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…

Comments

  1. #1 Ori Vandewalle
    June 4, 2014

    I’m not sure if this is related, but I’m hoping it is. During my intro E&M class, there was a subset of problems that always kind of bothered me. They were the, “If you put a point charge X meters away from a conducting sphere, what’s the electric field strength inside the sphere?” and other related questions.

    The answer always depended on the fact that electrons on the surface of the conducting sphere rearrange themselves into whatever pattern is required. This bothered me because it seemed as if either (a) the electrons were rearranging themselves instantaneously within a material, or (b) for the purposes of an intro E&M course, we were simply ignoring that motion because it wasn’t to the final state.

    If the electrons are rearranging themselves instantaneously, though, is that a consequence of the fact that, quantum mechanically speaking, they’re smeared out across the whole conducting sphere and not really localized?

  2. #2 MsPoodry
    June 4, 2014

    The electrons do not rearrange instantaneously. There will be some finite time that it takes for them to move, and physicists routinely ignore transition states like that to ponder the final state. Because the transitions are messy, and physicists don’t like anything more complicated than what can be shown on a cocktail napkin. (I was a physics major in undergrad and taught HS physics for 20 years, so take this with a certain amount of tongue in cheek, please!) ;-)

  3. #3 Eric Lund
    June 4, 2014

    This bothered me because it seemed as if either (a) the electrons were rearranging themselves instantaneously within a material, or (b) for the purposes of an intro E&M course, we were simply ignoring that motion because it wasn’t to the final state.

    The rearrangement is not instantaneous, but the relevant timescale is short compared to the timescales of interest in a freshman E&M course. Since the electrons will have reached the final state, or at least be asymptotically approaching it, by the time you make the measurement in question with the equipment typically available in an undergraduate physics lab, we can neglect the transition state.

    But in a scenario where we are rapidly switching between states, the transition does matter. You have to worry about the fact that your multi-GHz clock pulse is not a square wave, because even with a rise time of ~0.1 ns that is a substantial fraction of a clock cycle, whereas you didn’t have to worry about it when clock speeds were 33 MHz. So if you are talking about that kind of application, then you do need to worry about the transition state. Thus you are more likely to encounter this discussion in an electrical engineering class than a physics class: it may be purely a physics matter, but it’s mostly the EEs who need to worry about it.

  4. #4 Chad Orzel
    June 4, 2014

    The re-arrangement definitely isn’t instantaneous, as that would violate relativity, but it’s very fast– nanosecond sorts of time scales. This is true even for microscopic systems– there’s a modification of the interatomic van der Waals force at long range that comes from the finite speed of light, which means that the electrons within an atom can’t re-arrange themselves quickly enough to perfectly follow the fluctuating field from another nearby atom.

  5. #5 Chad Orzel
    June 4, 2014

    (“This” in my comment #4 is referring to the re-arrangement requiring a finite time, not the nanosecond time scale. The time scales involved in the retardation shifts for things like van der Waals forces are much, much shorter.)

  6. […] The Internet Exists Because of (Schrödinger’s) Cats […]

  7. #7 Ori Vandewalle
    June 4, 2014

    Gotcha. Thanks for the clarification, folks.

  8. #8 bob
    I seem to be in Oklahoma
    June 5, 2014

    Go ahead and run with it. You’re not lying i.e. trying to deceive them into believing something that is not true. Presentation should be tailored to the audience. You can talk about inter-fibrous friction fasteners and perhaps even start a debate over whether it is inter- or intra- or if fibrous is too limiting a factor, but if you’re talking to an audience of do-it-yourselfers just call it a nail and everything will be fine. As for inconsistency, you’ve been confronted with some new evidence. What does a scientist do when confronted with new evidence?

  9. #9 CCPhysicist
    June 6, 2014

    @1 and 7:

    It is often the case that freshman physics problems are poorly posed. That problem statement is missing the phrase “and wait until they system is in static equilibrium”. That context is often only found in a chapter title!

    Replies @2 through 4 explain why that is a reasonable assumption for a good conductor under quasi-static conditions, but no assumption is needed for a well-posed (as opposed to an “open”) question. And if you think for a bit about the difference between solving for static fields or working within a very restrictive class of time-varying problems and the messy world of antennas and the presence of other objects made of real conductors of varying quality. That nanosecond is short for many applications but long for a cell-phone signal!

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