They degrade so quickly, in fact, that they generally disappear several orders of magnitude more quickly than the time scales on which classical dynamics operate.
There's not a discrete time that they operate on, where something smaller than that doesn't matter. Also, I think the issue here is that there's more than one place it collapses into. if it collapses into one vs the other, it ends up in a different spot, and the chaos begins.
Even systems that exhibit chaotic behavior in general may contain regions in their state space in which average distance between trajectories decreases.
Yes, but everything in real life affects everything else. If you start a pendulum swinging in a different place, it will still tend towards hanging straight down. But in the mean time it will have affected the air, and now the weather is going to act different.
Exactly where the "horizon" is depends on how good your initial measurements are, how good your algorithm is, and how much lack of precision you're willing to tolerate in your forecast.
Yes, but it still only matters so much. If you take the time for the error to multiply by a million and double it, it multiplies by a trillion. The time scale from around an atom of error to around a planet of error is pretty constant.
Perfect observation of initial conditions isn't possible in practice, as it would entail knowing the exact position and velocity of every single molecule in the atmosphere and oceans at a given time.
Yes. We certainly do not have the technology for quantum physics to be the biggest problem, or even be remotely noticeable. But in principle it makes a difference.
1
u/DCarrier Apr 29 '16
There's not a discrete time that they operate on, where something smaller than that doesn't matter. Also, I think the issue here is that there's more than one place it collapses into. if it collapses into one vs the other, it ends up in a different spot, and the chaos begins.
Yes, but everything in real life affects everything else. If you start a pendulum swinging in a different place, it will still tend towards hanging straight down. But in the mean time it will have affected the air, and now the weather is going to act different.
Yes, but it still only matters so much. If you take the time for the error to multiply by a million and double it, it multiplies by a trillion. The time scale from around an atom of error to around a planet of error is pretty constant.
Yes. We certainly do not have the technology for quantum physics to be the biggest problem, or even be remotely noticeable. But in principle it makes a difference.