Our friend and colleage Henry Minsky has written a short paper describing some of his discoveries studying the BusyBoxes cellular automata. It’s worth noting that this work brings up intriguing points that relate to digital physics. The “particles” he creates rotate in a circle at a frequency that is proportional to their translational velocity:
The utterly fantastic success of Mathematical Analysis (the mathematics of continuous functions of continuous variable) as applied to physics and engineering, tends to blind us to the possibility that the ultimate nature of space and time might be discrete. It is enlightening to recall the resistance of prominent physicists, such as Mach, to the atomic theory. But there is a simple reason why a discrete system can be well modeled by Mathematical Analysis. Completely discrete space-time-state physics, where quantities such as momentum, angular momentum and energy are also discrete, and where those same quantities are conserved (perhaps exactly, as is obviously true of electric charge) will exhibit symmetries, asymptotic to continuous. (A consequence of Noether’s Theorem). As a result, the gross behavior of such microscopically discrete space-time-state systems will be asymptotically well modeled by mathematical analysis. Today, we know that electric charge, angular momentum, matter, photons etc. are discrete, but it’s hard for almost everyone to imagine that space and time could be also be discrete. The major stumbling block is the mathematical beauty and simplicity of the assumption of translation symmetry… along with the absence of any experimental evidence to the contrary. However, I am certain that translation symmetry is an informational impossibility!
The rules of this Blog involves some key assumptions: At some microscopic level, we assume that physical space, time and state are all, ultimately, discrete and deterministic. Further, we also assume that there are no physical infinities, infinitesimals, continuity, differentiability, nor any local sources of true non-deterministic behavior. Such concepts play no role in models we shall discuss. Thus, we assume that all information must have finite and discrete means of its representation and we assume that the evolution of state is governed by local, deterministic rules.
Given all of the constraints, we nevertheless wish to solicit posts to this blog. While we will not indulge in arguments about the ground rules, we believe that there are reasonable explanations as to how sub-microscopic systems, with all the constraints we are imposing, could nevertheless result in higher level processes that behave in ways consistent with the known laws of physics.
This blog is for the exchange of ideas related to discrete models of the most microscopic fundamental processes in phyics.