Another Famous Quantum Experiment Was Just Debunked (Patreon)

[This is a transcript with links to references.]

The quantum Cheshire Cat is a famous experiment that’s attracted a lot of attention in the past decade. In this experiment, a particle is supposedly separated from one of its properties, for example its spin or polarization. It’s called the Cheshire cat because that particle is kind of like the cat and its disembodied property is kind of like the grin of the cat.

But maybe I should better say there was this famous experiment, because it was just debunked in a new paper. Let’s have a look.

The idea of the Cheshire Cat experiment goes back to a paper from 2012. The original idea was theoretical, but it has since been realized in several experiments that have shown that it actually works. So no one doubts that the experiment works as they said it does, the question is what it means.

The idea is this.  You take a photon and send it through a beam splitter. The photon has a 50 percent chance to either go straight through the beam splitter or be reflected. This means that if you describe the photon with this mysterious thing that we call a wave-function, then after the beam splitter, the photon’s wave-function is in a superposition of both paths. So it seems that the photon goes two ways at the same time.

Then you recombine the beams again using two mirrors and a second beam splitter. And put two detectors at the two possible output directions. I’ll call them detector 1 and 2. This entire setup is known as a Mach-Zehnder interferometer. It has the interesting property that if the arms are the same length, then the photon goes out only in the direction that it came in.

It’s because on the other possible output direction, there is destructive interference. So, set up properly, all photons go out to the right into detector 1, and never into detector 2.

For the Cheshire cat experiment, we then also need a second property for the photon, usually that’s polarization.  Polarization roughly speaking tells you which way the photon waves twist along the axis of propagation. Doesn’t really matter if you don’t know exactly what that means because we won’t need it. Only thing we need to know is that there are two different polarizations, let’s just call them plus and minus.

We start with a photon of polarization plus. If we just send it through the beam splitter it will come out the same way, nothing interesting going on.

Then we put a polarization flipper on the lower path which makes the polarization there change from plus to minus. What happens now is that the parts of the photon wave-function from the two paths can no longer recombine when they exit the interferometer because their polarizations don’t fit together. Then you get a mix of both polarization on each output port.  

The Cheshire experiment now works by throwing away some of those photons that come out of the interferometer. First you disregard everything that went into detector 2,  and before detector 1 you put a polarization filter that sorts out all minus polarization, so that only plus polarization passes. What you have left then at detector 1 has the same properties as the original photon. Goes into the same direction, has the same polarization.

Now the question is: if a photon arrives at detector 1, which path did it go?  

Well, remember that you looked only at the photons in the final detector which had polarization plus , the same as the initial one. But on the lower path, you flipped the polarization to minus.  So this seems to mean the photon must have come on the upper path. Or to put it differently, whatever goes along the lower path doesn’t make a contribution to what goes to detector 1.

 Okay, so the photon is on the upper path. Now you want to know what the polarization does. Unfortunately you can’t go and actually measure it. Because quantum mechanics has this funny property that if you make a measurement you change the properties of the wave-function.

But you can do a sneaky tiny measurement, known as a “weak measurement.” That the measurement is weak doesn’t mean it’s stopped going to the gym, it means that you don’t measure enough to get a definite result. Because this definite result is what would collapse the wave-function. With a weak measurement, just change the quantity you want to measure a little bit and see what the result is.

 In the Cheshire cat experiment, you just change polarization on this lower path a little bit. You then repeat this for many photons and see what else changes along with this tiny change. It’s not irrelevant to note that it’s actually a very specific change that they do to the polarization, and it’s designed so that if you did this particular change on the upper path, it will not do anything to the + state on that path. But if you do it on the lower path with the minus polarization, this will mix some of the plus polarization back in. And this will change how well the interference works at the end of the interferometer, and that makes a measurable change in detector 1.

So you’ve changed the polarization on the lower path and that made a difference for the measurement outcome. You conclude that even though the photon was on the upper path,its polarization was on the lower path. Because if there wasn’t anything there, how could you have changed it. It seems like the polarization has been separated from the particle.

This is where the story of the Cheshire cat comes from. Because it’s like the grin, that is the polarization, has an existence independent of the cat that is the particle.

The authors of the new paper  now point out that these two arguments about the location of the photon and its polarization are both correct, but they can’t be correct at the same time. Basically, you can’t have your cat and eat it too. Cake I mean, cake.

 You see the issue is that if you make this weak measurement to show that the polarization was supposedly on the lower path, then you do this by mixing back in some of the plus polarization.  But then you can no longer conclude that the photon must have been on the upper path.  You could also put a detector on the lower path and if that doesn’t click, you will know that the photon is on the upper path. But then you can no longer do the weak measurement for the polarization.

So if you know that the cat is on the upper path, you can’t tell where the grin is, and if you know that the grin is on the lower path you can’t tell where the cat is. Mystery solved.

It's no fun doing these debunking videos really. It’s kind of uninspiring. Isn’t it. What are you grinning at?