A Curious Observer’s Guide to Quantum Mechanics, Pt. 6: Two Quantum Spirits

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A Curious Observer's Guide to Quantum Mechanics, Pt. 6: Two Quantum Spirits

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One of the quietest revolutions In our current century, quantum mechanics has entered our everyday technology. Quantum effects used to be limited to physical laboratories and delicate experiments. But modern technology increasingly relies on quantum mechanics for its basic operation, and the importance of quantum effects will only grow in the coming decades. As such, physicist Miguel F. Morales has taken on the daunting task of explaining quantum mechanics to laymen in this seven-part series (no math, we promise). Below is the sixth story in the series, but you can always find the starting story plus a landing page for the entire series so far on the spot.

In our quantum adventures so far, we’ve seen a lot of interesting quantum effects. So, for our last great excursion, let’s venture into a particularly scary corner of the Quantum Forest: today we’re going to see entanglement and measurement sequence

Together, these two concepts create some of the most counterintuitive effects in quantum mechanics. They are so counterintuitive that now is probably a good time to reiterate that nothing in this series is speculative – everything we’ve seen is supported by hundreds of observations. Sometimes the world is much weirder than we expect.

I’ve always thought of the world of spies and espionage as strange and creepy, so perhaps it’s fitting that cryptography is one of the uses we’re talking about today. But there is still a lot to do before we get there.

Playing in the sunlight

After a long walk through an increasingly dark and gloomy forest, gnarled trees dripping from the vines, we unexpectedly arrive in a meadow that sparkles in the bright sun. Blinking in the light, we pull out our polarized sunglasses.

The lenses in polarized sunglasses are polarized vertically, which means that when worn normally, they transmit vertically polarized light, but completely block horizontally polarized light. This is advantageous because light shimmering off the water is usually horizontally polarized; a lens that transmits only vertically polarized light will greatly reduce the reflection.

Being a bit suspicious of the beautiful sun in our mysterious clearing, we start looking through several sunglasses. Looking through two or three sunglasses at once makes you look ridiculous, but those are the sacrifices we make for science. We will graph the results you would see, but if you can get three pairs of polarized sunglasses together, you can perform all of the experiments in this article at home.

What you see when you look through two polarized sunglasses. Each polarized lens only transmits light polarized in the direction of the arrow on the temple. All lenses let through half of the unpolarized light (the medium gray shade). But if the light has to pass through both lenses, the relative orientation of the glasses matters. On the left, both lenses transmit vertically polarized light, so any light that comes through the first lens also passes through the second lens. In contrast, on the right side, the rear goggles are rotated to allow only horizontally polarized light through, which is completely blocked by the front goggles. If you hold the glasses at an angle of 45 ° to each other, half of the light passing through the first pair will pass through the second pair (1/2 x 1/2 = 1/4 of the backlight ).
Enlarge What you see when you look through two polarized sunglasses. Each polarized lens only transmits light polarized in the direction of the arrow on the temple. All lenses let through half of the unpolarized light (the medium gray shade). But if the light has to pass through both lenses, the relative orientation of the glasses matters. On the left, both lenses transmit vertically polarized light, so any light that comes through the first lens will also pass through the second lens. In contrast, on the right side, the rear goggles are rotated to allow only horizontally polarized light through, which is completely blocked by the front goggles. If you hold the glasses at a 45 ° angle to each other, half of the light that passes through the first pair will pass through the second pair (1/2 x 1/2 = 1/4 of the backlight) .

Miguel Morales. Placeholder image

If you hold two pairs of glasses in front of you and then turn one of the glasses, you will notice that the amount of light that passes through them varies dramaticWhen the glasses are at a 90 ° angle (one is held normal and the other sideways), almost no light will come through. The combined image through the lenses looks almost completely black – for really well polarized lenses, they become almost dark from welding glass. Conversely, when held in the same orientation, they transmit almost the same amount of light as glasses alone (with well polarizing lenses that are kept perfectly aligned, this is exactly true).

This is fairly easy to understand. If both glasses are held vertically, the first glasses will only transmit light vertically. Since the second pair also lets light through vertically, it has nothing to block – any light that has passed through the first pair will also get past the second pair. Conversely, if we hold the first pair sideways so that only horizontal light passes and the second pair normally so that it blocks horizontal light, then there is no light that can pass through both. Together they look very dark. And if you hold the glasses at an angle of 45 ° to each other, it is intermediate; half of the light that passes through the first glasses passes through the second.

Only the orientation between the lenses matters, not how they are oriented with respect to the environment.
Enlarge Only the orientation between the lenses matters, not how they are oriented with respect to the environment.

Miguel Morales. Placeholder image

It’s only the angle between the lenses that matters. If we choose a relative orientation, such as crossed, and rotate both lenses together, we will see that the opacity stays the same. The green lenses on the right are held at ± 45 ° from vertical, but since the first pair transmits polarized light 45 ° to the left of vertical, all light is blocked.

This all seems to make sense. But then you remember that this is quantum mechanics and the ominous movie music starts playing in the background. Let’s add a third pair of glasses. And to keep all orientations straight, we will always use blue boxes for the horizontal / vertical orientations and green boxes for the ± 45 ° orientations.

Starting with crossed lenses, we'll add a diagonal lens behind it.
Enlarge Starting with crossed lenses, we’ll add a diagonal lens behind it.

Miguel Morales. Placeholder image

We start with two crossed glasses, as shown on the left. We will then add a third lens aimed at an angle of 45 ° behind the two we already had. On closer inspection, this behaves as we would expect. Wherever the original glasses block, the light is still black. In the small corners where there is no complete overlap, the light passes through the 45 ° lens and one of the other lenses and we get the slightly darker hue that we saw in Figure 1. Looking at what’s new, see we know that the region where light must pass through all three lenses is also black.

Rearranging the order of the glasses makes a big difference.
Enlarge Rearranging the order of the glasses makes a big difference.

Miguel Morales. Placeholder image

But we see something remarkable when we reorder the glasses. We start again with crossed glasses, but now slide the 45 ° lens between them. When we do this, light comes through where all three lenses overlap. Where only two lenses overlap, we get the expected results – black for crossed and tinted for 45 ° relative orientation. But even though the front and rear lenses are crossed and would normally not transmit light, if you insert another lens with intermediate polarization, light can suddenly pass through.

This is weird. The to order of the glasses is important. If you’re watching at home, try reversing the order of the lenses. When crossed lenses are next to each other in the stack, almost no light comes through. But if you alternate between blue (horizontal / vertical) and green (± 45 °) frames, some light will come through.

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