Inspired by this question, I wonder if classical (chaotic) double pendulums are actually in a quantum superposition when not observed.
Chaotic physical systems are systems where slightly different initial positions eventually produce substantially different outcomes after some time.
For example, after enough time, even the smallest differences of starting positions of a double-pendulum will end up producing very different outcomes. Now (loosely speaking) even a massive system will have some quantum uncertainty to its center-of-mass position (yes, a pendulum really is a more complicated system but I suspect there is some level of truth to this...there surely is some quantum uncertainty to a massive quantum system's center-of-mass, right?). So, a massive system is therefore in a superposition of different tiny changes in positions (as long as these tiny positions are not "measured").
If you consider the classical evolution of each of these superpositions (of tiny changes in position of the massive quantum system) - they evolve chaotically, and eventually there will be a time when the outcomes are completely different. Yet, if the pendulum is completely isolated - wouldn't it remain in a superposition until measured? This would suggest that you could have "Schrodinger's Pendulums" where the macroscopic outcome is substantially different upon measurement.
Is there any sense to this idea? I suspect the responses will insist that decoherence ruins the fun, but I don't exactly get the intuition for why this can be argued for in general. If you think of a pendulum as a gigantic mass of particles all with harmonic oscillator potentials all connected to their nearest neighbor - then how does this system's positional uncertainty decohere without being explicitly measured by an observer?
