Q:

Defining Measurement in Quantum Mechanics

I should begin by saying that I am a total newbie when it comes to Quantum Mechanics. Therefore my question might sound metaphysical to people who know their stuff. So please forgive.
What I am trying to understand is the basic system of an electron in a box. Suppose I place a detector at a fixed point inside and try to detect the presence of an electron. There are two possibilities:
(1) The detector detects an electron. The Copenhagen interpretation explains this by saying that the act of measurement forced the wave function to collapse at that point.
(2) The detector did not detect anything. Would this "not detecting an electron" qualify as a true measurement in the Copenhagen sense? I mean, if this qualified as a measurement would it change the wave function?
What led me to this confusion is the explanation in Griffiths' Quantum Mechanics. He states that the same experiment when done soon after possibility (1) gives us the same result i.e, observe the electron (which does not confuse me.) But what happens when you do the experiment soon after possibility (2)? Would I still not observe the electron?
What if I extend this to the two-slit experiment and place the detector at only one slit. If I didn't observe the electron, it means that it passed through the other hole, which doesn't lead to the pattern. So again, does this make "not detecting the electron" a true observation which collapses the wave function?

A:

Yes, not detecting an electron is also a fully-qualified measurement, provided you make sure the measurement would have detected the electron, had it been there. That condition is usually not given in real quantum mechanics experiments. Keep in mind that "measuring an electron" actually means you let something interact with it; it's not possible to register an electron going through a slit in the way a hidden camera can register a car passing a bridge. Pretty much the only way to make sure an electron will be detected if it's there is to use a bulky solid-state detector, which will completely absorb the electron. If you have a box with an electron and such a detector and have not measured the electron yet, you can be sure that it is "still outside of the detector" and you will not measure it if you do another measurement very quickly after the first one, either (you need to be really quick though: the state "outside of the detector" is not an energy eigenstate and therefore unstable in time). If you have measured the electron, you can be sure it's not out in the box anymore, simply because it's stuck in the detector!

