Краткое резюме : если на сферического коня в вакууме не смотреть, то он, по прошествии некоторого времени, окажется не там, где мы думали, а черт знает где. Но мы об этом не узнаем, потому что смотреть на него будет по-прежнему нельзя. И все из-за квантовой механики.

Зачем далеко ходить за примерами? Миллиардный член логистического отображения с коэффициентом 3.58 больше или меньше 1/2?

Ага. Я писал: http://fregimus.livejournal.com/9268.html, если кому интересно.

The author of the blog entry does not seem to understand that chaos is a wholly deterministic phenomenon, having nothing to do with quantum non-determinism.

(Some of the comments down there alluding to naive Copenhagen interpretation are just too hilarious...)

No, the author understands that, you're just misreading his explanation. The whole point is that in a deterministically chaotic isolated system it's possible for the classical mechanical description to cease being a good approximation of the quantum mechanical one.

Все с точностью до наоборот: система в данном случае не является изолированной, см. http://www.phy.bris.ac.uk/people/berry_mv/the_papers/berry337.pdf :

Now, the chaotic rotation of Hyperion was discovered less than 37 years ago [estimated time for the quantum suppression of classical chaos], but nobody thinks that after the year 2020 astronomers will begin to see quantum effects – specifically the calming of Hyperion’s instability and its replacement by some more moderate multiply periodic motion. And indeed, the predicted quantum suppression of chaos is itself suppressed, and classicality restored, by another quantum effect. This is decoherence. It arises from the fact that Hyperion is not isolated.

Это не "с точностью до наоборот", а ровно то же, что я и написал (только подробнее объясненное). Если бы система была изолированной, случилось бы расхождение между квантовым и классическим. Поскольку она не изолирована, благодаря декогеренции это не происходит.

Well, his explanation doesn't make sense. He's discussing a spherical horse in vacuum and is surprised that the real world behaves differently.

First of all, Hyperion is moving chaotically *only because* it is interacting with outside world. Trying to imagine isolated chaotic Hyperion and wonder how its quantum description will diverge from classical is just plain silly - because it's rotation will cease being chaotic the moment it is isolated.

Secondly, external random inputs (such as solar rays) are not as important as internal state of the matter. Simply put, isolated quantum systems "cannot" be chaotic because they can only contain limited number of bits describing their state. This means that any evolution of such systems has to be periodic.

However, with macroscopic objects the amount of information which can be encoded in the internal state of its atoms can quite easily produce periods exceeding lifetime of the Universe - so, for all practical purposes such quantum object may have aperiodic "chaotic" behavior even if completely isolated.

You may want to read Baez's comment on the same subject
http://math.ucr.edu/home/baez/week223.html

Sean Carrol is notorious for making a stir-fry out of his thoughts.
His "cosmological origins of entropy" being a major example.

Thanks for the link! (and see my take on it above)

А хаотический магнитный маятник - менее удивителен?

С прошлого года это не так: Oracle купила Hyperion (http://www.oracle.com/hyperion/index.html), и баланс гравитационных сил изменился.

:)

Гиперактивный Гиперион