7 ms·

The point the article (apparently unsuccessfuly) tries to hammer home is that the findings here are mathematical, they go beyond simulation and take a deeper bi

The point the article (apparently unsuccessfuly) tries to hammer home is that the findings here are mathematical, they go beyond simulation and take a deeper bite into the problem, proving that all planetary systems are unstable. The first paragraph of the linked article talks about simulation experiments from 2009, so your criticism here that there is some spurious claim to novelty is pretty unfounded. Simulation runs that show instability are old hat; mathematical proof that this instability is inherent and unavoidable is the story.

PaulHoule 3y ago
I got a PhD in quantum chaos and my take was that real breakthroughs in classical chaos happen every 50 years or so.
- thechao 3y ago
  My desire for "real breakthroughs ... in chaos theory" to be exactly every 50 years (to the day! the minute!) is extremely high.
- MichaelRazum 3y ago
  If you could comment. Is it true that "classic" quantum field theory can't describe chaos, because the operators are linear?
  - PaulHoule 3y ago
    Yep. Quantum chaos, at least insofar as I was involved with it, is about semi classical analysis of quantum systems which would have chaos if they were classical. Remember quantum mechanics started with the Bohr atom which was an approach that would generalize to any system that has quasi periodic (solar system in the short term) dynamics. Circa 1917 Einstein wrote a paper that said that this approach wouldn’t generalize because Poincaré proved that chaos is generic, soon after that we got Schrodinger’s equation and similar approaches. (Although that Einstein paper killed a line of development it barely got cited for 50 years) Later on there were mathematical developments in quantum chaos such as Gutzwiller’s trace formula and also numerical work where people discovered various properties of the quantum levels of systems that were classically chaotic. Linear operators in quantum mechanics don’t precluded observing chaos in the real world because the true “long term” is very long indeed. That is, classically or quantum mechanically if you wait some really absurdly long time (say much more than 10^120 years) the universe is expected to come arbitrarily close to the state it is in today. See https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theor...
    - jfengel 3y ago
      Though note that the recurrence theorem applies to a finite phase space. An expanding universe such as ours is not subject to that. We just get heat death instead.
csense 3y ago
> proving that all planetary systems are unstable The article implies this is what was proved, but later contradicts itself. Based on my reading, only a couple specific initial conditions were proved to be unstable.

PaulHoule 3y ago

I got a PhD in quantum chaos and my take was that real breakthroughs in classical chaos happen every 50 years or so.

thechao 3y ago
My desire for "real breakthroughs ... in chaos theory" to be exactly every 50 years (to the day! the minute!) is extremely high.
MichaelRazum 3y ago
If you could comment. Is it true that "classic" quantum field theory can't describe chaos, because the operators are linear?
- PaulHoule 3y ago
  Yep. Quantum chaos, at least insofar as I was involved with it, is about semi classical analysis of quantum systems which would have chaos if they were classical. Remember quantum mechanics started with the Bohr atom which was an approach that would generalize to any system that has quasi periodic (solar system in the short term) dynamics. Circa 1917 Einstein wrote a paper that said that this approach wouldn’t generalize because Poincaré proved that chaos is generic, soon after that we got Schrodinger’s equation and similar approaches. (Although that Einstein paper killed a line of development it barely got cited for 50 years) Later on there were mathematical developments in quantum chaos such as Gutzwiller’s trace formula and also numerical work where people discovered various properties of the quantum levels of systems that were classically chaotic. Linear operators in quantum mechanics don’t precluded observing chaos in the real world because the true “long term” is very long indeed. That is, classically or quantum mechanically if you wait some really absurdly long time (say much more than 10^120 years) the universe is expected to come arbitrarily close to the state it is in today. See https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theorem https://en.wikipedia.org/wiki/Poincar%C3%A9_recurrence_theor...
  - jfengel 3y ago
    Though note that the recurrence theorem applies to a finite phase space. An expanding universe such as ours is not subject to that. We just get heat death instead.

csense 3y ago

> proving that all planetary systems are unstable The article implies this is what was proved, but later contradicts itself. Based on my reading, only a couple specific initial conditions were proved to be unstable.