Saturday, October 30, 2021

The delayed choice quantum eraser, debunked

[This is a transcript of the video embedded below. Some of the explanations may not make sense without the animations in the video.]

A lot of you have asked me to do a video about the delayed choice quantum eraser, an experiment that supposedly rewrites the past. I haven’t done that simply because there are already lots of videos about it, for example Matt from PBS Space-time, the always amazing Joe Scott, and recently also Don Lincoln from Fermilab. And how many videos do you really need about the same thing if that thing isn’t a kitten in a box. However, having watched all those gentlemen’s videos about quantum erasing, I think they’re all wrong. The quantum eraser isn’t remotely as weird as you think, doesn’t actually erase anything, and certainly doesn’t rewrite the past. And that’s what we’ll talk about today.

Let’s start with a puzzle that has nothing to do with quantum mechanics. Peter is forty-six years old and he’s captain of a container ship. He ships goods between two places that are 100 kilometers apart, let’s call them A and B. He starts his round trip at A with the ship only half full. Three-quarters of the way to B he adds more containers to fill the ship, which slows him down by a factor of two. On the return trip, his ship is empty. How old is the captain?

If you don’t know the answer, let’s rewind this question to the beginning.

Peter is forty-six years old. The answer’s right there. Everything I told you after that was completely unnecessary and just there to confuse you. The quantum eraser is a puzzle just like this.

The quantum eraser is an experiment that combines two quantum effects, interference and entanglement. Interference of quantum particles can itself be tested by the double slit experiment. For the double slit experiment you shoot a coherent beam of particles at a plate with two thin openings, that’s the double slit. On the screen behind it, you then observe several lines, usually five or seven, but not two. This is an interference pattern created by overlapping waves. When a crest meets a trough, the waves cancel and that makes a dark spot on the screen. When crest meets crest they add up and that makes a bright spot.

The amazing thing about the double slit is that you get this pattern even if you let only one particle at a time pass through the slits. This means that even single particles act like waves. We therefore describe quantum particles with a wave-function, usually denoted psi. The interesting thing about the double-slit experiment is that if you measure which slit the particles go through, the interference pattern disappears. Instead the particles behave like particles again and you get two blobs, one from each of the slits.

Well, actually you don’t. Though you’ve almost certainly seen that elsewhere. Just because you know which slit the wave-function goes through doesn’t mean it stops being a wave-function. It’s just no longer a wave-function going through two slits. It’s now a wave-function going through only one slit, so you get a one-slit diffraction pattern. What’s that? That’s also an interference pattern but a fuzzier one and indeed looks mostly like a blob. But a very blurry blob. And if you add the blobs from the two individual slits, they’ll overlap and still pretty much look like one blob. Not, as you see in many videos two cleanly separated ones.

You may think this is nitpicking, but it’ll be relevant to understanding the quantum eraser, so keep this in mind. It’s not so relevant for the double slit experiment, because regardless of whether you think it’s one blob or two, the sum of the images from both separate slits is not the image you get from both slits together. The double slit experiment therefore shows that in quantum mechanics, the result of a measurement depends on what you measure. Yes, that’s weird.

The other ingredient that you need for the quantum eraser is entanglement. I have talked about entanglement several times previously, so let me just briefly remind you: entangled particles share some information, but you don’t know which particle has which share until you measure it. It could be for example that you know the particles have a total spin of zero, but you don’t know the spin of each individual particle. Entangled particles are handy because they allow you to measure quantum effects over large distances which makes them super extra weird.

Okay, now to the quantum eraser. You take your beam of particles, usually photons, and direct it at the double slit. After the double slit you place a crystal that converts each single photon into a pair of entangled photons. From each pair you take one and direct it onto a screen. There you measure whether they interfere. I have drawn the photons which come from the two different places in the crystal with two different colors. But this is just so it’s easier to see what’s going on, these photons actually have the same color.

