Nature Abhors an Empty Vacuum,

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, well construct analogs of particles and fields -- and ask what it would mean for these to satisfy constraints like conservation of momentum. In each case classical mechanics will break down -- on 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.