So far, we have seen particles move like waves and learned that a single particle can take multiple, widely spaced paths. There are a number of questions that naturally arise from this behavior – one of which is: “How big is a particle?” The answer is remarkably subtle, and over the next two weeks (and articles) we examine various aspects of this question.
Today we start with a seemingly simple question: “How long is a particle? ”
Go a long time
To answer that, we need to think about a new experiment. Previously, we posted a photon on two very different trails. While the paths were widely separated in this experiment, their lengths were identical: each went around two sides of a rectangle. We can improve this setup by adding a few mirrors so we can gradually change the length of one of the trails.
When the paths are the same length, we see stripes, as we did in the first article. But when we make one of the paths longer or shorter, the stripes slowly fade. This is the first time we see streaks slowly disappear; in our previous examples, the stripes were either there or not.
For the time being, we can connect this fading of the stripes when we change the stable length with length of the photon traveling down the path. The stripes appear only if the photons’ waves overlap when recombined.
But if particles move like waves, what do we even mean by a length? A useful mental image may be to throw a pebble into a slippery pool of water. The resulting ripples spread in all directions like a set of rings. If you draw a line from where the rock fell through the rings, you will find that there are five to ten of them. In other words, there is a thickness of the wave ring.
Another way of looking at it is as if we were a cork on the water; we sense no waves, a period of waves and then smooth water again after the ripple had gone. We would say that the ‘length’ of the ripple is the distance / time at which we experienced waves.
Similarly, we can think of a wandering photon as a set of ripples, a clump of waves coming into our experiment. The waves split naturally and take both paths, but they can only be recombined if the two style lengths are close enough for ripples to interact when brought back together. If the trails are too different, one set of ripples has already passed before the other arrives.
This image nicely explains why the stripes slowly disappear: they are strong when there is perfect overlap, but fade when the overlap diminishes. By measuring how far until the stripes disappear, we have measured the length of the particle’s wave crust.
Dig through the light bulb drawer
We can review our usual experiments and see the same features we saw before: turning the photon velocity far down (which produces a paintball pointillism of stripes), changing the color (bluer colors mean closer distance), etc. But now we can also measure , how the stripes behave when we adjust the course length.
While we often use lasers to generate light particles (they are good photons), any kind of light will do: an incandescent bulb, an LED room lamp, a neon lamp, sodium street lights, star lights, lights conducted through colored filters. No matter what kind of light we send through, streaks are created when the course lengths match. But the stripes disappear at distances ranging from micron for white light to hundreds of kilometers for lasers of the highest quality.
Light sources with different colors tend to have the longest ripples. We can examine the color properties of our light sources by sending their light through a prism. Some of the light sources have a very narrow range of colors (the laser light, the neon lamp, the sodium street light); some have a wide rainbow of colors (incandescent, LED room light, starlight); while others such as sunlight transmitted through a colored filter are intermediate within the composite colors.
What we notice is that there is a connection: the narrower the color range of the light source, the longer the path difference can be before the stripes disappear. The color itself does not matter. If I choose a red filter and a blue filter that allow the same width of colors, they will make their stripes disappear with the same path difference. It is range color that matters, not the average color.
Which brings us to a rather surprising result: the length of a particle wave is given by the range of colors (and thus energies) it has. Length is not a set value for a particular particle shape. Just by digging through our drawer with light sources, we made photons with lengths from micron (white light) to a few cm (a laser pointer).