In 1909, Einstein derived a formula for the mean square energy fluctuation in blackbody radiation. This formula is the sum of a wave term and a particle term. In a key contribution to the 1926 Dreim¨.

In October 1924, The Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck used Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum formulae for the emission, absorption, and dispersion of radiation. The paper is similar but in many ways superior to the well-known paper by Kramers and Heisenberg published the following year that is widely credited (...) to have led directly to Heisenberg's Umdeutung paper. As such, it clearly shows how strongly the discovery of matrix mechanics depended on earlier work on the application of the correspondence principle to the interaction of matter and radiation. (shrink)

In early 1927, Pascual Jordan published his version of what came to be known as the Dirac-Jordan statistical transformation theory. Later that year and partly in response to Jordan, John von Neumann published the modern Hilbert space formalism of quantum mechanics. Central to both formalisms are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in the new (...) theory. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identification of sets of canonically conjugate variables, i.e., p’s and q’s. Jordan ran into serious difficulties when he tried to extend his approach from quantities with fully continuous spectra to those with wholly or partly discrete spectra. For von Neumann, not constrained by the analogy to classical physics and aware of the daunting mathematical difficulties facing the approach of Jordan ), the solution of a problem in the new quantum mechanics required only the identification of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p’s and q’s. Related to their disagreement about the appropriate general formalism for the new theory, Jordan and von Neumann stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan was the first to state those rules in full generality, von Neumann rephrased them and then sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan’s approach by Hilbert, von Neumann, and Nordheim. We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics. (shrink)