batmanandjoker said:
What is the diffrence between pure and mixed states in lamen terms I reasearched it but I am not exactly sure I understood the concept and how it applies to how the enviorment (decoherance) collapses particles.
Also if someone could explain the density matrix and how it applies to all this it would be much appreciated.
If a system is in a pure state, and you know what the pure state is, then your knowledge of the system is complete, and all uncertainty is quantum. If we take a state to apply to an ensemble, this means that every member of the ensemble has been identically prepared and is in the same state.
A proper mixed state means that you do not know exactly what the quantum state is, but only what the state is with some probability, so uncertainty is due to intrinsic quantum uncertainty, as well as your ignorance of the state. In an ensemble, this means that not all members of the ensemble have been identically prepared.
An improper mixed state comes about when the entire system is in a pure state, but you restrict yourself to observing a subsystem. The improper mixed state describes the behaviour of the subsystem.
The density matrix is a way of writing the quantum state so that pure states, proper and improper mixed states can be described in the same mathematical language.
As I understand, decoherence does not collapse the state. In order to have a definite outcome, one must postulate collapse (or use Bohmian or many-worlds formulations). I believe this is also what is said in bhobba's link to Bas Hensen's essay
http://philsci-archive.pitt.edu/5439/1/Decoherence_Essay_arXiv_version.pdf concerning the "Ignorance interpretation" where one postulates "The mixed states we find by taking the partial trace over the environment can be interpreted as a proper mixture. Note that this is essentially a collapse postulate." (p39). For decoherence to give definite outcomes (see Table 3.1 on p39, where "D. Interactions with the environment explain the apparent definiteness of measurement outcomes." needs all 4 assumptions, including assumption 4 that an improper mixture can be interpreted as a proper mixture.
Decoherence does not explain collapse. Decoherence solves the "preferred basis" or "pointer basis" problem. In particular, decoherence says that position is a usually a very good pointer basis, because interactions are usually local in space. From Hensen's p17: "Summarising, the point is that the basis with respect to which decoherence takes place - i.e. superpositions of eigenstates of this basis decohere into a improper mixture of these eigenstates - is determined by the form of the system/apparatusenvironment interaction Hamiltonian. Therefore the'classical' observables, the ones that we perceive as classical, are exactly those determined by this basis. One of the consequences of this is that any interaction described by a potential V(r), is diagonal in position, and therefore position is always the pointer observable measured by the interaction. many interactions in nature are described by such a potential V (R)." See also sections 2.4 and 3.4 of Bas Hensen's essay.
