| Cellular automata and the foundations of physics Peter Rowlands1; 1UNIVERSITY OF LIVERPOOL, Liverpool, United Kingdom; PAPER: 58/Mathematics/Plenary (Oral) SCHEDULED: 11:30/Wed. 30 Nov. 2022/Arcadia 3 ABSTRACT: <p>Previous work by the author has proposed a foundation for physics based on a Klein-4 symmetry between the four fundamental parameters mass, time, charge and space. These parameters and the algebras which specify their properties can then be seen as generated by a computational universal rewrite system, based on a zero totality state for the universe. The algebras, remarkably, combine to a 64-component group which is isomorphic to the gamma algebra of the Dirac equation, the equation which defines the fundamental (fermionic) state in physics. A very powerful version of relativistic quantum mechanics emerges from the application of this algebra, based on a state vector which is nilpotent or squaring to zero. In view of the various proposals made for founding physics on the behaviour of cellular automata, and the claim that long-range order in automata is only possible via the Klein-4 group (1), it is proposed to investigate possible connections between the Klein-4 group as used by the author in fundamental physics and the Klein-4 group as it becomes relevant to cellular automata, along with the computational developments with which they are each connected.</p> References: <p>1 Mainzer, K. and Chua, L., The Universe as Automaton From Simplicity and Symmetry to Complexity, Springer, 2012</p> |
