I’m working on some short pop-quantum explainers for reasons that I’ll be a little cagey about. In casting around for a novel way to introduce Schrödinger’s cat states, I hit on something that probably works, but illustrates the problems inherent in being both a professional physicist and a pop-science writer.
The hook, as I mentioned on Twitter a little while back (early on a weekend morning, so nobody read it) is that you have Schrödinger’s cat to thank for the computer you’re reading this on. The core idea of the infamous cat paradox is that it’s both alive and dead at the same time, existing in a mix of both right up until the box is opened. This isn’t just a matter of it being in an unknown but definite state, either– it’s really in two states at once, and that seems weird and troubling.
However, while we can’t see quantum effects with something as large as a cat, we can readily see them with electrons. If you do a double-slit experiment with electrons– the results of which are on the screen behind me in the featured image above– you see electrons detected at single points tracing out a pattern characteristic of wave behavior. One way to understand this is that the electron exists in a superposition of two states at one: the state of having gone through the left-hand slit, and the state of having gone through the right-hand slit. The interference pattern requires both of these, showing that the electron isn’t just in a single unknown state, but a mix of both.
(Obligatory disclaimer here that I’m doing an injustice to a number of interpretations of quantum physics– Bohmian models in particular– that look at this a different way. I’m trying to get across a fairly mainstream version of the key ideas, though, and only have a few minutes to do it.)
This superposition business isn’t restricted to slits, though– it also works within and between atoms. If you bring two atoms close together, and look at the state of one of their electrons, you won’t find it in a state that corresponds to being on Atom A or Atom B, but a state that looks like a superposition of both at the same time. The electron is shared between the two, existing in both states at the same time (technically, it’s in one of two combinations: A + B or A – B, which have slightly different energies, but each give a 50/50 chance of finding the electron on either atom). This is what leads to chemical bonds within molecules (well, one way to understand it).
If you bring in more atoms, this process continues: three atoms, and each electron exists in one of three states that you can understand as a superposition of states associated with each of the atoms. Four, and the electrons are shared between all four. This goes all the way up to macroscopic numbers of electrons (“macroscopic” being a term of art in physics that means “more than you’d care to count”). If you look at a chunk of a solid, and think about one electron within that solid, the state of the electron is not a state bound to a particular atom, but an extended, smeared-out state within a band of same, shared between all of the atoms making up that material.
And this is the connection to technology. Those extended electron states, shared over all the atoms in a piece of material, determine the electrical properties of the material. And understanding how those states work allows us to control them, which in turn enables us to fabricate transistors by butting together bits of material with different properties in just the right way. And the ability to chain together huge numbers of transistors is what makes computers possible. Thus, the computer you’re using to read this is a consequence of Schrödinger’s cat: if electrons couldn’t exist in multiple states at once, the modern semiconductor industry would be impossible.
So, that’s my attempt at a new “hook” for talking about the quantum physics of superposition and cat states and the like. I can’t be 100% sure I didn’t subconsciously get this from somebody else, but as far as I know, I thought it up while walking the dog. I wanted something distinct from my prior discussion of it with Emmy:
and this is what I ended up with. Bringing in a bit of practical solid state physics was a bonus.
But as I hinted at the beginning, there’s a good deal of dithering about this. For one thing, calling the extended states of electron band structure superposition states isn’t quite right– you can write those states as some complicated combination of more tightly-bound individual atomic states, but for most purposes, that’s a lousy choice of a basis in which to express the state. The more typical way of looking at it treats those states as their own separate thing, and not a combination of localized atomic states.
On the other hand, though, while it’s not an ideal choice for calculational purposes, you certainly could choose to describe electrons in a material in the basis of localized states. And I don’t think it’s wrong to do so, at least not at the lying-to-children level where this explanation is working.
There’s also a more philosophical sort of argument in that what Schrödinger was worried about wasn’t really superposition per se but the probabilistic nature of the theory and the fuzziness about what constitutes a measurement for purposes of the quantum-to-classical transition. That’s why it’s a cat in the story, because a cat is unquestionably classical in most respects, but there’s no clear dividing line between microscopic systems that follow quantum rules and macroscopic ones that lok classical. And it’s true, I don’t really touch that, but then that’s part of an ongoing argument that’s really difficult to summarize. But I’m also not sure the subtleties matter, again at the current lying-to-children level.
And, you know, if you were to construct a power ranking of arrant nonsense written in pop-physics discussions of quantum mechanics, this would be really, really, really low on the list. At the same time, though, my training as a physicist and an academic makes me twitchy about these questions, even if the only people who will be bothered by them are other academic physicists. There’s also a question of internal consistency, given that I have previously engaged in nit-picking over fine technical points of another pop-physics writer’s discussions of weird quantum stuff.
So. Dither, dither, dither. In the end, I think I’ll probably run with this, because my qualms about it aren’t quite severe enough to force me to abandon it. But it has led to a lot of waffling, and now to a blog post with both a sketch of the argument and a description of the waffling, with a handy comment section in which people with really strong feelings about this argument can try to sway me into abandoning it…