Moving Frames of Reference, Relativity and Invariance in Transfer Entropy and Information Dynamics

Abstract: We present a new interpretation of a local framework for informationdynamics, including the transfer entropy, by defining a moving frame of reference for theobserver of dynamics in lattice systems. This formulation is inspired by the idea ofinvestigating “relativistic” effects on observing the dynamics of information - in particular,we investigate a Galilean transformation of the lattice system data. In applying thisinterpretation to elementary cellular automata, we demonstrate that using a moving frameof reference certainly alters the observed spatiotemporal measurements of informationdynamics, yet still returns meaningful results in this context. We find that, as expected,an observer will report coherent spatiotemporal structures that are moving in their frame asinformation transfer, and structures that are stationary in their frame as information storage.Crucially, the extent to which the shifted frame of reference alters the results dependson whether the shift of frame retains, adds or removes relevant information regarding thesource-destination interaction.