5. Finding physics-like behavior
We have tried to imagine the kinds of cellular automaton behavior that would be necessary to model various aspects of physics, and we have sought to find examples of such behavior. A simple example was the successful search for a CA that exhibited spherical propagation of any sort, which was undertaken and completed successfully in 1969. Not long afterwards we found a new approach to creating simple and symmetric UCA. This work culminated in Bank's dissertation [7]. In the early 70's we began to look for reversible models of computation. We recognized the desirability of finding reversible, universal systems. Reversibility makes it easy and natural to create systems that can conserve quantities (such as energy or angular momentum) exactly, despite the fact that translational invariance or angular isotropy cannot be microscopically exact in a discrete cellular space. We then found a path to solving the problem of reversible computation in general with the Fredkin gate and conservative logic [14]. Bennett [15] and Toffoli [8] found other means of solving the same problem. That led to the billiard ball model [14] as a Newtonian mechanics realization of conservative logic, which led to the Margolus rule [9], which is the basis of many interesting applications of cellular automata to physics.
As the armamentarium of known kinds of behavior increased, it became possible to hypothesize new behavior that we could expect to find, in order to match such hypothetical behavior against the needs of modelling physics. The computational approach started with a struggle to see if objects (like particles) could be created, made to persist, move and interact. Once John Conway showed us that possibility (the Game of Life) [2], we continued by looking for ways to represent other basic and simple properties of nature; of space, time, matter and energy. We ask:
"What are the ways in which we can get the right kind of conservation laws?"
"Where will the information that represents a particle's momentum be, and how will it be encoded?"
"How will the RUCA rule support both superposition and interaction?"
"How might the groups that define particle families arise from the lattice neighborhood and the nature of a multi-phase clock?"
"What aspect of the fundamental properties of the RUCA might be related to charge, spin, color, energy, momentum, ...?"
"What is the significance in DM of Planck's constant, speed of light, unit of charge, particle masses, CPT symmetry, ...?"
It is natural to wonder how a DM model of nature, based on a Cartesian lattice, can be Lorentz invariant (be relativistically correct). The space of the DM is certainly not the space of the RUCA. Consider the space in which the space shuttle simulation flies; it is very different than the space in which the computer is (the computer doing the simulation of the space shuttle). We now know of reasonable approaches that allow the physics of DM to be Lorentz invariant even though the process runs on a Cartesian lattice. The lattice remains Cartesian, but measurements made from within the DM model by sending simulated photons back and forth to make measurements can be expected to give relativistically correct results.
[2] M. Gardner, The fantastic combinations of John Conway's new solitaire game of 'Life', Sci. Am. 223 (April 1970) 120-123.
[7] E. Banks, Information processing and transmission in cellular automata, Doctoral Dissertation and Technical Rep6rt MAC TR-81, MIT Project MAC (1971).
[8] T. Toffoli, Cellular automata mechanics, Technical Report 208, Computer and Communication Sciences Department, University of Michigan (1977).
[9] N. Margolus, Physics-like models of computation, Physica D 10 (1984) 81-95.
[14] E. Predkin and T. Toffoli, Conservative logic, Int. J. Theor. Phys. 21 (1982) 219-253.
[15] C. Bennett, Logical reversibility of computation, IBM J. Res. Devel. 6 (1973)