The two-slit experiment.
1. Single photon still produces interference pattern!
2. Ask which slit photon passes - pattern disappears
This kind of explanation is common, and it has always bothered me, because it's the wrong sort of mental model.
The interference pattern doesn't disappear "because we're looking", or "because we're asking", or "because we thought about finding the answer".
It disappears because in order to check which slit a photon passed through, we need some way of measuring that. To do so, we need some way to "see" the photon; to do that, we need to shine photons on it; and it is that which destroys the interference pattern.
The reason quantum mechanics is "weird" is because it (currently) is fundamentally impossible to invent a device to answer the question "which slit did the photon pass through?" without destroying the interference pattern.
However, that doesn't mean it disappears "because we're asking". The interference pattern is destroyed because our device, no matter what it is, will always interfere with the experiment (shining photon A at a photon B == "well obviously that would change the behavior of photon B"). Nothing more, nothing less.
A better example of "weird" than the two slit experiment is the the quantum bomb detector, which basically answers the question "if I sent a photon through point X, would it be absorbed?" without actually sending a photon (or anything else measurable) through point X.
There's no attempt with this to determine where photons are going, so you don't have the pesky issues of observation attempts messing with your photons.
Two photons interfering is just two photons interfering; that's not measurement. More precisely, the wavelike photon, which is the "cause" of the interference pattern, hits a component of a photodetector, which generates a voltage and sends an electron current through a cable, that feeds into a computer which is running a program that displays photon counts. On the other hand, if you isolate parts of the setup, for example if the interference pattern of the photon hits just a very thin slice of photosensitive material that would otherwise be part of the photodetector, I'm sure you may very well observe an electron interference pattern, for example (and a non-rigorous one, at that).
In "real life" (meaning in the laboratory), measurement isn't some discrete process that can be isolated at a specific point in an experimental setup. Otherwise, there would be much better explanations for measurement in undergraduate physics curriculums.
In fact, even in top physics curriculums, the problem of measurement is barely treated at all, since the interpretation of measurement in quantum mechanics is a "philosophical" problem that apparently has no place in real physics, which instead must concern itself with mathematics that is phenomenologically accurate.
I'm about as far from an expert as you can get, so hopefully someone more knowledgeable can shed some light on this:
"A classical computer seems to need time exponential in n to predict precisely the behavior of a general quantum mechanical system of n particles. (Yet nature manages to do it in real time.)"
How could we know this from inside that system? For all we know it could take a billion [whatever unit is used to measure time outside of our dimension] to calculate each step, and it would still look fluid to us.
The usual time measure of computational complexity is in units of computation, not in terms of the wall clock time it takes to for a calculation to run.
The interference pattern doesn't disappear "because we're looking", or "because we're asking", or "because we thought about finding the answer".
It disappears because in order to check which slit a photon passed through, we need some way of measuring that. To do so, we need some way to "see" the photon; to do that, we need to shine photons on it; and it is that which destroys the interference pattern.
The reason quantum mechanics is "weird" is because it (currently) is fundamentally impossible to invent a device to answer the question "which slit did the photon pass through?" without destroying the interference pattern.
However, that doesn't mean it disappears "because we're asking". The interference pattern is destroyed because our device, no matter what it is, will always interfere with the experiment (shining photon A at a photon B == "well obviously that would change the behavior of photon B"). Nothing more, nothing less.