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One of the quietest revolutions Our century today was the entry of quantum mechanics into our everyday technology. In the past, quantum effects were limited to physics laboratories and delicate experiments. However, modern technology increasingly relies on quantum mechanics, and the importance of quantum effects will only increase in the coming decades. As such, the physicist Miguel F. Morales has taken on the Herculean task of explaining quantum mechanics to the rest of us laypeople in this seven-part series (not mathematics, as we promise). Below is the third story in the series, but the starting story can always be found here.
Exploring the quantum world
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So far we've seen particles move as waves, and we've found that a single particle can take multiple, widely spaced paths. There are a number of questions that naturally arise from this behavior – one of them is, "How big is a particle?" The answer is remarkably subtle, and over the next two weeks (and articles) we'll be exploring various aspects of this question.
Today we start with a seemingly simple question: "How long is a particle?"
To answer that, we need to think about a new experiment. Before that, we sent a photon in two very different ways. While the paths in this experiment were far apart, their lengths were identical: each went around two sides of a rectangle. We can improve this setup by adding some mirrors so that we can gradually change the length of one of the paths.
Enlarge /. An improved two-way experiment where we can adjust the length of one of the paths.
If the paths are the same length, we will see stripes like in the first article. But if we make one of the paths longer or shorter, the stripes slowly fade. This is the first time streaks are slowly disappearing. In our previous examples, the stripes were either present or not.
We can tentatively associate this bleaching of the stripes by changing the path length with the length of the photon moving along the path. The stripes only appear when the waves of a photon overlap during recombination.
But when particles move as waves, what do we mean by length? A useful mental image can be dropping a pebble into a smooth pool of water. The resulting waves propagate in all directions as a set of rings. If you draw a line that the stone fell from through the rings, you will find there are five to ten of them. In other words, the wave ring has a thickness.
Another way of looking at it is as if we were a cork on the water; We wouldn't feel any waves, a period of waves, then smooth water again after the ripple had passed. We would say the "length" of the ripple is the distance / time over which we experienced ripples.
Enlarge /. Waves on a pond. Note the thickness of the shaft ring.
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Similarly, we can think of a wandering photon as a series of waves, a clump of waves, that enters our experiment. The waves split naturally and take both paths. However, they can only be combined again if the two path lengths are close enough for the waves to interact when they are brought back together. If the paths are too different, one set of waves is over before the other arrives.
This picture explains well why the streaks are slowly disappearing: they are strong when there is a perfect overlap, but fade when the overlap decreases. By measuring how far the stripes disappear, we have measured the length of the wave waves of the particle.
Dig through the lightbulb drawer
We can go through our usual experiments and see the same features we saw before: decreasing the photon rate (which results in paintball pointillism of the stripes), changing the color (bluer colors mean closer spacing), etc. But now we can, too Measure how the strips behave as we adjust the path length.
While we often use lasers to create particles of light (they are great photon pea shooters), any type of light will do: an incandescent lamp, an LED room light, a neon lamp, sodium street lights, starlight, and light passed through colored filters. Regardless of the type of light we are sending through, streaks appear when the path lengths match. However, the stripes disappear at distances of micrometers for white light to hundreds of kilometers for the highest quality lasers.
Light sources with different colors tend to have the longest waves. We can study the color properties of our light sources by sending their light through a prism. Some of the light sources have a very narrow color range (the laser light, the neon lamp, the sodium street light); some have a broad rainbow of colors (the light bulb, LED room light, star light); while others, such as sunlight sent through a color filter, are in the range of composite colors.
We can measure the length of a ripple by seeing how far we can extend one arm of the experiment before the streaks disappear. A long ripple has a narrow range of colors
A medium length ripple has a wider range of component colors.
A very short pulse of light necessarily encompasses a wide range of colors that turn white.
What we notice is that there is a correlation: the narrower the color range of the light source, the longer the path difference can be before the stripes disappear. The color itself doesn't matter. If I choose a red filter and a blue filter that allow the same color width, the streaks disappear with the same path difference. It's the range of colors that matters, not the average color.
A medium wave of blue light and its component colors.
A medium wave of orange light. Notice that the orange wave is longer than the blue wave (shown by a colored line), but the length of the ripple is the same (shown by a gray area). The length of the ripple depends on the color range, not the central color.
This brings us to an astonishing result: The length of a particle wave results from the color range (and thus the energies). The length is not a fixed value for a specific type of particle. By simply rummaging through our drawer with light sources, we have produced photons with lengths from micrometers (white light) to a few cm (laser pointer).