If you create these entangled pairs after the double slit, then the wave-function of the photon depends on which slit the photons went through. This information comes from the location where the pairs were created and is usually called the “which way information”. Because of this which-way information, the photons on the screen can’t create an interference pattern.

What’s with the other side of the entangled particles? That’s where things get tricky. On the other side, you measure the particles in two different ways. In the first case, you measure the which-way information directly, so you have two detectors, let’s call them D1 and D2. The first detector is on the path of the photons from the left slit, the second detector on the path of the photons from the right slit. If you measure the photons with detectors D1 and D2, you see no interference pattern.

But alternatively you can turn off the first two detectors, and instead combine the two beams in two different ways. These two white bars are mirrors and just redirect the beam. The semi-transparent one is a beam splitter. This means half of the photons go through, and the other half is reflected. This looks a little confusing but the point is just that you combine the two beams so that you no longer know which way the photon came. This is the “erasure” of the “which way information”. And then you measure those combined beams in detectors D3 and D4. A measurement on one of those two detectors does not tell you which slit the photon went through.

Finally, you measure the distribution of photons on the screen that are entangled partners of those photons that went to D3. These photons create an interference pattern. You can alternatively measure the distribution of photons on the screen that are partner particles of those photons that went to D4. Those will also create an interference pattern.

This is the “quantum erasure”. It seems you’ve managed to get rid of the which way information by combining those paths, and that restores the interference pattern. In the delayed choice quantum eraser experiment, the erasure happens well after the entangled partner particle hit the screen. This is fairly easy to do just by making the paths of those photons long enough.

If you watch the other videos about this experiment on YouTube, they’ll now go on to explain that this seems to imply that the choice of what you measure on the one side of the experiment decides what happened on the other side before you even made that choice. Because the photons must have known whether to interfere or not before you decided whether to erase the which-way information. But this is clearly nonsense. Because, let’s rewind this explanation to the beginning.

The photons on the screen can’t create an interference pattern. Everything I told you after this is completely irrelevant. It doesn’t matter at all what you do on the other side of the experiment. The photons on the screen will always create the same pattern. And it’ll never be an interference pattern.

Wait. Didn’t I just tell you that you do get an interference pattern if you use detectors D3 and D4? Indeed. But I’ve omitted a crucial part of the information which is missing in those other YouTube videos. It’s that those interference patterns are not the same. And if you add them, you get exactly the same as you get from detectors 1 and 2. Namely these two overlapping blurry blobs. This is why it matters that you know the combined pattern of two single slits doesn’t give you two separate blobs, as they normally show you.

What you actually do in the eraser experiment, is that you sample the photon pairs in two groups. And you do that in two different ways. If you use detector 1 and 2 you sample them so that the entangled partners on the screen do not create an interference pattern for each detector separately. If you use detector 3 and 4, they each separately create an interference pattern but together they don’t.

This means that the interference pattern really comes from selectively disregarding some of the particles. That this is possible has nothing to do with quantum mechanics. I could throw coins on the floor and then later decide to disregard some of those and create any kind of pattern. Clearly this doesn’t rewrite the past.

This by the way has nothing to do with the particular realization of the quantum eraser experiment that I’ve discussed. This experiment has been done in a number of different ways, but what I just told you is generally true, these interference patterns will always combine to give the original non-interference pattern.

This is not to say that there is nothing weird going on in this experiment. But what’s weird about it is the same thing that’s weird already about the normal double slit experiment. Namely, if you look at the wave-function of a single particle, then that distributes in space. Yet when you measure it, the particle is suddenly in one particular place, and the result must be correlated throughout space and fit to the measurement setting. I actually think the bomb experiment is far weirder than the quantum eraser. Check out my earlier video for more on that.

When I was working on this video I thought certainly someone must have explained this before. But the only person I could find who’d done that is… Sean Carroll in a blogpost two years ago. Yes, you can trust Sean with the quantum stuff. I’ll leave you a link to Sean’s piece in the info.

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