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Imagine a crystalline world of tiny, discrete "cells", each knowing only what its nearest neighbors do. Each volume of space contains only a finite amount of information, because space and time come in discrete units. In such a universe, we'll construct analogs of particles and fields ??d ask what it would mean for these to satisfy constraints like conservation of momentum. In each case classical mechanics will break down ?? scales both small and large, and strange phenomena emerge: a maximal velocity, a slowing of internal clocks, a bound on simultaneous measurement, and quantum-like effects in very weak or intense fields. This fantasy about conservation in cellular arrays was inspired by this first conference on computation and physics, a subject destined to produce profound and powerful theories. I wish this essay could include one such; alas, it only portrays images of what such theories might be like. The "cellular array" idea is popular already in such forms as Ising models, renormalization theories, the "Game of Life" and Von Neumann's work on self-producing machines. This essay exploits many unpublished ideas I got from Edward Fredkin. The ideas about field and particle are original; Richard Feynman persuaded me to consider fields instead of forces, but is not responsible for my compromise on potential surfaces. I also thank Danny Hillis and Richard Stallman for other ideas. |
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