New proof finds the ‘ultimate instability’ in a solar system model
quantamagazine.org
quantamagazine.org
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
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.
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...
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.
> (In this context, Newtonian mechanics gives such a good approximation of reality that these models don’t need to consider the effects of general relativity.)
But wasn't the precession of Mercury already known to be inadequately explained by Newtonian gravity, even before Einstein?
Humans have probably already done this by slingshotting spacecraft around planets.
I wonder if future people will say 'if only we hadn't shifted the planet by a meter back in 1969, the solar system wouldn't have fallen apart!'
Generously assuming all meteorites hit from the same direction, given the mass of the meteorite swarm is 1e-21 smaller, the total delta v is 10 to the minus 16. Double integrate that, and you get x^2/20000000000000000
Set equal to your desired difference, say one meter. You get over 100,000,000 days. That's 273,973 years to affect a 1 meter difference in position in the worst case.
Caveat: I am probably wrong.
It is also a cold, calm beauty for technically developed species instead of immediate joy of having multiple visible hot Jupiters in the system.
We take all that for granted, but it really isn't. Many of other solar systems we know contain an irregular set of planets.
It could also be well possible that this sort of stability is required for multi-billion year evolutionary processes to take place. Systems with more chaos would likely also have chaotic seasons even if their planets were to have the other needed conditions for live. If the summer-winter cycle were more unpredictable that it is on earth, maybe that acts as a limit on the complexity that live can achieve as it would constantly be getting pruned back.
Systems with "unstable" or "irregular" planetary arrangements are probably just in an earlier stage of development, and might likely lose planets or push them into more stable orbits eventually.
Similarly "stable" or "ordered" systems are likely just older systems which have been able to develop without being disrupted by outside phenomena. In that sense looking for well structured systems might be a good place to start looking for life, as they are likely old and stable enough to have had evolution take place.
The puddle looked at itself and its surroundings. The puddle saw that it had a very peculiar and specific shape, and yet its surroundings matched it perfectly. "It's amazing that the world is shaped just right and fits me perfectly" thinks the puddle.
I think there's a very good chance that we are one of the first intelligent species in our galaxy.
Obvious literature reference:
> https://en.wikipedia.org/wiki/The_Three-Body_Problem_(novel)
and its two sequels
There are also rogue stars[1].
They didn't seem to account Sun's global warming. In 500 million years it will boil out all the Earth oceans, and in 1 billion years it will swallow Mercury, Venus, Earth.
Those models are all perfectly Newtonian. The solar system isn't.
It's usefully Newtonian on the timescales we use to push things around it. But over much longer timescales planetary orbits are influenced by variations in the solar wind, visits from external objects, redistributions of mass in the Kuiper Belt and Oort cloud, and so on.
These are mostly tiny influences, but enough to make claims of unconditional stability rather questionable.
I was just astonished by the title of the article, because it seemed to contradict KAM. Yet, upon careful reading, you can interpret the title in that "a solar system model" is unstable, but not all of them. Which does not contradict KAM.
If I understand it well, KAM is compatible with the following two sentences: (1) the set of stable initial conditions is of volume 1 in phase space (2) the set of unstable initial conditions is dense in phase space. Like the rationals are dense inside the reals, but still most reals are irrational.
What is the case here? I'm not knowledgeable enough to read past the abstract of these publications.