I’m listening to Richard Feynman’s physics lectures in the car, and I just finished what might be the best, his description of the double-slit experiment with electrons. The ideas are so profound and amazing that the audience several times bursts into laughter, I think without Feynman even trying to be funny. No one can describe the double-slit experiment as well as Feynman, but once you understand this experiment, you own a piece of this amazing and bizarre universe that will be yours forever.

Here goes. It will be better with pictures, so hopefully I can find some.

First consider things that are definitely lumpy, like bullets. The bullets are indestructible, they start as a lump and end as a lump. Shoot bullets at a wall with two small holes. Each bullet either goes through the top hole or the bottom hole. They might richochet off the edges or something, so when you’re done you have a distribution that looks like this:

double-slit-bullets

Notice that the bullets gather right behind the slits. A reasonable conclusion is that the bullets behind each slit passed through that slit.

OK, now consider water waves. Immerse the whole experiment in water, and instead of a gun shooting bullets, have a finger or something moving up and down in the water. This makes ripples. When the ripples reach each slit, they start two new sets of ripples, one from each slit. But when the two new sets of ripples meet each other, they interfere, creating a different sort of pattern against the far wall.

double-slit-waterInterference can be hard to understand; I always like to think of trampolines. You know how bouncing on a trampoline you can get higher and higher if you match your jumping to the bouncing of the trampoline. But if you hit the trampoline at just the wrong time, your bounce gets “swallowed up” by the trampoline. Your crest met the tramp’s trough, and you lose your bounce. Sad, but that’s destructive interference. Well, sort of. Anyway, if you think of it that way, you’ll see that along some parts of the wall you get even bigger waves (constructive interference) and along other parts you get nothing (destructive interference). It’s a very different pattern than you get from bullets.

What about electrons? Now Feynman springs his beautiful paradox. He states what he calls “Proposition A.” That is, each electron either passes through slit 1 or it passes through slit 2. This makes sense, because everything we know about electrons says they are more like bullets than like water. But when you do the experiment, here’s what you get:

double-slit-electrons

Notice that the electrons, as far as we can tell, as far as we can measure them, are still like bullets. That’s an important point to remember. No one has ever “seen” an electron wave. We don’t know what such a thing would look like. Electrons are bullets, as far as we can tell. We never find half an electron. They’re bullets going in, they’re bullets when we catch them on the other side. And yet . . .

In between, when we’re not looking, the electrons act like water! They create an interference pattern on the far wall.

OK, fine, electrons do this bizarre thing when we’re not looking. But surely proposition A still holds, right? Somehow the electrons must move either through slit 1 or slit 2, right? Let’s see.

We set up an experiment. We shine light on the holes. If an electron comes through, we see the light. And indeed, when we do this, we see that electrons come through one hole or the other hole, never both at the same time, never part of an electron here, another part there. Great. Now we turn around and look at the pattern on the wall. What do we see?

double-slit-bullets1

Argh! The electrons form a pattern like bullets! The act of looking at the electrons has disturbed them! When we look the electrons do one thing (and proposition A is upheld, every time). When we don’t look, they do something entirely different, and we can’t say whether proposition A is true or not. We get the sense that nature is playing with us.

Feynman then shows how by using less intense light, or light of a longer wavelength, the bullet pattern gradually, bullet by bullet, morphs into the water pattern. It’s a beautiful thing. Nature has covered all her bases. We can’t catch her in her strange act of doing funny things with electrons. And yet,the pattern we get when we’re not looking at the slits shows us that something funny is, indeed, going on.

For instance, suppose you use longer wavelength light. This light is less energetic, so that it is less likely to knock the electron off its path. But by an exact relationship, when you get light of low enough energy not to knock your electrons silly, that light is of just long enough wavelength that you can’t tell anymore which hole the damn electron went through! And guess what kind of pattern you get?

double-slit-electrons1

You get the water wave pattern again! Nature has beaten us once more. We try to look with just enough force to see what’s going on, and she turns the electrons into bullets. We look with just too little force to see what’s going on, and the electrons turn back into water waves again! Argh!

To emphasize the strangeness, consider closing one slit. You get half the bullet pattern. Now open the slit and don’t watch. You get the wave pattern. In the bullet pattern, you get electrons in particular spots, say spot Q, even with one slit closed. If you open the second slit (remember, don’t look!), spot Q has no electrons hitting it! For certain spots, you get fewer electrons with two slits than you get with one. More paths, less electrons!

Now for my favorite part, not something Feynman emphasized in his lecture, but something I find completely mind-blowing. We can shoot electrons as fast or as slow as we want. If we’re really patient (read obsessed), we might shoot one electron a year, or one a decade, or (imagining we will live forever) one every thousand years. As long as we’re not looking at the slits, the electrons will, one by one, fall into just the right places to form an interference pattern! But how did the electron from yesterday know that it can’t land in spot Q, because an electron a thousand years from now will enter the apparatus and interfere with it at that spot? Can electrons know the future?

The answer seems to be that the electrons are not interfering with each other. Rather, each electron interferes with itself. In other words, each electron somehow goes through both slits.

But we know that’s not true! We know it because every time we look, we see an electron going through either slit 1 or slit 2. There’s never any ambiguity. Yes, this act of looking destroys the interference pattern. But still, how can an electron that is always observed to be a lump pass through both slits? When we’re looking, electrons go through one slit or the other. Proposition A holds. When we’re not looking, something strange happens, and we just don’t know what it is.

We don’t know how nature does it. We don’t know why nature does it. We just know she does. And we know that we can’t catch her.

It is a beautiful, frustrating, beautifully frustrating thing. And it makes the world an amazing place.

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