Question: How does quantum mechanics contradict common sense?
David Albert: Here's the deal: quantum mechanics allows physical systems -- and the easiest systems in which to observe phenomena like this are very tiny systems like subatomic particles, electrons or neutrons or protons -- quantum mechanics apparently allows for the existence of physical conditions of material objects like electrons in which questions about where the electron is located in space seem to fail to make sense. Let me back up a little bit and explain this a little more slowly. There are experiments we can do where an electron passes through a certain apparatus, is fed into one end of an apparatus, comes out the other side of the apparatus. And the apparatus has several routes inside of it which the electron could potentially have taken from the input to the output. And there are experiments we can do with pieces of apparatus like this which, taken together, make a compelling case that although the electron went from here to there, it didn't go by route A, it also didn't go by route B, and it didn't go in any intelligible sense by both routes; that is, it didn't split in half, with one half taking one route and one half taking the other route; and it also didn't take neither route, okay?
And what's puzzling about that is that that would seem to be all the logical possibilities that there are. These experiments, you know, are now very routine experiments to do in physics laboratories. We've been good at doing experiments like this for something on the order of 70 years now. We're very good at doing them now. The results are very, very compelling. And after enormous soul-searching and puzzlement and confusion and so on and so forth, the sort of standard consensus understanding that evolved in physics of situations like this is that electrons could apparently be in situations where asking a question of the form "which route did the electron take?" was something like asking a question of the form "what is the marital status of the number five?" Or "what are the political affiliations of this tuna sandwich?" or something like that. These are questions that philosophers often refer to as category mistakes, okay? The very raising of a question about the political affiliations of a tuna sandwich or the marital status of the number five indicates that there's something basic that you're misunderstanding of what it is that you're asking a question about.
And the strikingly strange thing about quantum mechanics -- and indeed it seems to me a case could be made that this is the strangest and most unsettling result to come out of the natural sciences since the scientific revolution of the Renaissance -- is that even things like particles can be in conditions where it simply radically fails to make sense even to ask where the thing is located in space. What's particularly strange about this is that of course there are other circumstances where it does make sense to ask those questions about where it's located in space. The electron determinately goes into the box over here and comes out over there, okay? But we can give good arguments from these experiments that while it's inside, it's not merely that we don't know where it is, it's something much more radical and much more unsettling than that: that the very act of raising a question about where it is represents some kind of misunderstanding of what mode of being that electron is participating in while it's going through this device.
David Albert: Anyway, here's a further fact about electrons: if we go -- if we do one of these experiments that I just described and stop it in the middle, rip the box open, okay, and go look for the electron, as a matter of fact we always find it in some determinate position, okay? We have equations, we have basic laws of motion: the Schrödinger equation in the case of nonrelativistic quantum mechanics; in the case of relativistic quantum mechanics the fundamental equations are the Dirac equation or the Klein-Gordon equation. Anyway, we have these fundamental laws of motion for things like electrons; indeed, for all material things. And these laws are very successful at predicting when these strange -- let me back up and say these conditions in which it fails to make sense to ask whether the electron is here and here -- in a long, distinguished tradition of facing a mystery that one doesn't understand by at least making up a name for it, a name has been made up for this condition. People speak of electrons in such circumstances as being in a superposition of going along route A and going along route B. And although it's very difficult for us to get our heads around what this word means, we are very adept at treating these situations mathematically. We have very reliable equations that tell us when and under what circumstances these superpositions are going to arise and when they're going to go away, and blah blah blah blah blah. Good.
Further empirical fact: when we rip open these boxes and look for these electrons, we always find them in one position or another, okay? So that somehow the act of looking at them makes these superpositions go away, okay? Good. On the other hand, we could perform the following exercise: take these fundamental equations that we have discovered and which we have very good reason to believe are reliable at predicting when superpositions are going to arise and when they're going to go away and so on and so forth; use those equations to predict what ought to occur when we rip the box open and look inside. That may sound like a very difficult calculation to do. It involves this macroscopic human being and his brain and so on and so forth. Actually, there's a mathematical trick for getting this calculation done, as miraculous as that sounds.
And it's very easy to show that what these equations predict ought to occur when we rip this box open is that we ourselves go into a superposition of seeing the electron on route A and seeing the electron on route B, okay? That is, that we ourselves go into some condition in which not only does it fail to make sense to ask where the electron is; it fails to make sense even to ask about our beliefs about where the electron is, okay? Or it fails to make sense to ask whether we're in the brain state corresponding to believing that the electron is on route A or in the brain state corresponding to believing that the electron is on route B. Good. God knows what the hell that would feel like, okay? But the usual way of setting up this measurement problem is merely to observe that whatever it is that would feel like, that's not what happens to us when we rip open these boxes. When we rip open these boxes, there is always a perfectly determinate matter of fact about where we take the electron to be. Sometimes we see it on route A; sometimes we see it on route B; it's never the case that anything else is going on. It's never the case that it looks fuzzy, or we get nauseous, or we become disoriented, or in any sense that one can put one's finger on there fails to be a fact about where we see the electron. Good.
So we have a flat-out contradiction. And this is the more explicit version of the way this story about the glass breaks down. We have a flat-out contradiction between, on the one hand, the predictions of the fundamental quantum mechanical equations of motion about what ought to happen when we rip open these boxes, and our everyday introspective experience of what's going on when we rip open these boxes, which is that in each of those occasions we either see an electron there, or we see an electron there. These two claims flatly contradict one another. Of course, you know, the empirical claim is the one that's true; that's the one that we see from our observations. There's something wrong with these equations.
On the other hand, we also know that there's an enormous amount that's right about these equations. These equations are where, you know, indescribably vast swathes of 20th century science and technology come from. These equations get an enormous amount right. On the other hand, it couldn't be more obvious from our everyday experience of the world and of ourselves that something is wrong with them. There's a problem about how to put these two facts together. There's a problem more specifically about how to modify the theory in such a way that this contradiction goes away without ruining the rest of the good predictions of the theory. This problem, once again, is called the measurement problem.