How is the act of observation defined in quantum mechanics?

[Yoni]

Can anyone explain to me what how is the act of observation defined in quantum mechanics?
It is commonly said that the double slit experiment shows that if one simply observes the state of the electron as it passes through the slits, it effects the results.
Many forms of observations are possible, from measurements of small currents induced by the passing of the charged electron, though measurements of the transferred momentum in the interaction with the slit.
But are all these kinds of measurements and others considered observations?
Would simply plugging off the machine which makes the measurements, cancel the observation? Would a burning of the output also eliminate it?
So I guess my question is: What makes an observation an observation?

 

[Fra]

The basic idea is that an observation or a measurement is a kind of communication between observer and the observed where each party responds to the communication.

So I'd associate observation ~ communication ~ interaction.

Communication/observation/interactions takes place between observers/systems.

In QM the idea is to describe measurements as projections, defined by the measurement operators, which corresponds to questions. Each question, and measurement operator is assumed to have a well defined spectrum of possible answers. And this set is assumed to exists, and before measurement the questioner only know the spectrum of possible answers and their respective probability. This probability is dynamically updated. this is why the set of possible answers to a given observation given certain premises, changes if you make other observations in between.

So when you formualte a question - a given experimental setup. Then you have asked a question given X. If you then modify this apparatous by inserting stuff then the premise X is different - and so will the spectrum of possible answers be.

/Fredrik

 

[Fredrik]

Can anyone explain to me what how is the act of observation defined in quantum mechanics?
It is commonly said that the double slit experiment shows that if one simply observes the state of the electron as it passes through the slits, it effects the results.
Many forms of observations are possible, from measurements of small currents induced by the passing of the charged electron, though measurements of the transferred momentum in the interaction with the slit.
But are all these kinds of measurements and others considered observations?
Would simply plugging off the machine which makes the measurements, cancel the observation? Would a burning of the output also eliminate it?
So I guess my question is: What makes an observation an observation?

No one has a complete answer to that question, but these are a few different ways to think of an "observation":

1. It's the action of a projection operator $|a\rangle\langle a|$, which projects the state onto an eigenstate $|a\rangle$ of an observable A. (Of course, we can't know which eigenstate that will be in advance).

2. It's an interaction with another physical system which "magnifies" the effect to the classical level.

3. It's an interaction with another physical system which selects a preferred basis of the Hilbert space of possible states of the combined system and makes the off-diagonal components of the density matrix in that basis rapidly go to zero.

Burning the output will definitely not cancel the observation. Unplugging the measuring device might, e.g. if it's a photocell used to detect movement, but it usually won't because the interaction that "collapses" the wave function will happen anyway.

One fact that you should find interesting is that if you put polarization filters behind the slits in the double-slit experiment (e.g. one that only let's light through with a left circular polarization and one that only let's light through with a right circular polarization), this is enough to destroy the interference pattern. The polarization filters have "tagged" the photons with "which-way information". The really cool part is that if you insert a linear polarization filter in front of the screen, it restores the interference pattern. So in this case, it is possible to "cancel" an observation.

 

[Yoni]

Thanks Fredrik,
After reading you answer I have 2 other questions:
1) How fast do the off-diagonal components of the density matrix rapidly go to zero? How fast does a quantum particle collapse into one of the possible states? And how long would it stay in this state? Does it matter how long after making a first observation I make the next one?
2) You previously said that measuring a quantum particle is like asking a question that has several possible answers. In the double slit experiment it is possible to ask about a single electron in which slit it passed, making it collapse into one state (either of the slits). But is it possible to ask the fallowing question: "Of the next three electrons how many passed through the right slit?". Say the answer is 2. This still limits your knowledge, you still don't know which of the three passed where, just that 2 went right and 1 went left. Marking each electron on the screen you won't know for each electrons where did it pass... With this kind of question (is actually possible to ask?), what kind of pattern would we get on the screen, an interference pattern or a regular curve of intensity? Maybe something in between?
So my question is, can you make a measurement that doesn't make the particle completely collapse into a single state but partially collapse dismissing just some of the possible states?

 

[Fra]

There is two Fredrik in this thread. My handle is Fra, but my name is Fredrik. The other Fredrik is has the handle Fredrik :)

This is an interesting question, and I guess you can see this in different ways. Your asking about decoherence times. http://en.wikipedia.org/wiki/Quantum_decoherence.

But I think one can see this in different ways. The way I personally see it is that you are
asking when is the answer confident enough to collapse the question? Here I would like to think that questions and answers are relative, and the questions and answers might also be described a relative confidence. And also time is clearly relative. Decoherence time by what clock?

One can conceptually imagine that you have very high confidence in the formulation of question, and you can try to rate the confidence in a tentative answer. So I imagine here that questions and answer can be assigned inertia. Because, you must be able to distinguish the answer from fluctuations. This means that one can imagine that the answer is delivered slowly, because the "answer" is really a process of increasing certainty. But I don't have a full understanding of this myself. I think there are both internal and external processes. But it's equally possible to imagine the cases where the question is constructed so that you can not distinguish anything between hit or not hit. So it could be that what appears like a collapse to one observer, is smooth to another. There isn't necessarily a contradiction

IMHO a nice think about questions & answers is that it is easy to find conceptual intuition. Much more accurate that those you typically get from visual mechanical analogies. But I guess first you have for yourself see the analogy between measurements and questions.

So in this case it's easy to imagine that a less confident answer will deform your question, but not collapse it entirely.

/Fredrik