Fundamental notions of QM have to do with observation, a major example being The Uncertainty Principle.
What is the technical definition of an observation/measurement?
If I look at a QM system, it will collapse. But how is that any different from a bunch of matter "looking" at the same system?
Can the system tell the difference between a person's eyes and the bunch of matter?
If not, how can the system remain QM?
Am I on the right track?
Answer
An observation is an act by which one finds some information – the value of a physical observable (quantity). Observables are associated with linear Hermitian operators.
The previous sentences tautologically imply that an observation is what "collapses" the wave function. The "collapse" of the wave function isn't a material process in any classical sense much like the wave function itself is neither a quantum observable nor a classical wave; the wave function is the quantum generalization of a probabilistic distribution and its "collapse" is a change of our knowledge – probabilistic distribution for various options – and the first sentence exactly says that the observation is what makes our knowledge more complete or sharper.
(That's also why the collapse may proceed faster than light without violating any rules of relativity; what's collapsing is a gedanken object, a probabilistic distribution, living in someone's mind, not a material object, so it may change instantaneously.)
Now, you may want to ask how one determines whether a physical process found some information about the value of an observable. My treatment suggests that whether the observation has occurred is a "subjective" question. It suggests it because this is exactly how Nature works. There are conditions for conceivable "consistent histories" which constrain what questions about "observations" one may be asking but they don't "force" the observer, whoever or whatever it is, to ask such questions.
That's why one isn't "forced" to "collapse" the wave function at any point. For example, a cat in the box may think that it observes something else. But an external observer hasn't observed the cat yet, so he may continue to describe it as a linear superposition of macroscopically distinct states. In fact, he is recommended to do so as long as possible because the macroscopically distinct states still have a chance to "recohere" and "interfere" and change the predictions. A premature "collapse" is always a source of mistakes. According to the cat, some observation has already taken place but according to the more careful external observer, it has not. It's an example of a situation showing that the "collapse" is a subjective process – it depends on the subject.
Because of the consistency condition, one may effectively observe only quantities that have "decohered" and imprinted the information about themselves into many degrees of freedom of the environment. But one is never "forced" to admit that there has been a collapse. If you are trying to find a mechanism or exact rule about the moments when a collapse occurs, you won't find anything because there isn't any objective rule or any objective collapse, for that matter. Whether a collapse occurred is always a subjective matter because what's collapsing is subjective, too: it's the wave function that encodes the observer's knowledge about the physical system. The wave function is a quantum, complex-number-powered generalization of probabilistic distributions in classical physics – and both of them encode the probabilistic knowledge of an observer. There are no gears and wheels inside the wave function; the probabilistic subjective knowledge is the fundamental information that the laws of Nature – quantum mechanical laws – deal with.
In a few days, I will write a blog entry about the fundamentally subjective nature of the observation in QM:
http://motls.blogspot.com/2012/11/why-subjective-quantum-mechanics-allows.html?m=1
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