  Lattice gauge theories are fundamental to such distinct fields as particle
physics, condensed matter, and quantum information science. Their local
symmetries enforce the charge conservation observed in the laws of physics.
Impressive experimental progress has demonstrated that they can be engineered
in table-top experiments using synthetic quantum systems. However, the
challenges posed by the scalability of such lattice gauge simulators are
pressing, thereby making the exploration of different experimental setups
desirable. Here, we realize a U(1) lattice gauge theory with five matter sites
and four gauge links in classical electric circuits employing nonlinear
elements connecting LC oscillators. This allows for probing previously
inaccessible spectral and transport properties in a multi-site system. We
directly observe Gauss's law, known from electrodynamics, and the emergence of
long-range interactions between massive particles in full agreement with
theoretical predictions. Our work paves the way for investigations of
increasingly complex gauge theories on table-top classical setups, and
demonstrates the precise control of nonlinear effects within metamaterial
devices.

Mesoscale and Nanoscale Physics;Quantum Gases;High Energy Physics - Lattice;Quantum Physics