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Superpositions

David Albert

There are no circumstances in which the number five has a marital status, okay? There's no circumstances in which this table has a political affiliation, okay? With electrons, the case, if you want to try to tell the story this way, the case seems to be different. Bohr is adamant because of arguments more or less along the lines of the one I've given you, that, um, any attempt to tell yourself, to, to offer yourself a picture, to tell yourself an intelligible story about what, what's going on in between the time you fed the electron in here and the time you measured its color out there. Any attempt to do anything like that is stupid, okay?

And is gonna fail and is gonna collapse into paradox and contradiction. And this is a profound moment in the history of science, um, in the history of the aspirations of the scientific activity. There's a, a-- let me just mention, there's a lot one could say about this, and I don't think a good history of this has been written yet. But, but this is going on at the same time as various other intellectual movements are going on. The rise of modernism in literature and in painting, uh, so on and so forth.

All kinds of-- you know, there's some sense in which in the zeitgeist that was around then, the original aspirations of the scientific activity were, were sort of akin to the aspirations of, say, the nineteenth century naturalistic novel, um, um, or something like that. That there was some possibility of just straightforwardly saying what happened, okay? Saying who did what. Um, and these were thought to have collapsed under pressure from all kinds of angles, from the development of psychoanalysis, all kinds of-- or there was supposed to be a crisis of representation that was affecting things like the novel, that was affecting things like painting, uh, so on and so forth. And it seems to me that at least part of what must have been going on with Bohr was, was some kind of idea like, "You think you have a crisis of representation?" You know?

"You got trouble-- you, you have trouble getting to the bottom of people's motivations of, of this. I got trouble with rocks here." Okay? Um, um, it's coming up at, at a much more elementary level in a much more shocking and radical way. There were certainly a lot of people in literary modernism, especially people like people in the Bloomsbur- Bloomsbury Circle, like Virginia Woolf, who were very aware of what was going on in physics and who were clearly trying to reflect it, trying to find connections between what was going on in physics and what they took to be a crisis of representation in the sort of hopes espoused by, by something like the nineteenth-century European novel. This wasn't completely independent of a larger historical zeitgeist that was around at the time.

And, um, um, and in that context, this sounded really cool. There were smart people who said, "Well, here's another attitude you could take." It's not that-- you know, once again, go back to the fact that we seem to have run out of logical possibilities here. It was said-- this was much later than Bohr. This was, uh, around the nineteen sixties. Um, um, people said, "Look, another attitude you could take is no, no, no.

There's a story to tell about how the electron got from there to there, but the story violates logic." Okay? The story represents the first case in history of an empirical scientific discovery about the laws of logic. There were people at the time, people like John von-- the mathematician von Neumann, um, or, uh, Schrödinger, uh, the discoverer of the Schrödinger equation, so on and so forth, who were, um, uh, not as comfortable as Bohr apparently was with just giving up the possibility of telling any story at all about what's going on between there and there. Um, and thought-- and what I'm a-- the way I'm about to describe this story isn't explicitly what any of them said, but sort of how things looked after the dust settled, um, um, after a while. The idea was, well, wait a minute.

There's a way to get out of this straightforward logical contradiction by saying something like this. Maybe In the period between the initial color measurement and the final color measurement, when the electron is inside the apparatus, the electron is in some kind of a situation, a situation which has never been dreamt of before for something like a material particle, but which is not obviously a logical contradiction in the way we were suggesting it might be. Maybe there are modes of being available to things like electrons. Maybe there are situations that electrons can be in where, for some reason, a question of the form, is it on the soft path or is it on the hard path, doesn't make sense, okay? In the same way that, for example, a question of the form, is the number five married or single, doesn't make sense, okay?

Or a question of the form, does Catholicism weigh more or less than five grams, okay? Or a question of the form, is this table a Republican or a Democrat, okay? These are kinds of questions that philosophers are very familiar with. They're referred to as category mistakes, okay? If you ask, if somebody says, by the way, is the number five married?

You say no. And the guy says, I see, so number five is a bachelor. You say no, neither of those is the case. And there's no logical contradiction there, okay? The number five is not the kind of thing that has a marital status, okay?

I'm not making a contradiction as if I were saying the number five is both married and unmarried. It's neither. The category doesn't apply to the number five, okay? And it's not the case that if this table isn't a Democrat, it must be a Republican or an independent, okay? That's not the case, okay?

These questions of political affiliation just don't apply to tables. Now, if we take that approach here, it's admittedly a much stranger situation. Because there are circumstances, like before we feed the electron in here, where there seems to be, where it seems to make perfect sense to ask where the electron is. And the question has an answer. The electron is right here, okay?

And when the question, when the electron comes out the other side of the apparatus, it again makes perfectly good sense to ask where the electron is. The question has an answer. The electron is here, okay? But the suggestion here is that when this white electron passes through a hardness box, the hardness box puts it into some condition, okay? In which asking about whether it's taking the hard path or whether it's taking the soft path is like asking about the marital status of the number five.

And of course, there's a long and venerable tradition in all areas of human speculation that if you don't understand something, at least you can make up a name for it. So people say in circumstances like this, when they're trying to tell the story this way, that this white electron, after it emerges from the hardness box, is in a superposition of traveling along the soft path and traveling along the hard path. And what that means is the following set of things. One, if you look for it anywhere other than on the soft path or the hard path, you won't find it, okay? But there is no fact of the matter about whether it's on the soft path or it's on the hard path, okay?

Asking about whether it's on the soft path or on the hard path is like asking about the marital status of the number five.