Microscopic and Macroscopic Randomness
A common reaction to QM is that it doesn't matter since quantum randomness will never manifest itself at the macroscoic level -- that is, in the world of sticks and stones we can see with the naked eye. An appeal is usually made to the "law of large numbers", according to which random fluctuations at the atomic (or lower level) will cancel each other out in a macrscopic object, so that what is seen is an averaged-out behaviour that is fairly predictable.
Something like this must be happening in some cases, assuming QM is a correct description of the micro-world, or there would not even be an appearance of a determinstic macro-world. Since deterministic classical physics is partially correct, there must be a mechanism that makes the QM micro-world at least approximate to the classical description.
However, it it were the case that all macroscopic objects behaved in a 100% deterministic fashion, there would be no evidence for QM in the first place -- since all scientific apparatus is in the macro-world ! A geiger-counter is able to amplify the impact of a single particle into an audible click. Richard Feynman suggested that if that wasn't macroscopic enough, you could always amplify the signal further and use it to set off a stick of dynamite! It could be objected that these are artificial situations. This is rather desprate, however, because there is a well-known natural mechanism that could do the same job: classical chaos.
A clasically chaotic system is by definition one that is critically sensitive to its initial conditions. "critically" sensitive means that any variation in initial conditions, no matter how slight, can bring about a change in the macroscopic behaviour of the system, no matter how large. Since there is no lower limit to critical sensitivity, it must extend all the way "down" to me microscopic world of quantum phsyics. Thus, hurricans need not be started by butterfly wings, they can be started by electrons!
The term "classical" misleads some people. Chaos can be defined within the framework of classical physics, which is strictly deterministic. This is sometimes taken to mean any chaotic system encountered in nature (such as a weather system) is classical and deterministic. However, when we tall about ordinary, non-chaotic systems being classical, we mean they are *approximately* classical. Classical physics is not entirely wrong; it worked for 100's of years after all. But it is not entirely right either. "Classical" systems are quantum systms that approximate classical behaviour.
Thus any chaotic system that you can actually encounter, such as a weather system, is only approxiamtely classical. It has no underlying determinism. At the most fundamental level it is a quantum system -- because everything is.
So we can have classical system that behave predictably (ordinary Newtonian phsyics), quantum systems that behave predictably on the macroscopic level (through the Law of Large Numbers), classical systems that behave unpredictably (through classical chaos) and quantum systems that unpredictably on the macroscopic as well as microscopic level (chaos and othe "quantum amplifiers").
In fact, this is not just theoretical. Conventional big-bang theories generally require an input of quantum indeterminism to provide the large-scale structure of the universe. A singularity exploding according to classical laws would expand evenly in every direction, leading to a boring universe consisting of an evenly dispersed cloud of gas. So when you look at the night sky, you are seeing evidence for macroscopic randomness!
One last word: Heisenberg's uncertainty principle does include a constant "h", and it is very small. But is is not an upper limit that prevents uncertainty from leaking into the macroscopic world. In fact, the mathematical form of the Uncertainty principle:
delta_x . delta_p >= h_bar
is an inequality. It sets a lower limit on the amount of uncertainty but no upper limit.