Until now, we have seen particles move like waves and learned that a single particle can follow multiple, widely separated 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’ll explore 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. Previously, we sent a photon along two very different paths. Although the paths in that experiment were widely spaced, their lengths were identical: each went around two sides of a rectangle. We can improve this setup by adding a few mirrors, which will allow us to gradually change the length of one of the paths.
If the paths are the same length, we see stripes just 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 we’ve seen streaks fade away; in our previous examples, the stripes were either there or not.
We can tentatively associate this blurring of the stripes if we change the path length with the length of the photon traveling along the path. The streaks only appear if a photon’s waves overlap when they are recombined.
But when particles travel as waves, what do we actually mean by length? A helpful mental image might be dropping a pebble into a smooth pool of water. The resulting ripples spread in all directions like a series of rings. If you draw a line from where the stone fell through the rings, you will see that there are five to ten. In other words, the ring of waves has a thickness.
Another way of looking at it is as if we were a cork on water; we would feel no waves, a period of waves, and then smooth water again after the ripple passed. We would say that the ‘length’ of the ripple is the distance/time over which we have experienced waves.
Similarly, we can think of a traveling photon as a series of ripples, a clump of waves entering our experiment. The waves naturally split and take both paths, but they can only recombine if the two path lengths are close enough for the ripples to interact when brought back together. If the paths are too different, one set of ripples will be over before the other arrives.
This photo nicely explains why the stripes fade: they are strong when there is a perfect overlap, but fade when the overlap gets smaller. By measuring how far the stripes disappear, we measured the length of the particle’s wave ripples.
Digging through the lamp drawer
We can do our usual experiments and see the same features that we saw before: turning the photon speed way down (which produces a paintball pointillism of stripes), changing the color (bluer colors mean shorter distance), etc. But now we can also measure how the stripes behave when we adjust the path length.
While we often use lasers to generate light particles (they are great photon pea shooters), any kind of light will suffice: an incandescent lamp, an LED room light, a neon lamp, sodium street light, starlight, light passing through colored filters. Whatever kind of light we transmit, it creates streaks when the path lengths match. But the stripes fade at distances ranging from microns for white light to hundreds of kilometers for the highest quality lasers.
Light sources of different colors usually have the longest ripples. We can examine the color properties of our light sources by sending their light through a prism. Some light sources have a very narrow color palette (the laser light, the neon lamp, the sodium street lamp); some have a wide rainbow of colors (incandescent, LED room lighting, starlight); while others, such as sunlight sent through a colored filter, lie between the composite colors.
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 pass the same width of colors, their streaks will disappear at the same path difference. It is the reach of color that matters, not the average color.
Which brings us to a rather startling result: the length of a particle wave is determined by the range of colors (and thus energies) it has. The length is not a fixed value for a particular kind of particle. By simply digging through our drawer of light sources, we created photons ranging in length from microns (white light) to several centimeters (a laser pointer).