3 ms·

>"The path of a meteor is only going to be deterministic on a timescale given roughly by the largest Lyapunov exponent associated with its orbit. On longer time

by nonbel 8y ago

>"The path of a meteor is only going to be deterministic on a timescale given roughly by the largest Lyapunov exponent associated with its orbit. On longer timescales, even the very tiny irreducible quantum uncertainty in its initial state would be enough to cause it to miss the Moon." My understanding is that chaotic systems are still deterministic, the state at some later time is just very sensitive to the initial conditions (which it may be impossible to know with much precision). "Irreducible quantum uncertainty" is something else that has nothing to do with Lyapunov time. I also see Lyapunov died in 1918,[1] while the uncertainty principle was introduced in 1927.[2] [1] https://en.wikipedia.org/wiki/Aleksandr_Lyapunov https://en.wikipedia.org/wiki/Aleksandr_Lyapunov [2] https://en.wikipedia.org/wiki/Uncertainty_principle https://en.wikipedia.org/wiki/Uncertainty_principle

nine_k 8y ago
Solar wind can be strong close to Sun during flares. If you can predict flares on the scale of millions of years, then likely you could reduce uncertainty to just quantum noise which is way weaker.
adrianN 8y ago
Quantum effects have an influence on macroscopic objects, including asteroids. We can't really see them because of decoherence. Here's a paper that looks at the tumbling of Hyperion from a quantum viewpoint: https://arxiv.org/abs/quant-ph/0503170 https://arxiv.org/abs/quant-ph/0503170
Someone 8y ago
”the state at some later time is just very sensitive to the initial conditions” I am sure it has zero impact in practice, but theoretically, there’s a random component that isn’t part of the initial conditions. Our current understanding of radioactive decay is that it is 100% random, and that the law of conservation of momentum also holds at quantum scale. If so, radio-active decay that emits a particle that escapes from an orbit around the meteor (relatively easy, given the lack of atmosphere and low mass of the meteor) has a (minute) random effect on the velocity vector of the remaining larger part. Because individual decay events are uncorrelated, adding up all the effects of radio-active decay over time will make the already extremely tiny effect a lot smaller (by the square root of the number of decays, if I’m not mistaken, but there may the timing of decays gives earlier decays a larger effect on the eventual course, so it may be slightly less dramatic). That’s why I doubt it has any practical impact.
- tomp 8y ago
  > Our current understanding of radioactive decay is that it is 100% random Isn't it only locally random? I.e. there could still be some global "initial conditions" that make it deterministic (yet unknowable for us)... As in, given a sequence of numbers, there's no way to tell if it was generated randomly or just pseudorandomly (e.g. by RSA/SHA).
  - db48x 8y ago
    That would be called a "hidden variable", and it's already proved that no theory involving hidden variables can be correct.
jessriedel 8y ago
> My understanding is that chaotic systems are still deterministic, Classical chaotic systems are indeed deterministic in principle, and only effectively unpredictable due to finite measurement precision. But the world isn't classical, it's quantum, and quantum systems are fundamentally indeterministic. (You can make a philosophical move where you say the wavefunction is deterministic even if the results of our measurements are indeterministic, and the wavefunction is the "real" thing, but that's orthogonal to the point I'm making. All I'm saying is that the meteor's path, on long enough timescales, is random in the same sense as radioactive decay.) > "Irreducible quantum uncertainty" is something else that has nothing to do with Lyapunov time. I think I'm going to have to pull rank on you and just say you're wrong on this one :) There's a whole field of quantum chaos that explores the relationship between these things in depth. Here's one of my favorite papers: https://arxiv.org/abs/gr-qc/9402006 https://arxiv.org/abs/gr-qc/9402006 > I also see Lyapunov died in 1918,[1] while the uncertainty principle was introduced in 1927.[2] I'm discussing the implications of chaotic dynamics for quantum systems, and scientists generally do not live to see the implication of all their ideas. Maxwell realized that light is just vibrations in the electromagnetic field, and he died in 1879, yet we still start by writing down Maxwell's equations when learning how light operates under the laws of quantum electrodynamics.

by nonbel 8y ago

nine_k 8y ago

Solar wind can be strong close to Sun during flares. If you can predict flares on the scale of millions of years, then likely you could reduce uncertainty to just quantum noise which is way weaker.

adrianN 8y ago

Quantum effects have an influence on macroscopic objects, including asteroids. We can't really see them because of decoherence. Here's a paper that looks at the tumbling of Hyperion from a quantum viewpoint: https://arxiv.org/abs/quant-ph/0503170 https://arxiv.org/abs/quant-ph/0503170

Someone 8y ago

”the state at some later time is just very sensitive to the initial conditions” I am sure it has zero impact in practice, but theoretically, there’s a random component that isn’t part of the initial conditions. Our current understanding of radioactive decay is that it is 100% random, and that the law of conservation of momentum also holds at quantum scale. If so, radio-active decay that emits a particle that escapes from an orbit around the meteor (relatively easy, given the lack of atmosphere and low mass of the meteor) has a (minute) random effect on the velocity vector of the remaining larger part. Because individual decay events are uncorrelated, adding up all the effects of radio-active decay over time will make the already extremely tiny effect a lot smaller (by the square root of the number of decays, if I’m not mistaken, but there may the timing of decays gives earlier decays a larger effect on the eventual course, so it may be slightly less dramatic). That’s why I doubt it has any practical impact.

tomp 8y ago
> Our current understanding of radioactive decay is that it is 100% random Isn't it only locally random? I.e. there could still be some global "initial conditions" that make it deterministic (yet unknowable for us)... As in, given a sequence of numbers, there's no way to tell if it was generated randomly or just pseudorandomly (e.g. by RSA/SHA).
- db48x 8y ago
  That would be called a "hidden variable", and it's already proved that no theory involving hidden variables can be correct.

jessriedel 8y ago

> My understanding is that chaotic systems are still deterministic, Classical chaotic systems are indeed deterministic in principle, and only effectively unpredictable due to finite measurement precision. But the world isn't classical, it's quantum, and quantum systems are fundamentally indeterministic. (You can make a philosophical move where you say the wavefunction is deterministic even if the results of our measurements are indeterministic, and the wavefunction is the "real" thing, but that's orthogonal to the point I'm making. All I'm saying is that the meteor's path, on long enough timescales, is random in the same sense as radioactive decay.) > "Irreducible quantum uncertainty" is something else that has nothing to do with Lyapunov time. I think I'm going to have to pull rank on you and just say you're wrong on this one :) There's a whole field of quantum chaos that explores the relationship between these things in depth. Here's one of my favorite papers: https://arxiv.org/abs/gr-qc/9402006 https://arxiv.org/abs/gr-qc/9402006 > I also see Lyapunov died in 1918,[1] while the uncertainty principle was introduced in 1927.[2] I'm discussing the implications of chaotic dynamics for quantum systems, and scientists generally do not live to see the implication of all their ideas. Maxwell realized that light is just vibrations in the electromagnetic field, and he died in 1879, yet we still start by writing down Maxwell's equations when learning how light operates under the laws of quantum electrodynamics.