A Curious Observer Guide to Quantum Mechanics, pt. 3: Rose-colored glasses

So far, we have seen particles as waves move and learned that a single particle can take multiple 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 explore different aspects of this question.

Today we start with a seemingly simple question: ‘How tall is a particle? ‘

Go long

To answer this, we need to think about a new experiment. Earlier, we sent a photon on two different paths. While the paths in that experiment were widely separated, their lengths were identical: each went around two sides of a rectangle. We can improve this setup by adding a few mirrors so that we can gradually change the length of one of the roads.

If the roads are the same length, we see stripes as in the first article. But if we make one of the roads longer or shorter, the stripes slowly fade. This is the first time we have seen stripes slowly disappear; in our previous examples the stripes were there or not.

We can associate this blurring of the stripes for the time being if we change the length of the path with the length of the photon moving along the road. The stripes appear only when the waves of a photon overlap when reassembled.

But if particles move like waves, what do we mean even by a length? A useful mental image can make the fall of a pebble fall into a slippery pool of water. The resulting wrinkles spread in all directions as a set of rings. If you draw a line from which the rock fell through the rings, you will find that it is five to ten of them. In other words, the ring of waves is thick.

Another way to look at it is as if we are a cork on the water; we would not feel any waves, a period of waves and then again smooth water after the ripple had passed. We would say that the ‘length’ of the ripple is the distance / time over which we experienced waves.

Similarly, we can think of a moving photon as a set of ripples, a bunch of waves entering our experiment. The waves tear naturally and take both paths, but they can only recombine if the two path lengths are close enough so that the ripples can interact when brought back together. If the paths are too different, one set of ripples will have passed before the other one arrives.

This photo explains nicely why the stripes slowly disappear: they are strong when there is perfect overlap, but fade as the overlap decreases. By measuring how far until the stripes disappear, we measured the length of the waves of the particle.

Dig through the light bulb tray

We can go through our usual experiments and see the same characteristics as we have seen before: to turn down the photon tempo (which produces a paintball punctilism of stripes), to change the color (blue colors mean a narrower distance), etc. measure how the stripes behave as we adjust the length of the road.

Although we often use lasers to generate particles of light (these are fantastic photon pea shooters), every kind of light will do: a light bulb, an LED room lamp, a neon lamp, sodium street lights, starlight, light emitted by colored filters moves. Whatever kind of light we transmit creates streaks when the length of the path matches. But the stripes fade at distances ranging from micron for white light to hundreds of kilometers for the highest quality lasers.

Light sources with clear colors have the longest wrinkles. We can investigate the color properties of our light sources by sending the 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 colors (the light bulb, LED room light, star light); while others like sunlight sent through a colored filter are mediocre in the range of compound colors.

What we notice is that there is a correlation: the smaller the color range of the light source, the longer the path difference may be before the stripes disappear. The color itself does not matter. If I choose a red and a blue filter that allow the same width of colors, their stripes with the same path difference will disappear. This is the series of color that matters, not the average color.

This brings us to a rather striking result: the length of a particle wave is given by the variety of colors (and therefore energies) it has. The length is not a fixed value for a specific type of particle. Just by digging through our load of light sources, we made photons with lengths ranging from micron (white light) to a few cm (a laser pointer).