Computational Wave Field Theory

We propose a framework for thinking about computation in the way physicists think about quantum mechanics: as the dynamics of a wave-like field, with events occurring probabilistically according to the squared amplitude of that field at each location. The proposal is not that computation is quantum mechanics, nor that physical quantum mechanics gives rise to computation. Computation is treated as a domain in its own right --- formal systems, cellular automata, neural networks, brains, distributed systems --- and the claim is that this domain admits a wave-mechanical description with structure parallel to (but distinct from) the wave mechanics of physical particles. The framework introduces a substrate-relative quantum of action playing the role analogous to Planck's h, and a substrate-relative speed bound c_c analogous to the speed of light; both depend on the substrate and span many orders of magnitude across the substrates considered.