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Luke_A_Somers comments on Ask an experimental physicist - Less Wrong
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The different cases of an observation are different components of the wavefunction (component in the vector sense, in a approximately-infinite dimensional space called Hilbert Space). Observation is the point where the different cases can never come back together and interfere. This normally happens because two components differ in ways that are so widespread that only a thermodynamically small (effectively 0) component of each of them will resolve and contribute to interference against the other.
This process is called Decoherence.
What? I'm looking for a specific experimental condition where collapse happens and where it doesn't. E.g. suppose an electron (or rather the waveform that represents it) is impinging on a sheet of some fluorescent material. I'm guessing it hasn't collapsed yet, right? Then the waveform interacts with the sheet and causes a specific particle of the sheet it to eject a photon. Is that collapse? Or does collapse not happen until some "observer" comes along? Or is collapse actually more subtle and can be partial?
The waveform interacts with the sheet such that a small part of many many different parts of the sheet interact, and only exactly one in each case. Since it's fluorescent, and not simply reflective, the time scale of the rerelease is finely dependent on local details, and going to wash out any reasonable interference pattern anyway.
This means that it is thermodynamically unlikely for these different components to 'come back together' so they could interfere. That's also when it loses its long-range correlations, which is the mathematical criterion for decoherence.
Due to the baggage, I personally avoid the term 'collapse', but if you're going to use it, then it's attached to the process of decoherence. Decoherence can be gradual, while 'collapse' sounds abrupt.
A partially decoherent system would be one where you have a coherent signal passing repeatedly around a mirror track. Each lap, a little bit of the signal gets mixed due to imperfections in the mirrors. The beam becomes decreasingly coherent.
So, where in there is a collapse? Eh. It would be misleading to phrase the answer that way.
Wikipedia seems to indicate that the answer is that we don't know when or if collapse happens. This is interesting, because when I was taught quantum mechanics, the notion seemed to be "of course it happens.... when we observe it... now back to Hilbert spaces" which rather soured me on the enterprise. I don't mind Hilbert spaces by the way, I just want to know how they relate to experiment. So is wikipedia right?
"It doesn't" is a decidedly possible interpretation of the data. It's called the Many Worlds Interpretation, and is the interpretation advocated by the Less Wrong sequence on QM. Have you read that sequence?
No. I've been thrown off by the terminology "many worlds" and nonsense I've heard elsewhere (see below). Hope to give the sequence a fair shot soon.