If th behavior of a system is measured exactly and understood for a period of time, does it follow that in the future behavior of that system can be predicted? (Is there a difference between predictability and measurable properties?)
2007-06-12 06:50:34 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Physics
As answer 1 says, no. One famous example is the "three-body problem" (see ref.). If two bodies orbit each other and there are no outside influences, they will continue to do so in a stable, predictable way. In fact, their future state can be predicted by a relatively simple set of equations (a "closed-form" solution), without the necessity of a time-stepped simulation.
But three bodies behave very differently. The slightest differences in the initial conditions (position, velocity) can cause wildly different outcomes. Simulations are needed to model three-body behavior, and they show this exquisite sensitivity. So essentially no state measurement can be accurate enough to predict future behavior. This is an example of chaos in a dynamic system. Google chaos theory to learn much more.
2007-06-12 12:05:19 · answer #1 · answered by kirchwey 7 · 0⤊ 0⤋
There is a huge difference between predictability and measurable properties. And it has to do with stability in dynamic systems. And that is --way-- more than we have time to get into here âº
Doug
2007-06-12 14:00:25 · answer #2 · answered by doug_donaghue 7 · 0⤊ 0⤋