“The Creative Force of Mathematical Formulations”: Werner Heisenberg and the Past, Present, and Future of Quantum Theory

This article offers a new argument concerning the relationships between mathematics and physical reality in quantum theory. While, as dedicated to the centenary of Heisenberg’s invention of quantum mechanics, the article contains a historical discussion, it is not historical, but physical and philosophical. Heisenberg’s thinking leading him to QM and beyond is only part of the genealogy of this argument, which also differs from that of Heisenberg and builds on the previous work of the present author. Among the contributions in the article are a new conception of the ultimate reality responsible for quantum phenomena; a new understanding, based on this conception, of the role of mathematics in physics in quantum theory; a critique of Heisenberg’s and all Platonism in quantum theory and beyond; a new perspective on the role of symmetries in quantum field theory; and a new understanding of the relationships between continuity and discontinuity in quantum physics.