A curious observer’s guide to quantum mechanics, pt. 3: Rose colored glasses 

Thus far, we’ve seen particles transfer as waves and realized {that a} single particle can take a number of, extensively separated paths. There are a variety of questions that naturally arises from this conduct—considered one of them being, “How huge is a particle?” The reply is remarkably refined, and over the subsequent two weeks (and articles) we’ll discover completely different elements of this query.

In the present day, we’ll begin with a seemingly easy query: “How lengthy is a particle?”

Go lengthy

To reply that, we want to consider a brand new experiment. Earlier, we despatched a photon on two very completely different paths. Whereas the paths had been extensively separated in that experiment, their lengths had been an identical: every went round two sides of a rectangle. We will enhance this setup by including a few mirrors, permitting us to progressively change the size of one of many paths.

When the paths are the identical size, we see stripes simply as we did within the first article. However as we make one of many paths longer or shorter, the stripes slowly fade. That is the primary time we’ve seen stripes slowly disappear; in our earlier examples, the stripes had been both there or not.

We will tentatively affiliate this fading of the stripes as we modify the trail size with the size of the photon touring down the trail. The stripes solely seem if a photon’s waves overlap when recombined.

But when particles journey as waves, what will we even imply by a size? A helpful psychological picture could also be dropping a pebble right into a clean pool of water. The ensuing ripples unfold out in all instructions as a set of rings. Should you draw a line from the place the rock fell via the rings, you’ll discover there are 5 to 10 of them. In different phrases, there’s a thickness to the ring of waves.

One other approach to have a look at it’s as if we had been a cork on the water; we’d sense no waves, a interval of waves, then clean water once more after the ripple had handed. We’d say the ‘size’ of the ripple is the space/time over which we skilled waves.

Equally we are able to consider a touring photon as being a set of ripples, a lump of waves coming into our experiment. The waves naturally cut up and take each paths, however they will solely recombine if the 2 path lengths are shut sufficient for the ripples to work together when they’re introduced again collectively. If the paths are too completely different, one set of ripples may have already gone previous earlier than the opposite arrives.

This image properly explains why the stripes slowly disappear: they’re sturdy when there’s good overlap, however fade because the overlap decreases. By measuring how far till the stripes disappear, we now have measured the size of the particle’s wave ripples.

Digging via the sunshine bulb drawer

We will undergo our traditional experiments and see the identical options we noticed earlier than: turning the photon fee approach down (which produces a paintball pointillism of stripes), altering the colour (bluer colours imply nearer spacing), and so on. However now we are able to additionally measure how the stripes behave as we modify the trail size.

Whereas we frequently use lasers to generate particles of sunshine (they’re nice photon pea shooters), any form of mild will do: an incandescent mild bulb, an LED room mild, a neon lamp, sodium streetlights, starlight, mild handed via coloured filters. No matter form of mild we ship via creates stripes when the trail lengths match. However the stripes fade away at distances that vary from microns for white mild to a whole lot of kilometers for the very best high quality lasers.

Mild sources with distinct colours are likely to have the longest ripples. We will examine the colour properties of our mild sources by sending their mild via a prism. A number of the mild sources have a really slim vary of colours (the laser mild, the neon lamp, the sodium streetlight); some have a large rainbow of colours (the incandescent bulb, LED room mild, starlight); whereas others equivalent to daylight despatched via a coloured filter are intermediate within the vary of composite colours.

What we discover is that there’s a correlation: the narrower the colour vary of the sunshine supply, the longer the trail distinction may be earlier than the stripes disappear. The colour itself doesn’t matter. If I select a purple filter and a blue filter that permit the identical width of colours via, they may have their stripes disappear on the identical path distinction. It’s the vary of shade that issues, not the typical shade.

Which brings us to a slightly startling consequence: the size of a particle wave is given by the vary of colours (and thus energies) it has. The size isn’t a set worth for a specific form of particle. Simply by digging via our drawer of sunshine sources, we made photons with lengths starting from microns (white mild) to some cm (a laser pointer).