I don't think you can assert that the universe has "solved" the n-body problem. It's certainly not obvious that it has.
The universe figures out
exactly -- not approximately -- where to put each and every particle, wave, quark, and galaxy ... each and every moment of time. To do that, a program would need to have a list of each object, from quarks to galaxies; and for each, the exact state of its position and momentum and electric charge and so on; and then compute where it's supposed to go next based on its relation to every other object on the list.
That's a hell of a computation. The universe implements that computation. How does it do it?
Either the universe is a TM; or the universe is a new kind of computation that breaks the Church-Turing thesis.
You can't substitute mind for universe - you can't even substitute brain for universe.
It seems to me that the question of whether the universe is a computation is the exact same question as whether the mind is. But even if they're two different questions, everything I'm saying does happen to apply to both situations. But it seems obvious that the questions are logically equivalent. How could the universe be a computation and the brain not? Or the brain a computation and the universe not? Well maybe that direction's possible. Ok I'll concede the point in this narrow technical sense. The brain could be a locally coherent object in an essentially random universe. A Boltzman brain. But Boltzman brains are nihilistic, like brain-in-vat scenarios. It seems clear enough that the universe is a computer if and only if the mind is.
https://en.wikipedia.org/wiki/Boltzmann_brain
Reporting back about the paper I linked earlier, I've skimmed through it a couple of times. Very interesting. Doesn't actually talk about QM. It turns out (according to the author) that although Newtonian physics is not simulable (can not be simulated exactly by a TM), relativity is.
The paper is extremely technical and way beyond my knowledge of physics. But he did make one very insightful point. In Newtonian gravity, g1*g2/r^2, you get arbitrarily large energy as two point-masses get closer. This is sort of the underlying reason that Newtonian physics isn't a TM. There are infinities.
On the other hand, he claims that relativity fixes that problem, and can be implemented by a TM.
If that were actually true, then it's not out of the question for the universe to be a computation. Or at least for the laws of known physics to be, which is the next best thing.
One problem from my point of view is that he does not talk about chaos at all. My argument is: Since we can't predict the stability of the solar system using computers because the accumulated rounding errors eventually lead to huge differences; therefore a TM can't run the solar system. Nor the universe, for the same reason.
Now the paper, in my first couple of flyovers, seems to play fast and loose with real numbers. I have a very clear understanding in my mind of real numbers, bitstrings, Turing machines and all that ... and I somehow feel that the author is either not being clear enough in his thinking, or else in his explaining. I'm really not convinced by this paper. He's not dealing with the rounding errors.
TMs can not implement real numbers. They can only
approximate real numbers. This was perfectly well appreciated by Turing in his 1936 paper. And it seems to me that this is a big problem for anyone trying to claim that the laws of physics, which are based on the math of real numbers, can be implemented as a TM. Whether it's relativity or QM doesn't matter, because those theories use mathematical continuity.
I think he addresses this point so I have to go back and trace this thread of reasoning.