Something Deeply Hidden: The Dual Dynamical Foundation of Orthodox Quantum Mechanics

          @misc{ scivideos_PIRSA:25100088,
            doi = {10.48660/25100088},
            url = {https://pirsa.org/25100088},
            author = {},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Something Deeply Hidden: The Dual Dynamical Foundation of Orthodox Quantum Mechanics},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2025},
            month = {oct},
            note = {PIRSA:25100088 see, \url{https://scivideos.org/index.php/pirsa/25100088}}
          }
          

Abstract

The two postulates of orthodox quantum mechanics that jointly exhaust the change of the quantum state over time—process 1, the collapse postulate, and process 2, the unitary dynamics—evoke the question: why two postulates, and why these two? The scholarship on the foundations of quantum theory has been largely conditioned, to borrow from Quine’s apt expression, by two dogmas. One is that the collapse postulate was appended to the formalism ad hoc, merely to account for observations, and the other is that the two processes stand in hopeless contradiction. In this talk I will show—on the basis of Studies in History and Philosophy of Science 109 (2025): 89–105, co-authored with Ricardo Correa da Silva—that both dogmas are ill-founded. They are, I will argue, myths. Von Neumann postulated nothing arbitrarily: his basic constructive assumption—the equivalence between Matrix and Wave Mechanics—renders the “dual dynamics,” as he called his processes 1 and 2, a logical necessity. The true paradox lies in the nature of the equivalence: how can Matrix Mechanics—a theory of discontinuous jumps—and Wave Mechanics—a theory built from the ground up on the notion of continuity—be equivalent? They rather seem—here lies the root of the second dogma—self-contradictory. Von Neumann himself asked why the unified quantum-theoretical formalism requires a dual dynamics, but he could not articulate a proper answer within his static Hilbert space framework. A proper answer must be grounded on a dynamical principle—and I will argue that we have identified it. I will show the exact sense in which Matrix Mechanics implicitly contains Wave Mechanics and vice versa, the exact sense in which they are versions of the same theory: their dynamics, though different, are unified at a deep level—there is a single variational structure determining the dual dynamics. It is generally taken for granted in physics that the dynamics of a physical theory must follow from the action functional, and, in this talk, I will show that orthodox quantum mechanics is no exception to this golden rule. If the quantum-theoretical formalism requires “a peculiar dual dynamics,” as von Neumann called it, that is because the formalism is based on the deeper dynamical symmetry that entails the equivalence of Matrix and Wave Mechanics: the dual dynamics of the quantum-theoretical formalism is completely determined by the constraints of a dual action.