One of the annoying/fascinating things about quantum mechanics is the fact the world doesn’t seem to be quantum-mechanical. When you look at something, it seems to have a location, not a superposition of all possible locations; when it travels from one place to another, it seems to take a path, not a sum over all paths. This frustration was expressed by no lesser a person than Albert Einstein, quoted by Abraham Pais, quoted in turn by David Mermin in a lovely article entitled “Is the Moon There when Nobody Looks?“:
I recall that during one walk Einstein suddenly stopped, turned to me and asked whether I really believed that the moon exists only when I looked at it.
The conventional quantum-mechanical answer would be “Sure, the moon exists when you’re not looking at it. But there is no such thing as `the position of the moon’ when you are not looking at it.”
Nevertheless, astronomers over the centuries have done a pretty good job predicting eclipses as if there really was something called `the position of the moon,’ even when nobody (as far as we know) was looking at it. There is a conventional quantum-mechanical explanation for this, as well: the correspondence principle, which states that the predictions of quantum mechanics in the limit of a very large number of particles (a macroscopic body) approach those of classical Newtonian mechanics. This is one of those vague but invaluable rules of thumb that was formulated by Niels Bohr back in the salad days of quantum mechanics. If it sounds a little hand-wavy, that’s because it is.
The vagueness of the correspondence principle prods a careful physicist into formulating a more precise version, or perhaps coming up with counterexamples. And indeed, counterexamples exist: namely, when the classical predictions for the system in question are chaotic. In chaotic systems, tiny differences in initial conditions grow into substantial differences in the ultimate evolution. It shouldn’t come as any surprise, then, that it is hard to map the predictions for classically chaotic systems onto average values of predictions for quantum observables. Essentially, tiny quantum uncertainties in the state of a chaotic system grow into large quantum uncertainties before too long, and the system is no longer accurately described by a classical limit, even if there are large numbers of particles.
Some years ago, Wojciech Zurek and Juan Pablo Paz described a particularly interesting real-world example of such a system: Hyperion, a moon of Saturn that features an irregular shape and a spongy surface texture.