Abstract

To infer ontological features in the domain of a physical theory from its mathematical structures often requires one to consider an interpretation of the structures which goes beyond that necessary to provide an empirically adequate theory. I undertake this task for a set of mathematical structures of classical electromagnetism known as potentials. ;Since their first use in the nineteenth century through to their role within contemporary quantum theory, their interpretation has posed a number of problems and has sometimes been the subject of controversy. The dominant interpretation outside the quantum context since the time of Heaviside and Hertz has been that they function as mere mathematical auxiliaries within the theory with no physical significance other than the electric and magnetic fields derived from them. ;By investigating the role of potentials in the field theory tradition of classical electromagnetism from its origins through to the present, I argue that this position is neither the necessary nor the proper one for interpreting potentials. My investigation begins with Faraday and includes the work of Maxwell, the "Maxwellians," and Weyl. I am able to counter the usual perspective by locating the precise reason for its establishment and showing why these reasons need not hold when the manner in which potentials represent empirical phenomena is properly understood. I further argue that there are good reasons to see the potential structures as vital to understanding the depth structure of electromagnetic theory. On this basis I argue to a number of ontological conclusions about the nature of the classical electromagnetic field. ;I also examine the role of the potentials as representing unquantized fields in quantum mechanics by a close examination of the Aharonov-Bohm effect. I argue that potentials now reveal fields as possessing a global, non-local property, with a sense of non-locality which I distinguish from the usual understanding of non-locality associated with this effect as well as from that associated with measurements on systems with correlated quantum states