- #36
bluecap
- 396
- 13
PeterDonis said:Unfortunately I'm still not sure you are. See below.
I did not say they were. In principle, one can define observables for multi-particle systems such that the multi-particle system will be in one particular eigenstate of that observable when the observable is measured. However, in practice, it is often very difficult to find such observables that can actually be measured, and it gets more and more difficult the more particles a multi-particle system has. For a macroscopic object it is practically impossible. Which means that most of the time, when we talk about observables for multi-particle systems, we are talking about observables like the center of mass position observable, that don't put the system into a single particular eigenstate when they are measured. There might not even be any definable eigenstates for such an observable at all.
This leads to a question: why are you so interested in eigenstates? It seems to me that you would be better served by taking a step back and looking at the way QM actually models multi-particle systems mathematically. Your current understanding seems to be based on misconceptions.
I'm interested in eigenstates because I want to know what observables were chosen in Decoherence Einselection (Environment Induced Superselection). Zurek wrote:
"Interactions that
depend on a certain observable correlate it with the environment,
so its eigenstates are singled out, and phase
relations between such pointer states are lost".
In an apple, what eigenstates were singled out by the environment in Decoherence, Einselection which cause "phase relations between such pointer states are lost"??