Using waves to explore our environment is a widely used paradigm, ranging from seismology to radar technology, and from biomedical imaging to precision measurements. In all these fields, the central aim is to gather as much information as possible about an object of interest by sending a probing wave at it and processing the information delivered back to a detector. In my talk, I will demonstrate that an electromagnetic wave scattered at an object carries locally defined and conserved information about all of the object’s constitutive parameters. Specifically, I will introduce the density and flux of Fisher information for general types of wave fields and identify the non-Hermitian sources and sinks of information through which all these new quantities satisfy a fundamental continuity equation [1]. These theoretical predictions are experimentally verified by studying a movable object embedded in a disordered environment and by measuring the corresponding Fisher information flux at microwave frequencies. These results open up the way to apply concepts from non-Hermitian physics to information theory and open up possibilities for tracking and designing the flow of information even in complex environments. [1] Jakob Hüpfl, Felix Russo, Lukas M. Rachbauer, Dorian Bouchet, Junjie Lu, Ulrich Kuhl & Stefan Rotter, Nature Physics 20, 1294 (2024)