Per quantum physics, the position of a particle is given by a probability function. When such particles make up a higher order system of molecules and crystals, is it reasonable to say that the existence of such a system is also non-deterministic because of the underlying non-deterministic nature of its components? In other words, is there a definite boundary between non-deterministic and classical behavior? Can someone please help me understand?

Strictly speaking there is no level for determinacy.: Effectively speaking the Schrodinger's cat scenario holds. Which is, of course, ridiculous on the face of it. However there appears to be no limit set upon it... A 1kg crystal of halite is an indeterminant system but clearly it doesn't quantum phase into the next room.

There are a couple of ideas bouncing around about how to take QM to a Classical limit. A good start on this is

**Ehrenfest's theorem**. The main idea here is if we have a property of an electron, say its velocity, we can "average out" the result and put it into a Classical Physics equation, such as <p> = m <v>, where <p> is the time averaged momentum of the electron. (You can derive a large number of Classical equations like this. However you need to make sure all the \(\displaystyle \hbar\)'s drop out.)

Note that this pretty much only works with the Schrodinger Equation. I've never seen this applied to relativistic wave equations.

There is a more advanced method to get beyond this, and I don't recall the name of the process (sorry!), where you start with an expression for a "coherent" state of the particle. The details are horrendous but doable if you've got a good computer.

-Dan