Friday, October 15, 2010

I try my hand at explaining part of the double-slit experiment

Having read quite a bit of Elsevier's quantum physics series (and experiencing the accompanying existential crisis), I feel like I have a way of explaining some of the more baffling aspects of the double-slit experiment in a way that ought to make sense to someone with just a minimal amount of background in physics and math.

Wikipedia has a decent resource on the double-slit experiment, so if you are unfamiliar with it and want detailed information, please go there. I want to focus on two particular aspects of it: the "spooky" effect of a single electron interfering with itself, and the fact that observing which slit the electron passes through eliminates the effect. So I will describe in my own words just enough of the experiment to cover those aspects. If you are already familiar with that, you can skip below the fold.

Feynman has famously said that all of quantum mechanics can be deduced from the double-slit experiment, but it is usually presented to students as an illustration of wave-particle duality -- that fundamental particles "behave like particles some of the time, behave like waves other times." (Really it would be more accurate to say that the macroscopic approximations of "particle" and "wave" both bear some resemblance to the true reality of the quantum field, but I digress...) The basic setup of the double-slit experiment is that you shoot a beam of electrons or photons or whatever through a screen with two very narrow slits cut in it, and project that onto another screen.

With both slits open, the interference pattern you see on the second screen is what you would expect to see if you sent a wave at the screen. There are ways of modifying the setup to also make it seem like it is particles (hence the "duality" notion) but I'm going to skip ahead some hundred-plus years and mention a more recent experiment that ought to really blow your mind: This interference pattern shows up even if you only fire one electron at a time. You see one electron hitting the second screen at one place a time, so that seems like it's a particle. But if you keep firing them, the place where these individual particles end up will eventually form a wave-like interference pattern -- as if each electron was interfering with itself somehow.

The other mind-blowing part of the experiment I want to talk about is what happens if you put a detector at one of the slits, so that it still lets the electron pass through, but now you know for each electron which slit it passed through. Suddenly, the interference pattern disappears! Why would observing it have any effect? Spooky, right?

And now, I will try to present what I think is a fairly easy to grasp explanation of how this is happening, by talking about the concepts of configuration space and decoherence. In order to make the explanation very simple, I am going to say a few things that I know are flat-out wrong, but that I think are "close enough" to the gist of things so as to illustrate the idea -- so be kind. This is not meant to instruct in quantum physics (like I'd be even remotely qualified!) but rather to show how something "kind of like" quantum physics could demystify these apparently bizarre effects.

Okay, so first the idea of configuration space. Imagine we have a 2-dimensional universe with only two particles in it. And for simplicity, let's say that the physics in this universe only care about the position of the particles. We could describe the entire state of that universe with a 4-component vector: (xa, ya, xb, yb). Those four numbers would tell us everything there was to know about that universe.

So now let's imagine a 4-dimensional space where the four axis are xa, ya, xb, and yb. Each point in this 4-dimensional space corresponds to one possible state of our little mini-universe.

Okay, now let's "imagine" (yeah right) a space with some 1080-odd dimensions, corresponding to everything there is to know about every single particle in the known universe. (It really should represent the state of the quantum field, but whatever) Any point in this "configuration space" corresponds to one possible state for the known universe to be in.

It turns out that one of the things quantum physics tells us is that -- very roughly speaking -- if your universe starts out at a particular point in this configuration space, what happens next is dependent on information about other parallel universes in nearby points in the configuration space. Well, somewhere a quantum physicist is having a heart attack right now, because it's not really like that at all -- but close enough for now. The point is that another possible universe that is very "close" in configuration space can affect what happens in your universe, but possible universes that are farther away exert little to no effect.

Okay then! On to the double-slit experiment. When I fire an electron -- a single electron -- at the screen, it could pass through the left slit or the right slit, apparently at random. Think of those two possibilities as two possible universes -- really, it's two massive sets of possible universes corresponding to all the other random shit that is happening at that time, but for now, just pretend it's only two. Those two universes are really damn close together in configuration space, since the only thing that is different between them is whether one single electron veered left or veered right. And as we already stated, quantum physics tells us, very roughly speaking, that two universes that are close together in configuration space can have an influence on each other.

Conceptually speaking, it's not that the electron in "our" universe is interfering with itself... instead, it is being interfered with by the electron in that other parallel universe! (IMO, the notion of subjectivity here -- "our" universe, a "parallel" universe -- is a complete illusion, but I think it is fine to visualize it this way for the purposes of this post)

That can only happen, remember, because the universes are so close together in configuration space. If for some reason those two possible universes got separated from each other in configuration space, then they wouldn't be able to interfere with each other anymore, because they'd be too far away.

Enter the sensor. We put a sensor at one of the slits, call it the left one. Now, we have one universe (really a set of universes) where the electron goes left and the sensor is triggered; and another universe (again, really an unimaginably large set of universes) where the electron goes right and the sensor is not triggered. This sensor does not exist sui generis outside of either of the universes -- it is part of the universes themselves. It is made of particles, and probably quite a few of them, even if it's a very small and simple sensor. And as such, when the sensor triggers or doesn't trigger, that affects where said universe finds itself in configuration space.

