So far, we have seen that particles move like waves, and we have learned that a particle can travel many, widely separated paths. There are a number of questions that naturally arise from this behavior – one of them is: “How big is the particle?” The answer is remarkably fine and in the next two weeks (and articles) we will explore various aspects of this question.
Today we will start with a seemingly simple question: “How long is a particle? “
To answer this, we need to think about a new experiment. Earlier we sent a photon in two very different ways. While the paths were widely divided in this experiment, their lengths were the same: each went around two sides of a rectangle. We can improve this setting by adding a few mirrors, which allows us to gradually change the length of one of the roads.
When the paths are the same length, we see stripes just like in the first article. But as we make one of the trails longer or shorter, the stripes slowly fade. For the first time, we see stripes slowly disappearing; in our previous examples, the stripes were either there or not.
We can conditionally associate this fading of the stripes as we change the path length with length of the photon traveling along the path. The bands appear only if the photon waves overlap when combined.
But if particles travel like waves, what do we mean by length? Putting a pebble in a smooth pool of water can be a useful mental image. The resulting waves propagate in all directions as 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 10 of them. In other words, there is a ring thickness of the waves.
Another way to look at it is as if we are a plug of water; we would not feel any waves, a period of waves, and then again smooth water after the wave passes. We would say that the “length” of a wave is the distance / time we have experienced waves.
In a similar way, we can think of the traveling photon as a set of ripples, a lump of waves entering our experiment. The waves naturally separate and take up both paths, but they can only recombine if the two path lengths are close enough for the waves to interact when reassembled. If the roads are too different, one set of ripples has already passed before the arrival of the other.
This picture explains well why stripes slowly disappear: they are strong when there is a perfect overlap, but fade when the overlap decreases. By measuring how far until the stripes disappear, we measured the wavelength of the particles.
Digging through the drawer of the bulb
We can go through our usual experiments and see the same characteristics we have seen before: reversing the speed of the photon (which produces paintball pontilism of stripes), color change (bluer colors mean closer distance), and so on. measure how the stripes behave as we adjust the path length.
Although we often use lasers to generate light particles (they are great photon pea shooters), any type of light will do the job: an incandescent light bulb, an LED room light, a neon lamp, sodium street lamps, a starlight, a light passing through color filters. Regardless of the type of light we send, it creates stripes when the path lengths match. But the stripes fade at distances that range from microns to white light hundreds of kilometers for the highest quality lasers.
Light sources of different colors usually 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 range of colors (laser light, neon lamp, sodium street lamp); some have a wide color arc (incandescent bulb, LED room light, starlight); while others, such as sunlight sent through a color filter, are intermediate in the range of 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 streaks 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 disappear their stripes at the same difference in path. It is scope of the color that matters, not the middle color.
Which leads us to a rather shocking result: the wavelength of the particles is determined by the range of colors (and thus the energies) it has. Length is not a set value for a specific particle type. Just by digging our drawer of light sources, we made photons with lengths of microns (white light) up to a few cm (laser pointer).