Now, it turns out, this is again, this is a universal property of quantum mechanics. It holds for any kind of particle — in practice, that means photons and electrons because that’s all there is in this universe unless you start getting into nuclear physics. And any kind of measurement, and any kind two-slit experiment, any experiment where you provide two different paths for the particle to potentially go down and bring it back together without knowing which way it actually went will produce interference and any modification that you make that lets you figure you out where it went will destroy that interference.
Now, this is still not intractably weird because we can still tell a reasonable story about why this might happen. So, maybe measurement does something to this system. These are after all very small particles and very delicate systems and so maybe it’s just physically impossible to make a measurement without disturbing the system in a way that is the cause of the destruction of this interference. Maybe the wave function collapses and becomes a particle somehow. This is the famous Copenhagen Interpretation of quantum mechanics.
But it turns out that we can rule out that possibility as well. And the way we rule out that possibility is by asking: How and when does this collapse, this purported collapse, happen? Collapse has a number of features that ought to make us very suspicious of it just at priority without even doing any experiments. It’s a discontinuous and non-reversible phenomenon, that once you know that a particle has gone through one slit or the other, you can’t go roll back time and undo that.
And if you look at the mathematics of quantum mechanics, which we’ll get to later, there’s nothing in the math that’s discontinuous. And more than that, all of the math is actually time reversible. So we can make a — hypothesize that this collapse happens, but this is fundamentally at odds with the mathematics of what quantum mechanics – of how quantum mechanics says that our universe works. So we can actually do better than that.
We can actually do an experiment to show that collapse, if it happens, is a much subtler phenomenon than it would’ve first appeared and this is the famous — this is the quantum mystery number two, the famous quantum eraser. Now, this is a two-slit experiment that I have now reduced to something more abstract. So we have some particle source, this can be photons or electrons. We have some abstract way of splitting up particles so that it has two different paths to go down and some abstract way of recombining that particle so that both of those paths end up in the same place so that we get interference.
And here notionally, we have one detector at one of these dark fringes and another one at a bright fringe so that if we introduce some kind of an abstract measurement on one of these branches, then the interference pattern fusses out, that we now have the path, the amount of light, at each detector. So now we don’t have fringes anymore, we have the spread-out pattern that we saw under the single slit version of the experiment.
Like I said, there are lots of different ways that you can do this — actually, let me go on to the next one. So it turns out that you can erase this, that there are physical ways that if this measurement, certain kinds of proto measurements, that you can do here, you can then go back and erase after the fact and restore the interference.
And here’s a concrete example of that. If we polarize light and — I’m actually going to show you this in just a second, so bear with me if you don’t understand what I’m about to say, you use polarized light and you do the measurement by rotating that light 90 degrees and then erase it by filtering it 45 degrees, that is an actual concrete example of a quantum eraser. And I can’t show you the interference part of it but I can show you the eraser part.
So what I have here is some Polaroid film, this is the same stuff that you find in polarized sunglasses. And, I first want to convince you, has anyone not played with this stuff before? Okay, so again, real quick. If the axis of the film are aligned then you can see through it. Can everybody see through this? And if I rotate it at 90 degrees, then you can’t see through it anymore and that effect is independent of the absolute orientation of the film. So the light that’s going through to your eyes starts out unpolarized over here, it gets — passes through this film and becomes polarized, let’s say in this direction. And I can demonstrate then that it has become polarized in that direction by filtering it out using a filter at 90 degrees.
And there’s also this cool adjunct to the experiment that you can do by adding a filter at 45 degrees. If you put it in front or behind, nothing happens which is pretty much what you’d expect. But if you slide this in between, then suddenly you can see through it again. Pretty cool, huh? And the reason for that is because if you start out with polarized light and you filter it at 45 degrees, then some of it gets through and it’s now polarized in this direction. And now I can do the same operation again, which is now the relative orientation of these two are 45 degrees so some of it gets through again.
But that’s not what I want to show you, that’s not the cool part. Cool part is this stuff. This is what they didn’t show you, what they didn’t show you in high school. This film is actually a polarization rotator. If I’d stick this in here, I can actually take this light that’s polarized in this direction, I can rotate it to 90 degrees that it’s polarized in the same direction as this film. And the thing to notice here is that the apparent brightness here in the center is the same as it is up here. There’s before, if we did the high school version of the experiment – whoops — you’ve gotten quite a bit of loss.
So, I really can take — I can take light and I can polarize it and I can take that polarized light and I can rotate it by 90 degrees and so I can create two different paths. So I can tell which way the light went through. I can tell whether the light is going through here or whether the light is going through here. Actually, let me back up a step. My claim is, without this filter, it’s a little hard.