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> for possibly billions of years with its unknown fate already sealed Probably not for quite that long. The path of a meteor is only going to be deterministic

> for possibly billions of years with its unknown fate already sealed Probably not for quite that long. 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. Not sure what the Lyapunov time is for these meteors, but typical time scales for planets are 2M-200M years. For small things like meteors, there are likely other sources of noise (e.g., solar wind pressure) with quantum uncertainty that lead to non-determinism even faster.

gerdesj 8y ago
>> for possibly billions of years with its unknown fate already sealed >Probably not for quite that long. No, you are right "Probably not for quite that long" - way longer. Parent was looking deep in wonder at something and frankly the bits that make up the meteor are as old as they are old. Those atoms have been hanging around the place for quite a while but I'm not too sure that anyone can really decide when they should be considered as "existing" as a meteor.
- azernik 8y ago
  GP was talking about determinism (chaos theory), not the Ship of Theseus problem. i.e. the same meteor has existed for a long time, but orbital dynamics in the real solar system aren't really deterministic on such long time scales.
bellerose 8y ago
Quantum uncertainty doesn’t change the outcome from being deterministic.
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).
    - 8y ago
nickysielicki 8y ago
Somehow, that is even more bone-chilling.
pdonis 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. No, it's only going to be predictable on that timescale. The uncertainty involved has nothing to do with quantum uncertainty; it's purely classical uncertainty because we can only make observations with finite accuracy.
- tlb 8y ago
  The Lyapunov time scale defines the time for any variation of position or momentum to be amplified by a factor of e. The exponential growth applies equally to a measurement error and a quantum event affecting the object's momentum. Quantum events such as alpha decay (shooting out a helium nucleus with momentum of about 1e-21 Ns) start off small but after 50 Lyapunov times can get huge.
jefurii 8y ago
This is why I read Hacker News.

gerdesj 8y ago

>> for possibly billions of years with its unknown fate already sealed >Probably not for quite that long. No, you are right "Probably not for quite that long" - way longer. Parent was looking deep in wonder at something and frankly the bits that make up the meteor are as old as they are old. Those atoms have been hanging around the place for quite a while but I'm not too sure that anyone can really decide when they should be considered as "existing" as a meteor.

azernik 8y ago
GP was talking about determinism (chaos theory), not the Ship of Theseus problem. i.e. the same meteor has existed for a long time, but orbital dynamics in the real solar system aren't really deterministic on such long time scales.

bellerose 8y ago

Quantum uncertainty doesn’t change the outcome from being deterministic.

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).
  - 8y ago

nickysielicki 8y ago

Somehow, that is even more bone-chilling.

pdonis 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. No, it's only going to be predictable on that timescale. The uncertainty involved has nothing to do with quantum uncertainty; it's purely classical uncertainty because we can only make observations with finite accuracy.

tlb 8y ago
The Lyapunov time scale defines the time for any variation of position or momentum to be amplified by a factor of e. The exponential growth applies equally to a measurement error and a quantum event affecting the object's momentum. Quantum events such as alpha decay (shooting out a helium nucleus with momentum of about 1e-21 Ns) start off small but after 50 Lyapunov times can get huge.

jefurii 8y ago

This is why I read Hacker News.