That bit in my last post, about Maxwell's coup de grâce to Laplace's Demon, was only a prelude to the quantum stuff below.
Laplace's hypothesis was based on principles of precision in nature. In keeping with classical mechanics, the overriding assumption was that it is possible to know simultaneously the position and momentum of a particle exactly. This was critical to the Demon to enable computation of the data. What drove LD out of a job though was Heisenberg's uncertainty principle.
In quantum mechanics, the position and momentum of particles no longer have precise values. The best assertion one can make about a particle is that there's a probability it exists at a particular location, or has a particular momentum. Heck, at the particle level, this becomes obvious when we consider that an effort to observe a particle will involve shining light (a stream of photons) on it. These photons themselves are particles (yes, yes, they're waves too) that will disrupt the peace of the particle we're trying to observe.
It's at this point in the Q.physics-101 lecture that even the jocks at the back of the class wake up and listen - A cat is placed in a sealed box along with a flask containing cyanide gas. In addition, a tiny amount of a radioactive substance is placed in the box, alongside a Geiger counter. The amount of radioactive substance is small enough that in an hour, there's as much chance of it decaying as not. If the Geiger counter detects radiation, it triggers a mechanism that releases the cyanide gas.
In the real world, if we were to look in the box after an hour, the cat would either be alive or dead. Binary. In the quantum world though, the cat is simultaneously alive and dead, in a quantum superposition of these two states. It's at this point that the Laplace Demon hypothesis falls off the rails. The demon, at the particle level, cannot know for sure positions and momenta. An error in approximation at the particle level will blow up when extrapolated to the level of objects at the human scale.
The short of it is that quantum physics throws a wrench into the Newtonian/Laplace Demon machine and messes up the impetus that the determinism juggernaut had built up.
The long of it though is where it's most interesting: Heisenberg's postulate is unproven when we consider that the precise observation of a particle isn't possible because of human limitation. It is our inability to observe or measure a particle's characteristics without disturbing it that lead us to conclude that the particle's position is hazy within a probability cloud.
What do we know about the particle at a moment when we aren't observing it? Could it be, is it possible that the particle is at point x, y, z exactly? What if the demon knows this particle and its every last characteristic? The future won't be much of a shock to LD then.