On Discrete Physics: a Perfect Deterministic Structure for Reality - And "The Mathematical Derivation of the Fundamental Field Equations of Physics"
Ramin Zahedi · arXiv (Cornell University) · 2015
In part I (pp. 1-10) of this article, I provide an analysis and overview of some notable definitions, works and thoughts concerning discrete physics (a.k.a. digital philosophy, digital physics or digital cosmology) that propose finite, discrete and deterministic characteristics for the physical world. Particular attention is given to theories which suggest cellular automata, as the basis of a (or the only) perfect mathematical deterministic model for the physical reality. In part II (the main part, pp.11-104, Ref. [37]) of the article, I've presented a new algebraic matrix approach based on the theory of Rings (including Integral Domains). On the basis of this approach, by linearization (and simultaneous parameterization) followed by quantization of the relativistic energy-momentum relation, a unique set of tensor field equations are derived. These tensor equations are shown to correspond uniquely to all the main fundamental field equations of physics, including the laws of the fundamental forces of nature (i.e. gravitational, electromagnetic and nuclear field equations) including the relativistic-quantum wave equations, and their generalizations. Notably, this result is primarily mathematical, assuming only the relativistic energymomentum is discrete (as a basic and ordinary quantum mechanical assumption). The general theory of relativity is shown to be obtained by quantization of the special theory of relativity. Moreover, through a systematic procedure and using the field equations derived, and assuming a basic discrete symmetry of physics (i.e. parity symmetry of the free particle fields), I've also shown that the universe cannot have more than four space-time dimensions (the same result for the absence of two spacetime dimensions is obtained). Subsequently, an argument for the asymmetry of the left-handed and right-handed (interacting) particles is presented.