# Subatomic particles to a solid object

#### jojimt

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?

#### topsquark

Forum Staff
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

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