Posted Nov 25, 2012 5:58 UTC (Sun) by rgmoore
(✭ supporter ✭
In reply to: Good piece
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.
to post comments)