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

We present a new interpretation of a local framework for information dynamics, including the transfer entropy, by defining a moving frame of reference for the observer of dynamics in lattice systems. This formulation is inspired by the idea of investigating “relativistic” effects on observing the dynamics of information in particular, we investigate a Galilean transformation of the lattice system data. In applying this interpretation to elementary cellular automata, we demonstrate that using a moving frame of reference certainly alters the observed spatiotemporal measurements of information dynamics, 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 as information 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 depends on whether the shift of frame retains, adds or removes relevant information regarding the source-destination interaction.