Computational Wave Field Theory
O. Cem Yilmaz
This book proposes a way of thinking about computation the way physicists think about quantum mechanics. In that picture, a computation is the dynamics of a wave-like field. Events happen at random. If one happens at a given tick, the chance that it happens at each place is the squared amplitude of the field there. The book doesn’t claim that computation is quantum mechanics. Nor does it claim that physical quantum mechanics gives rise to computation. It treats computation as a domain in its own right, e.g., formal systems, cellular automata, neural networks, brains and distributed systems. Each concrete system that carries out a computation, such as a cellular automaton or a brain, is called a substrate. The claim is that this domain has a wave-mechanical description of its own. Its structure runs parallel to the wave mechanics of physical particles, but it is a distinct theory. The framework introduces a substrate-relative quantum of action ℏ𝑐, which plays the role of Planck’s ℏ. It also introduces a substrate-relative speed limit 𝑐𝑐, the analog of the speed of light. Both depend on the substrate, and across the substrates the book considers they span many orders of magnitude. TheframeworkiscalledComputational Wave Field Theory, abbreviatedCWF.Initscurrent form it has two levels, and the key to reading it is to keep them apart. The first level is operational. CWFdefinesasubstrate-relativewavemodelforcomputationalevents. Thesecond level is explanatory. It asks why such a wave is the right object, and the present answer comes in layers. First, computational irreducibility conjecturally explains the wave’s epistemic part, the part that encodes what an observer can know. (Irreducibility means there is no shortcut, so the only way to learn the outcome is to run the computation. How far the epistemic part compresses tracks the causal structure.) Second, in the book’s model theorems, self-reference explains the wave’s genuinely complex phase. Third, holographic encoding, which stores information redundantly on a boundary, explains a substrate’s gravity-like structure. These three sources are distinct and separable. Irreducibility and encoding are two of the book’s three substrate axes, and the remaining axis is dynamical disorder. Self-reference sits off those axes. The book’s long-range target is that nature sits where all three sources meet. The operational postulate lets the framework run.
•Jan 1, 2026•0 citations