Question reguarding superpostion

[livethere]

This post will be using assumptions that are within the Copenhagen interpretation.

If I understand decoherence, the superposition of the wave function will crash upon interacting with a microscopic system.
However what really constitutes as a superposition interacting with a system? I thought that superpositions were spread out everywhere, and so shouldn't the wave functions be constantly collapsing?

 

[bhobba]

If I understand decoherence, the superposition of the wave function will crash upon interacting with a microscopic system.

It gets converted to a mixed state.

However what really constitutes as a superposition interacting with a system? I thought that superpositions were spread out everywhere, and so shouldn't the wave functions be constantly collapsing?

What happens is the state, when expanded in terms of position eigenstates (these are simply states of definite position), is called a wave-function. In that form it is a superposition of position. But it needs to be stressed its in a superposition of all sorts of other things as well. The reason its usually done that way is so the usual form Schroedinger's Equation can be used - that requires states to be in the form of wave-functions.

Quantum objects interact via what's called their Hamiltonian. Mostly that Hamiltonian has radial symmetry - meaning its the same regardless of how you orientate you coordinate system. It can be shown that leads to the position basis being singled out during that interaction (that's what decoherence is - an interaction) and the state after interaction is in a mixed state of position eigenstates.

Thanks
Bill