Pitt-CMU Colloquium: Michel Janssen (University of Minnesota)

Arch and Scaffold: Jordan’s statistical transformation theory and von Neumann’s Hilbert space formalism

In early 1927, Paul Dirac and Pascual Jordan, independently of one another, published their versions of a general formalism tying the various forms of the new quantum theory together and giving the theory’s statistical interpretation in full generality. This formalism has come to be known as the Dirac-Jordan (statistical) transformation theory. A few months later, in response to these publications, John von Neumann published his Hilbert space formalism for quantum mechanics. The relation between these two formalisms can be captured in terms of a metaphor for theory change in which one theory serves as the scaffold for the arch of another theory. What is unclear in this case is which formalism serves as the scaffold and which one as the arch. Did von Neumann build an arch on the scaffold built by Jordan? Or did von Neumann build a scaffold to prevent the arch built by Jordan from collapsing? Either way, the arch-and-scaffold metaphor is a promising alternative to Thomas Kuhn's paradigm shifts for understanding theory change.

Note: Based on joint work with Anthony Duncan (University of Pittsburgh)