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Comment by hindenburg | Hacker News Reader

The article is a little bit breathless about this work as though evidence of solar system instability is completely novel and unexpected, but investigation in the area using simulation isn't exactly unprecedented.

Gerry Sussman and Jack Wisdom were working on the question of solar system instability in the late 1980s and Sussman and his students built a specialized computer called the Digital Orrery at MIT. They ran some very long simulations and found strong numerical evidence that the orbit of Pluto is chaotic.

https://en.wikipedia.org/wiki/Stability_of_the_Solar_System#...

These weren't obscure results; further work was published in Science. See "Chaotic Evolution of the Solar System," in

https://www.science.org/doi/10.1126/science.257.5066.56

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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.

> 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.

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

My desire for "real breakthroughs ... in chaos theory" to be exactly every 50 years (to the day! the minute!) is extremely high.

If you could comment. Is it true that "classic" quantum field theory can't describe chaos, because the operators are linear?

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_theor...

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.

These are numerical simulations though. The novelty is the proof that these instabilities don't come from numerical artifacts, but are an inherent part of the system.

I have also built a digital orrery, that generates interestingly complex images:

https://news.ycombinator.com/item?id=34861546#34861552

I had it in my head that the lyapunov exponent for the solar system is approx 15 million years.

There’s no doubt at all that there is some chaos in the solar system (e.g. you can’t quite predict which side of the sun the Earth will be on in 100 million years) but the question is does something big happen, like a planet getting ejected. In a low number of configuration space dimensions (N=2) you get “KAM tori” in phase which are an absolute barrier to the evolution of the system so chaotic motion is hemmed in. In N>2, however, KAM tori are still there but it is possible for chaotic trajectories to go around them. It’s clear that the trajectories of the planets behave like KAM tori on short timescales (1000s of years, that is how each one seems to be on an independent stable orbit) but what happens in the long term is not clear at all.

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