Have you ever noticed drops of coffee skipping across the surface of your coffee as you have been preparing a V60? Or watched as globules of tea dance on the resonating surface of a take-away dragged across a table top? The dancing drops can be seen in this video of coffee being prepared in a V60:
These droplets are the result of some fascinating physics. Although we have encountered them on the Daily Grind before (here and here), the more physicists study them, the more surprises they throw up. While the droplets can be considered particles, they are guided around the coffee pot by the surface waves they create as they bounce. In a sense they are a macroscopic example of wave-particle coexistence. There is a significant temptation to explore whether they have relevance for the concept in quantum physics of wave-particle duality. But another aspect of this wave-particle coexistence has recently been shown to produce a different and unexpected connection. A connection between chaos and computing. And as you can create these droplets in coffee, perhaps we could say a connection between coffee, chaos and computing.
It is fairly simple to create these surface droplets in coffee at home. The secret to getting stable droplets on the surface is to create a vibration, a wave, on the surface of the coffee liquid. The droplets that then form on (or are introduced to) the surface ‘bounce’ on this wave. If you wanted to create surface droplets reliably at home, you would put your coffee on a loud speaker. I suspect that the reason that they appear in a V60 is that the first drops set up a standing wave on the surface of the coffee that acts to support later drops as they encounter the surface. If anyone has a different theory, please do let me know.
But how is it possible that these bouncing droplets connect chaos theory and computing? It is a consequence of the way that the globules of coffee on the surface interact with the waves that guide them around the coffee. Consider for one moment a particle bouncing around a confined space (the traditional example is of a ball on a billiards table). On an ordinary table, the billiard ball will behave quite predictably, start it off aimed roughly at the side of the table and it will bounce in an easily describable way. But if you make the ends curved or put circular objects in the middle of the table for the ball to bounce off, small differences in initial direction can result in large differences in the final path of the ball (for more details and an animation see here). The billiard ball behaves chaotically, and the initial path cannot be found from the final position, there is no way to re-trace the path of the ball, it is not “time-reversible”.
The droplet bouncing on the liquid surface appears to move chaotically, just as the billiard ball on a circular table. However, unlike the billiard ball, the droplet is not a mere particle, but a particle linked to a self-generated surface wave. Each time the droplet bounces on the surface, it creates a small wave, like ripples on a pond. The path taken by the droplet is a complex interaction between this self-generated wave, the vibration keeping the droplet bouncing and the droplet itself. This means that if you are able to shift the phase of the bounce by 180º (meaning, that rather than bounce on an upward motion of the surface, the drop bounces on a downward motion or vice versa), the bouncing droplet not only reverses the direction it travels in, it retraces its path. Rather than behave as the chaotic billiard ball, the path taken by the seemingly chaotic globule of coffee can be exactly reversed.
Which is where the link with computing comes in. It is as if each “bounce” of the droplet “writes” information on the surface of the coffee in the form of a wave. The subsequent bounces “read” the information while the reversal of the direction of the bouncing droplet “erases” the stored information by creating a surface wave opposite to the initial one. The authors of the recent paper suggest that “in that sense [the walking droplet can] be termed as a wave Turing machine”, giving the final link to computing.
Whether or not this turns out to be useful for computing is, to me, almost irrelevant. What is interesting is that such a simple phenomenon, that anyone who makes pour-over coffee should have seen fairly often, is linked to such complex, and fundamental physics. If you would like to read more, there is a great summary article here while the actual paper is here.