Research Assistant, Aesthetics and Computation Group, MIT Media Laboratory.

From humble and unfocused beginnings, this project rapidly evolved into something grandiose, ill-posed, and hard. After much thrashing about, speculation, agonizing, revision, and study of quantum mechanics, it became the relatively modest research project it is today. It was a very interesting ride.

The origin of this project is in my interest in information theory, discrete systems, modeling, and a nagging doubt about the validity of real numbers. It is very appealing (for me) to think that the universe might be bounded in information and energy, and that there might be a fundamental connection between the theory of bits (discrete computation) and the theory of atoms.

Why should the universe be discrete? Well, as Neil pointed out in class lectures, any model that relies on real numbers requires infinite information (and therefor infinite energy) for its representation. Since there appear to be bounds on the energy of any physical system (the universe included) this is aesthetically displeasing. I am told (though I do not yet know enough quantum to verify) that there are hints of a discrete structure at a very fine scale in quantum gravity, but in broader terms the history of modern physics has been a transition from continuous representations to quantized, discrete ones. And then there is that troubling similarity between the equations for thermodynamic entropy and information theoretical entropy...

There are also good reasons why things may not be discrete, as Marvin Minsky points out in "Cellular Vacuum." For one, a lattice implies a distinguished reference frame. For another, regular lattices are not rotationally invariant - things "look different" as one looks in different directions. And a discrete lattice imposes an upper bound on momentum. Of course, it has also been demonstrated that cellular automata are computationally general, so given a big enough system and enough time, one could "simulate" a continuous universe with arbitrary precision...

Trying to intuit the fundamental rewrite rules of the universe down at the Plank scale is a pretty hard problem, so I eventually decided on something simpler; to create a discrete, finite-precision model of the Schroedinger wave equation. After doing the literature search, I found that others had worked on this problem as well. I eventually settled on a paper called "Quantum lattice-gas models for the many-body Schroedinger equation" by Bruce M. Boghosian and Washingon Taylor IV (quant-ph/9701019 v2 8 Mar 1997) as my primary reference for this project.

The model I ended up constructing is somewhere in between the "classical" lattice gas/CA model I originally had in mind and the quantum computer q-bit/Hilbert space model described by Boghosian and Taylor. It might be called a discrete simulation of a quantum lattice gas. The simulation is discrete because it takes place on a classical digital computer (I hope to have direct control over the precision soon) and the update rules were derived from the q-bit/Hilbert space rules. This was a very interesting exercise. It involved:

- Learning enough quantum to understand the problem I was posing for myself, i.e. what does the Schroedinger wave describe and how is it used. For someone without any formal quantum mechanics background, this was very interesting in its own right.
- Learning still more quantum so that I could begin to understand the distinction between a quantum and classical computer. Quantum computing is fascinating, so this was also very interesting.
- Reviewing a lot of information theory and cosmology, although that did not enter into the final solution.
- Further developing the Sol programming language used to implement the solutions.

- "Quantum lattice-gas models fo the many-body Schroedinger equation," Bruce M. Boghosian and Washington Taylor IV. International Journal of Modern Physics C, vol.8, no.4, p705-16.
- Bibliography, including abstracts. Not a comprehensive list of sources, yet.
- SchrodingerOneApplet. This applet demonstrates a lattice-gas implementation of the Schrodinger wave equation for a single particle.
- SchrodingerOne2Applet. This applet is a variation on SchrodingerOneApplet showing the wave function propogating mostly in one direction.
- SchrodingerOne3Applet A variation on SchrodingerOneApplet with the addition of a quadratic potential well.