A classical theme in number theory involves thinking of arithmetic objects, like rings of integers in number fields, as rings of functions on some geometric objects. These objects behave surprisingly like three-dimensional spaces, which begs the question, what happens if we try to do physics on these spaces? Along these lines, in recent joint work with Sakellaridis and Venkatesh we propose that the duality between electricity and magnetism has as an arithmetic manifestation the relation between L-functions of Galois representations and integrals of automorphic forms known as the relative Langlands program. I will survey these ideas without assuming familiarity with either the physics or the number theory.