Ever heard of chaotic systems? Any dynamic system that shows extreme sensitivity to initial conditions is chaotic. For instance smoke curling from a cigarette, planetary orbits over time, weather, water dripping from a tap - all of these show extreme sensitivity to initial conditions.
Here is the fun thing. In quantum mechanics everything evolves linearly. Therefore extreme sensitivity to initial conditions is entirely impossible. We only think that we observe that. Yet the world is full of cases where we can demonstrate such sensitivity!
Thanks. A perfect example of the outright weirdness of quantum phenomena.
I read the first section of that paper ("Why quantum chaos?"), and its proposition makes no sense to me. None other than Poincare PROVED (proved!) ages ago that the motion and position of just three little points attracted to each other according to Newton's formulas are extremely sensitive to infinitesimal changes in their initial motions and positions (i.e., the system is chaotic in the classical sense). And as you point out, the world is full of cases that demonstrate such hyper-sensitivity. Yet, according to this paper, such a system is impossible in nature. I don't get it.
Instinctively, I have to believe there must be a more fundamental underlying explanation for this and other apparent contradictions... it's just that at the moment no one knows what this explanation might be.
>Here is the fun thing. In quantum mechanics everything evolves linearly. Therefore extreme sensitivity to initial conditions is entirely impossible
I'm not sure if that is true. You can have dense sets created by Linear Operators if you're in a infinite dimensional setting (which you _are_ in QM). That's what Hypercyclic Operators are.
In any case, although the wave function evolves linearly, the _square_ of the wavefunction obviously does not (by the product rule). Since all observations are going to be based on square of the wavefunction, or the product of it with it's gradient, all observable quantities will typically evolve nonlinearly.
Ever heard of chaotic systems? Any dynamic system that shows extreme sensitivity to initial conditions is chaotic. For instance smoke curling from a cigarette, planetary orbits over time, weather, water dripping from a tap - all of these show extreme sensitivity to initial conditions.
Here is the fun thing. In quantum mechanics everything evolves linearly. Therefore extreme sensitivity to initial conditions is entirely impossible. We only think that we observe that. Yet the world is full of cases where we can demonstrate such sensitivity!
See http://www.iqc.ca/publications/tutorials/chaos.pdf for some of the attempts to reconcile observed classical facts with what we think are true quantum truths.