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Good pieceGood piecePosted Nov 25, 2012 5:58 UTC (Sun) by rgmoore (✭ supporter ✭, #75)In reply to: Good piece by wolfgang Parent article: LCE: Don't play dice with random numbers
A chaotic system is by its very definition a deterministic system. Initially close states may diverge arbitrarily far by temporal propagation (loosely spearking; things become more involved when the associated phase space volume can shrink), but the individual trajectories are still governed by deterministic dynamics. They are very well predictable. If the initial conditions could be determined with infinite accuracy -- which, in the framework of classical mechanics, is theoretically possible -- there is no randomness involved. Sure, but that doesn't describe the real world. The real world exhibits quantum behaviors, and classical mechanics is just a simplifying assumption. We can't know the exact initial position and momentum for every particle in a system; our knowledge is limited by the Uncertainty Principle. Even if we could somehow bypass the Uncertainty Principle and determine objects' initial states perfectly, it wouldn't necessarily get us anything. There are other quantum effects that are truly random, like spontaneous emission of infrared photons from molecules that are in excited vibrational states. As long as a system is chaotic by classical mechanics, those real world quantum effects will guarantee that it is truly unpredictable.
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Good piece Posted Nov 27, 2012 0:12 UTC (Tue) by wolfgang (subscriber, #5382) [Link]
Precisely! I'm absolutely not arguing that it is not possible to generate randomness, and it is actually much simpler for all practical purposes than in theory. The point is that it is most important to state under which assumptions, especially under the assumed validity of which theory, one is trying to generate randomness. For instance, if you subscribe to the Bohmian interpretation of quantum mechanics, you're back to the same trouble as with classical mechanics, whereas you can safely relax with the Kopenhagen interpretation. And even if you assume the latter, a careful analysis is still required -- for instance, an enemy that also happens to be an experimental god could be entangled with the atom-photon system you mentioned in an apt way, and thus obtain perfect information about your measured state.
Uncertainty principle Posted Nov 28, 2012 12:45 UTC (Wed) by tialaramex (subscriber, #21167) [Link]
It doesn't mean anything to "bypass the Uncertainty Principle".
The principle is often misunderstood as a limitation on our observations of a system that really has properties like "exact momentum" and "precise location" - just like the observer effect in classical mechanics. Indeed it is sometimes explained this way in high school or in pop science books. That's not what's going on! The Uncertainty Principle actually says that these properties _do not exist_ not that we have some trouble measuring them. We can do experiments which prove that either an electron does not actually _have_ a specific position when its momentum is known or else that position is somehow a hidden property of the entire universe and not amenable to our pitiable attempts to discover it in the locale of the actual electron. The Uncertainty Principle says that the former is the more plausible explanation (and certainly the only one that's consistent with the remainder of our understanding about how the universe "works").
Uncertainty principle Posted Nov 29, 2012 18:02 UTC (Thu) by davidescott (guest, #58580) [Link]
AFAIK no experiment has shown that a non-local hidden variable theory is inconsistent with experimental evidence.
For a descriptive theory I would personally prefer determinism and non-locality. For a predictive theory non-determinism and locality are clearly better.
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