2. Modern scientific communication is often misleading and exaggerated.3. The internal workings of scientific institutions are broken.

You think she looks reasonable when she says &quot;most research in the foundations of physics isn&#x27;t based on sound scientific principles&quot; with absolutely 0 meta-analyses presented as evidence? This is an extraordinary claim to make. It requires extraordinary evidence.

I&#x27;ve never heard about that nobody before, but I&#x27;ve watched about 10 mins. of the first video you posted and it is a terrible critique to Sabine; it actually makes Sabine&#x27;s points look reasonable.He just doesn&#x27;t get the arguments she&#x27;s making, and &quot;defeats&quot; them with laughable strawmans. But anyway, it&#x27;s YouTube science so one shouldn&#x27;t expect much.Btw, Sabine&#x27;s video on the topic of this thread is a good one, the remark is unwarranted.

Cheers, and thank you for your service.

Please don&#x27;t do this here. If a comment seems unfit for HN, please flag it and email us at hn@ycombinator.com so we can have a look.We detached this comment from <a href="https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=44439647">https:&#x2F;&#x2F;news.ycombinator.com&#x2F;item?id=44439647</a> and marked it off topic.

To me, it looks like AI because it doesn&#x27;t really answer the question but instead answers something adjacent, which is common in AI responses.Giving a short summary of Hilbert&#x27;s biography &amp; his problem list, does not explain why this particular work is interesting, except in the most superficial sense that its a famous problem.

Not 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.)

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