Can 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. 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 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.
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.
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 "memory" of their complete trajectory between one collision and another. It's called the molecular chaos hypothesis.
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).
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'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.
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.
Strictly speaking, naturally on its own, it doesn'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't be verified.
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.
Agree 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
Agreed, 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.
(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.)
To me, it looks like AI because it doesn't really answer the question but instead answers something adjacent, which is common in AI responses.
Giving a short summary of Hilbert's biography & his problem list, does not explain why this particular work is interesting, except in the most superficial sense that its a famous problem.
Readit News
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
[1]: https://en.wikipedia.org/wiki/Liouville%27s_theorem_(Hamilto...
[2]: https://en.wikipedia.org/wiki/BBGKY_hierarchy
https://arxiv.org/abs/2408.07818
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 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.
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.
See https://en.wikipedia.org/wiki/Molecular_chaos
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.
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.
But this one was pretty good.
Dead Comment
We detached this comment from https://news.ycombinator.com/item?id=44439647 and marked it off topic.
(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.)
Giving a short summary of Hilbert's biography & his problem list, does not explain why this particular work is interesting, except in the most superficial sense that its a famous problem.
Dead Comment