A Curious Observer’s Guidance for Quantum Mechanics, P.T. 3: rose colored glasses

So far, we have seen particles as waves and learned that a single particle can be many, widely separated. There are many questions that naturally arise from this behavior – one of them being, “How big is a particle?” The answer is remarkably subtle, and in the next two weeks (and articles) we will explore various aspects of this question.

Today, we will start with a general question: “How long Is a particle? “

go all the way

To answer this, we need to think of a new experiment. Earlier, we sent a photon on two different paths. While the paths in that experiment were widely separated, their lengths were the same: each went around two sides of a rectangle. We can improve this setup by adding some mirrors, allowing us to gradually change the length of a single path.

When the paths are of equal length, we see the stripes as we did in the first article. But when we lengthen or shorten the paths, the stripes gradually fade. This is the first time we have seen stripes gradually disappear; In our previous examples, the stripes were either there or not.

We can add this extinction of stripes temporarily as we change the length of the path Length The photon is traveling down the path. Stripes are only visible when the waves of a photon overlap when recombined.

But if particles travel in the form of waves, what do we mean by an even length? A useful mental image can drop a pebble into a smooth pool of water. The resulting waves spread in all directions as a set of rings. If you draw a line where the rock falls through the rings, you will find that there are five to 10 of them. In other words, waves have a ring thickness.

Another way of looking at it is as if we were a cork on the water; We think there will be no waves, round waves, then smooth water again after the ripple has passed. We would say that the ‘length’ of the wave is the distance / time at which we experienced the waves.

Likewise we can think of a traveling photon as being a set of waves, a lump 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 to interact with the waves when they are brought back together. If the paths are very different, one set of waves will run past before the other arrives.

This picture explains well why the stripes gradually disappear: they are stronger when there is true overlap, but fade as the overlap decreases. By measuring until the stripes disappear, we have measured the length of the wavelength of the particle.

Digging through the light bulb drawer

We can go through our normal experiments and see the same characteristics that we saw earlier: turning the photon rate downward (which creates a paintball pointillism of stripes), changing color (mean of bluer colors Is close spacing), etc. But now we can also measure how the stripes behave as we adjust the path length.

While we often use lasers to generate particles of light (they are great photon pea shooters), any type of light will do: an incandescent light bulb, an LED room light, a neon lamp, sodium streetlights, Starlight, passed through light colored filters. Any kind of light we send creates stripes when the path length matches. But the strips fade away which range from microns to distances for white light Hundreds of kilometers For the highest quality lasers.

The light waves of different colors have the longest waves. We can examine the color properties of our light sources by sending their light through a prism. Some light sources have a very narrow range of colors (laser light, neon lamps, sodium streetlight); Some have a wide rainbow of colors (incandescent bulbs, LED room lighting, starlight); While others such as sunlight are routed through color filters, the overall colors are intermediate in range.

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. Color doesn’t matter. If I choose a red filter and a blue filter that allow the same width of colors to pass through, their stripes will disappear at the same path difference. this is Range The color that matters, not the average color.

Which brings us to a startling result: the length of a particle wave is given by the range of colors (and thus energy). Length is not a fixed value for a particular type of particle. Just by digging through our drawers of light sources, we created photons ranging in length from microns (white light) to a few cm (a laser pointer).