Wave-Based Turing Machine: Time Reversal and Information Erasing [pdf]
blog.espci.fr
blog.espci.fr
Edit: relevant passage from Cryptonomicon:
The sand at the surf line has been washed flat. A small child’s footprints wander across it, splaying like gardenia blossoms on thin shafts. The sand looks like a geometric plane until a sheet of ocean grazes it. Then small imperfections are betrayed by swirls in the water. Those swirls in turn carve the sand. The ocean is a Turing machine, the sand is its tape; the water reads the marks in the sand and sometimes erases them and some times carves new ones with tiny currents that are themselves a response to the marks. Plodding through the surf, Waterhouse strikes deep craters in the wet sand that are read by the ocean. Eventually the ocean erases them, but in the process its state has been changed, the pattern of its swirls has been altered. Waterhouse imagines that the disturbance might somehow propagate across the Pacific and into some super-secret Nipponese surveillance device made of bamboo tubes and chrysanthemum leaves; Nip listeners would know that Waterhouse had walked that way. In turn, the water swirling around Waterhouse’s feet carries information about Nip propeller design and the deployment of their fleets—if only he had the wit to read it. The chaos of the waves, gravid with encrypted data, mocks him.
> Droplets bouncing around on a surface is apparently a great way to think about quantum mechanics, or at least some system with a wave encoding information about a discrete object. Here's a nice video showing how a bouncing particle on a liquid surface has a chaotic trajectory. The probability distribution of that particle's position ends up being something like the most unstable mode of the boundaries for the particle. But this paper shows that the droplet's trajectory can be totally reversed, even though the trajectory is chaotic. This is because the droplet's trajectory is completely encoded in the resonating wave it's riding. In other words, the system totally remembers what the droplet is doing and that memory can be accessed and then totally reversed. A great physical (well, MORE physical than usual) example of what memory is.