Structure without Law: From Heisenberg's Matrix Mechanics to Structural Nonrealism

The article introduces a new concept of structure, defined, echoingWheeler's concept of'law without law,' as a'structure without law', and a new philosophical viewpoint, that of structural nonrealism, both of which, the article argues, emerged with Heisenberg's discovery of quantum mechanics and Bohr's interpretation of it in terms of complementarity. The article takes advantage of the circumstance that any instance of quantum data or, in present day terms, quantum information is a'structure' -- an organization of elements, ultimately bits, of classical information, manifested in measuring instruments. While, however, this organization can, along with the observed behavior of measuring instruments, be described by means of classical physics, it cannot be predicted by means of classical physics, but only probabilistically or statistically by means of quantum mechanics or quantum field theory (or possibly some alternative theories within their scope). By contrast, the emergence of this information and of this structure cannot, in the present view, be described by either classical or quantum theory, or possibly by any other means, which leads to the concept of'structure without law' and the viewpoint of structural nonrealism.