Furthermore, it doesn't take a particularly complicated sensor to put those two universes so far apart in configuration space that they can no longer affect each other. Even more so if a human happens to read the sensor! That phenomenon -- when a small divergence in configuration space (i.e. one particle going left or right) snowballs into a large divergence in configuration space (i.e. by causing a sensor to trigger or not trigger) is called quantum decoherence.

And it's happening all the time. In fact, it's the normal state of things. That's why we usually "don't observe quantum effects" at the macroscopic level. Usually, two universes (or really, sets of universes) don't stay close enough together for long enough to influence each other in any way that we humans can later observe. It's only by carefully constructed setups, like the double-slit experiment, that we are able to get "our" universe to cruise along close enough to a "parallel" universe for a sufficient amount of time to notice them affecting each other.

But they do effect each other, all the time. And if they didn't, the laws of physics as we know them wouldn't work.

I've got one more mental picture for you, somewhat ripped off from a diagram Elsevier drew, but simplified enough to describe in words. Imagine a 3-dimensional space. The Z-axis represents time, and the X and Y axes are stand-ins for what's really a gazillion different dimensions that we aren't going to visualize: Namely, the quantum state of the electron, and the sensor.

We fire an electron at the screen. Even before it hits the slit, there's still a bunch of possible different quantum states of the sensor, the electron, etc., so we're not just talking about one universe... but for our purposes, it's one pretty coherent thread. So visualize this universe-thread as a tube in our 3-space, forming a circular cross-section in the X/Y axes, and travelling upwards in the Z-axis (i.e. forward in time).

Now we hit one slit or the other. Our universe-thread now splits into two tubes, one corresponding to the left slit, and the other corresponding to the right slit. But that's such a tiny difference, that even though the center of the tubes has shifted a bit, they still overlap -- a lot. In fact, it's not really two tubes, it's more like a figure-8, or like a standard AC power cord. The overlap allows them to influence each other in "quantum"-like ways, like the weird phenomenon of an electron apparently interfering with itself.

Suddenly, one universe-thread encounters a sensor. Uh-oh. A whole shitload of particles change states in rapid succession, and WHAM! that tube splits off from the figure-8 and goes shooting off into the sunset. Now we really have two distinct tubes, two completely independent universe-threads. One of them (where the sensor didn't trip) is still going straight-up the Z-axis, but the other suddenly had a violent diagonal shift that sends it off to another part of the X/Y plane altogether. Now they don't overlap, so they can't interfere with each other. And hence, that spooky "observer" effect.

Again, I reiterate that I was speaking very approximately throughout. For instance, to say that the universes "interfere with" each other is really not quite right -- it's really about quantum amplitudes (which are represented by a complex number) flowing through configuration space. But for everything in my account, I think you could at least make an analogy to quantum physics.

My hope is that by avoiding talking about the specifics, I've presented it in a way that makes intuitive sense. The idea of parallel universes affecting each other is still freaky shit, but at least now it all seems like physics, rather than weird uncaused phenomena and consciousness-causes-collapse nonsense. (In fact, I am now convinced that the very phenomenon of "wavefunction collapse" is, as Wikipedia puts it, "just an epiphenomenon of...quantum decoherence." Which is rather unfortunate, since one of the songs my band plays uses the sudden collapse of a quantum waveform as the central metaphor, but whatever...)

Comments are welcome.


  1. Interesting analogy, and very clearly explained.

    Having not thought about quantum physics in a while, I'm severely rusty. Do you know if there is any explanation (or even just a description) of what it is that might cause the mutual influence between two points that lie close together in configuration space?

  2. Re: the 'description' part of it... That's the whole part about summing the various contributions to the wavefunction. The clearest explanation I have encountered is here, in particular Figure 2. There are two ways to get to E, and the contributions to the wavefunction of those two possibilities exactly cancel each other out -- so the particle never gets to E.

    As far as 'explanation'... I suspect that might be asking the wrong question -- this is more real than any other description of the physical world we have had so far. In Newton's time, there was no 'explanation' to F=ma -- it just matched observations. It's still possible there is some deeper layer that would explain it (just as F=ma has been explained), though that is looking increasingly doubtful. But in any case, at present, the explanation would be "that's how the universe works."

    I think. I don't really even have a decent lay understanding of this stuff, TBH. This post was as much for clarifying it in my own mind. It's probably completely wrong :)

  3. I think "Elsevier" should be "Eliezer", in both places where it appears. :-)

  4. Probably the most likely explanation for quantum decoherence is that each electron actually contains a complete copy of it's initialized state as it passes through the slit. It's only when acted upon by phenomena that would cause duality to be observed that the "waveform collapses". There really isn't a paradox at play because the two states have always been present within the particle, it's just that there was no reason for it to behave otherwise until it was subjected to outside influence to choose one of the states. That's what is meant by the "epiphenomenon of quantum decoherence". Strange to us on the macro scale, but perfectly understandable rules for behavior as far as the electron is concerned.