A Curious Observer Guide to Quantum Mechanics, Pt. 6: Two quantum ghosts

One of the quietest revolutions of our current century is the entry of quantum mechanics into our everyday technology. It used to be that quantum effects were limited to physics labs and delicate experiments. But modern technology is increasingly relying on quantum mechanics for its basic operation, and the importance of quantum effects will only grow in the coming decades. As such, the physicist Miguel F. Morales took on the great task of explaining quantum mechanics to laymen in this seven-part series (no mathematics, we promise). Below is the sixth story in the series, but you can always find the start story plus a landing page for the entire series so far on the site.

During our quantum adventures to date, we have seen a lot of interesting quantum effects. So for our last big excursion, let’s venture a particularly creepy corner of the quantum wood: today we are going to see entanglement and measurement sequence.

Together, these two concepts create some of the most counter-intuitive effects in quantum mechanics. They are so counter-intuitive that it’s probably a good time to re-emphasize that nothing in this series is speculative – everything we’ve seen is backed up by hundreds of observations. Sometimes the world is much stranger than we expect.

I’ve always considered the world of spies and espionage strange and creepy, so maybe it’s appropriate that cryptography is one of the applications of the things we’re talking about today. But there is a lot to go over before we get there.

Play in the sunlight

After a long walk through an increasingly dark and gloomy forest, gnarled trees dripping vineyards, we unexpectedly emerge into a meadow glistening in bright sunshine. Flashing in the light, we take off our polarized sunglasses.

The lenses in polarized sunglasses are polarized in the vertical direction, which means that when worn normally, it can transmit light that is vertically polarized, but this will completely block the horizontal polarized light. This is advantageous because light shining from water is mostly polarized horizontally; a lens that transmits only vertically polarized light will significantly reduce the reflected glare.

Because we are a little suspicious about the beautiful sunshine in our mysterious gaze, we start looking through various sunglasses. When you look through two or three sunglasses at the same time, you look ridiculous, but these are the sacrifices we make for science. We will sketch the results you would see, but if you can scrape together three pairs of polarized sunglasses, you can perform all the experiments in this article at home.

What you see when you look through two polarized sunglasses. Each polarized lens lets only light through which is polarized in the direction of the arrow in the temple. All lenses transmit half the unpolarized light (the medium gray tint). But when light has to pass through both glasses, the relative orientation of the glasses is important. On the left, both lenses let vertically polarized light through, so that all the light that passes through the first lens also passes through the second lens. In contrast, the glasses are rotated to the right to transmit only horizontally polarized light, which is completely blocked by the front glasses. If you hold the glasses 45 ° relative to each other, half of the light passing through the first glasses will move through the second pair (1/2 x 1/2 = 1/4 backlight). — Enlarge / What you see when you look through two polarized sunglasses. Each polarized lens lets only light through which is polarized in the direction of the arrow in the temple. All lenses transmit half the unpolarized light (the medium gray tint). But if light has to pass through both glasses, the relative orientation of the glasses is important. On the left, both lenses let vertically polarized light through, so that all the light that passes through the first lens also passes through the second lens. In contrast, the glasses are rotated to the right to transmit only horizontally polarized light, which is completely blocked by the front glasses. If you hold the glasses 45 ° relative to each other, half of the light passing through the first glasses will move through the second pair (1/2 x 1/2 = 1/4 backlight).

Miguel Morales

If you hold two pairs of glasses in front of you and then turn one of the pairs, you will see that the amount of light passing through varies dramatic. If the glasses are at a 90 ° angle (eg one held normally and the other sideways), almost no light will pass through. The combined view through the lenses looks almost completely black – for very good polarized lenses, it almost gets dark glass. Conversely, if kept with the same orientation, they let through almost the same amount of light as one pair of glasses alone (with good polarizing lenses kept in perfect alignment, this is exactly true).

It’s pretty simple to understand. If both glasses are held vertically, the first glasses let only vertical light through. Since the second pair also transmits vertical light, it has nothing to block – all the light it made through the first pair will also make it past the second. Conversely, if we hold the first pair sideways so that it only goes horizontally and keep the second pair normal so that it blocks horizontal light, there is no light that can come through both. Together they look very dark. And if you hold the glasses 45 ° to each other, it’s meanwhile; half of the light that passes through the first glasses comes through the second.

Enlarge / Only the orientation between the lenses is important, and not how it is oriented with respect to the environment.

Miguel Morales

It’s just the angle between the lenses that matters. If we choose a relative orientation, such as crossed, and rotate both lenses together, we see that the coverage remains the same. The green frame glasses on the right are kept at ± 45 ° from the vertical point, but since the first pair has polarized 45 ° to the left of the vertical light, all the light is blocked.

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

Enlarge / Starting with crossed lenses, add an oblique lens at the back.

Miguel Morales

We will start with two crossed glasses, as shown on the left. We then add a third lens aimed at 45 ° behind the two we already had. Upon closer inspection, it acts as we would expect. Wherever the original glasses block, the light is still black. In the 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 we saw in Figure 1. If we look at what is new, we see that the region where the light must pass through all three lenses is also black.

Enlarge / Arranging the order of the glasses makes a big difference.

Miguel Morales

But we see something remarkable when we rearrange the glasses. We start again with crossed glasses, but now move the 45 ° lens between they. If we do, light comes through where all three of the lenses overlap. Where only two lenses overlap, we get the expected results – black for crossed and colored for 45 ° relative orientation. But even though the front and rear lenses are crossed and normally will not let any light through, light can suddenly pass through if you place another lens with intermediate polarization.

This is strange. The order of the glasses matter. Try to reverse the order of the lenses when following at home. When crossed lenses are stacked side by side, almost no light passes through. But if you switch between blue (horizontal / vertical) and green (± 45 °) frames, a little light will come through.

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Play in the sunlight

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