An Information Physics Derivation of Equations of Geodesic Form from the Influence Network

Abstract: Information physics considers physical laws to result from the consistent quantification and processing of information about physical phenomena. In previous efforts, one of us (Knuth) has shown that a simple model of particles that directly influence one another results in a partially ordered set referred to as the influence network, from which emerge the Minkowski metric and Lorentz transformations of special relativity. Here, we extend earlier work on receipt of influence to the case of one particle influencing another, finding that this gives rise to equations of the form of geodesic equations from general relativity in 1+1 dimensions. Future work will test the equivalence of the current result to general relativity in 1+1 dimensions.