ar X iv : 1 51 2 . 02 09 4 v 1 [ he p - ph ] 7 D ec 2 01 5 Unification of Force and Substance ∗

Maxwell’s mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as “dynamical systems”. That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly inspiring. A deep aspect of Maxwell’s work is its use of redundant potentials, and the associated requirement of gauge symmetry. Those concepts have become central to our present understanding of fundamental physics, but they can appear to be rather formal and esoteric. Here I discuss two things: The physical significance of gauge invariance, in broad terms; and some tantalizing prospects for further unification, building on that concept, that are visible on the horizon today. If those prospects are realized, Maxwell’s vision of the unity of field and substance will be brought to a new level. As we celebrate the sesquicentennial of Maxwell’s equations, there are many facets to celebrate: the triumph of the field concept, the roots of relativity, the cornerstone of a host of technologies. In many ways, the Maxwell equations mark the beginning of modern physics, and indeed of the modern world. Here I will discuss a special, hidden theme of Maxwell’s work, primarily important for fundamental physics, whose profundity only emerged gradually, and may still not stand fully revealed even today. This is the concept of gauge symmetry. Gauge symmetry is perhaps the supreme realization of Heinrich Hertz’s famous tribute to the Maxwell equations: ∗Talk at Royal Society Symposium, “Unifying Physics and Technology in the Light of Maxwell’s Equations”, November 2015.