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She 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.
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Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
61–70 of 106 posts
Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
#62Earlier quoted context omitted.
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.
Could she be correct in her assertion? Are we spending more on areas of physics which don’t require it?
She's correct. If you want theory of everything energy you need accelerator the size of our Solar system. Source: Stephen Hawking's Universe in a nutshell.
Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
#63Sabine Hossenfelder's video on this: https://youtu.be/mxWJJl44UEQ
Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
#64Sabine Hossenfelder's video on this: https://youtu.be/mxWJJl44UEQ
I found https://www.quantamagazine.org/epic-effort-to-ground-physics... much more informative. Sometimes you can't digest everything in 10min.
Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
#65Earlier quoted context omitted.
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.
It's lost at Boltzmann's "molecular chaos" or "Stosszahlansatz" step. If f(x1,x2) is the two-particle distribution function giving you (hand-wavingly) the probability that you have particles with position and velocity coordinates x1 and others with coordinates x2, then Boltzmann made the simplification that f(x1,x2) = f(x1) * f(x2), ie throwing away all the correlations between particles. This is where the time-asymmetry comes in: you're saying that after two particles collide, they retain no correlation or memory of what they were doing beforehand.
Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
#66Earlier quoted context omitted.
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.
The former. Diffusion in gases is similar.
Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
#67Earlier quoted context omitted.
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
That's high praise!
Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
#68Earlier quoted context omitted.
She 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.
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> [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.
Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
#69Sabine Hossenfelder's video on this: https://youtu.be/mxWJJl44UEQ
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.
Re: Hilbert's sixth problem: derivation of fluid equations via Boltzmann's theory
#70Earlier 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.
You lose the reversible behavior when you describe the system ignoring almost every degree of freedom.