6 ms·
That's correct, while taking away the entropy inequality as well. The thing is that very inequality is one of these laws of thermodynamics we so love, so I kind
by boxfire 9y ago
That's correct, while taking away the entropy inequality as well. The thing is that very inequality is one of these laws of thermodynamics we so love, so I kind of see this as hot air.
- ianai 9y agoAye either they have upturned a theory as august as general relativity or they’ve thrown the baby out with the bath water somewhere.
- im3w1l 9y agoBased on my fairly layman understanding it could be as simple as the "weak solutions" not being as useful as they were thought to be.
- contravariant 9y agoThat seems to be one of the explanations provided in the article.
- meri_dian 9y agoThe laws of thermodynamics are quite a bit more august than GR
- ianai 9y agoI’ll leave such distinctions to more seasoned minds.
- pencilhappen 9y agoWhat's funny is the article says this about the Navier-Stokes equations: "The equations work. They describe fluid flows as reliably as Newton’s equations predict the future positions of the planets" Newton's equations do not in fact reliably predict Mercury's orbit, and it took GR to do it. Lazy journalist!
- yorwba 9y agoThe Navier-Stokes equations do not in fact reliably predict the flow of all real-world fluids. The comparison to Newton's equations is perfectly apt. Good enough for most applications, but may be imprecise in some cases.
- taneq 9y agoSounds like a perfectly accurate statement to me, in both directions.
- alephnil 9y agoThe Navier-Stokes equations assume that the medium is continuous even at infinitely small scales, which obviously not the case for natural fluids, that are made of discrete atoms. Thus the equations are only correct at sufficiently large scales. They work fine for describing the airflow around an aeroplane, but not the airflow around the head of a hard drive, which is small enough that the finite size of atoms must be taken into account. On a more visible scale, you have Brownian motion of small particles, which can be seen even in a low magnification microscope. The Navier-Stokes equations predict that these effect does not exist. The equations are still useful approximation in a lot of cases.
- rusk 9y agoHow are Navier Stokes the other way, on the macro scale? e.g. in the context of meteorology. Asking because I had a discussion with somebody recently where they claimed the fundamental flaw to the science underlying Climate Change science is over-reliance on NS at macro scale as a way of predicting climate behaviour, or something. I took it to be Baloney, but I'm wondering if there is some strands of truth to it ...
- qubex 9y agoAs you intuit, there is no reason to presume that Navier-Stokes would be unreliable at macro scales relevant to meteorology, simply because it is so thoroughly tested in experimental settings and to such sensitivities that it is known that all relevant factors are accounted for. (Of course, why would one presume that if it is inaccurate at planetary scales, it biases observations towards the climate change narrative? It's just the typical “God of the gaps” kind argument.)
- rusk 9y agoWell general relativity breaks down at very small scales, and imparts the need for quantum mechanics ...
- qubex 9y agoIf you are really interested, somebody has bothered to make a special-relativity & quantum-indeterminacy compatible formulation of Navier-Stokes suitable for calculating shockwaves in extremely dense mediums such as the neutronium neutron stars are thought to be made of (where the speed of sound is comparable to the speed of light in a vacuum, hence the relativity, and the matter is degenerate and in states of superposition, hence the quantum indeterminacy). I don’t have the reference right with me at the moment (mainly because I just looked at it and though “oh horror!” and averted my eyes) but I know where and how to dig it up for you if you want. Of course... for obvious reasons it hasn't been experimentally verified... For the record: I also saw it coded in FORTRAN. Yeah. It's like catching grandma in starkers.
- R0b0t1 9y agoSir, would you please post a link to this code?
- qubex 9y agoIt wasn’t my code to link to and I probably last saw it in 1996, back in the era of dot-matrix printouts on green-and-white continuous paper (on a Windows NT 3.5 machine running FORTRAN PowerStation, if you care to commiserate). I think I can dig up the paper where the equation was published, though. EDIT: This isn't the paper I had in mind, and the equation presented is ‘merely’ relativistic, but it gives you a feel for the beast: https://arxiv.org/pdf/astro-ph/0402502.pdf https://arxiv.org/pdf/astro-ph/0402502.pdf (see section C).
- R0b0t1 9y agoThank you! If you have more time to look for the original, I would find it exceptionally interesting; however I understand if the keywords are lost to you. Can you explain roughly what the quantum corrections were?
- foota 9y agoIsn't that possible though if the fluid isn't a closed system? (which it probably isn't)
- qubex 9y agoAll of the above arguments obtain if the fluid is a closed system and is only acting as a result of the forces it itself is exerting upon itself, subject to the various boundary conditions around it. Of course if you open the system various outcomes are possible depending on what the external influences do to it (for example, the two solutions mentioned for the still water become entirely plausible if there's somebody roaming around who might put a lighter under the glass and cause the water in it to boil, but that isn't the point of the exercise).
- mar77i 9y agoWho would have guessed that this story about the behavior of fluids seems to kind of leak.