Statistical Interpretation

Arkady Plotnitsky

Alexander A. Pechenkin

In his 1939 Lectures, the prominent Soviet physicist L. I. Mandelstam proposed an interpretation of quantum mechanics that was understood in different ways. To assess Mandelstam's interpretation, we classify contemporary interpretations of quantum mechanics and compare his interpretation with others developed in the 1930s (the Copenhagen interpretation and the statistical interpretations proposed by K. R. Popper, H. Margenau, and E. C. Kemble). We conclude that Mandelstam's interpretation belongs to the family of minimal statistical interpretations and has much in common with interpretations developed by American physicists. Mandelstam's characteristic message was his theory of indirect measurement, which influenced his discussion of the “reduction of the wave packet” and the Einstein, Podolsky, and Rosen argument. This article also reconstructs what lay behind Mandelstam's interpretation of quantum mechanics. This was his operationalism, by virtue of which his interpretation resembled Kemble's, in which the statistical and Copenhagen views had been combined. Like Popper and Margenau, Mandelstam followed R. von Mises's empirical conception of probability. Mandelstam, like the other proponents of the statistical approach to quantum mechanics, was affected by the culture of macroscopic experimentation with its emphasis on statistical (collective) measurement.

Folkert Kuipers

Holger Friedrich Hofmann

In a recent paper (arXiv:1111.3328), Pusey, Barrett and Rudolph claim to prove that statistical interpretations of quantum mechanics do not work. In fact, their proof assumes that all statistical interpretations must be based on hidden variable realism. Effectively, the authors demand from the start that reality must be decided by mathematics, and not by measurements. If this unjustified assumption is dropped, the quantum formalism has a natural statistical interpretation that fully explains the paradox presented by the authors. It is therefore possible to conclude that the paradox actually supports the statistical interpretation, demonstrating once more that quantum mechanics should not be explained by measurement independent realities that are never observed and therefore lie beyond the reach of empirical tests.

Linda Wessels

When Max Born introduced his statistical interpretation of wave mechanics in mid-1926, the reactions were mixed. His most recent collaborator, Pascual Jordan, was delighted; his former assistant, Werner Heisenberg, was horrified. The interpretation served as grist for Neils Bohr's philosophical mill. For Bohr's former collaborator, John Slater, it inspired a strange hybrid interpretation, a sort of statistical version of Schrödinger's electrodynamic model. What was the interpretation that engendered these varied reactions? Neither Born nor most of his contemporaries saw in it anything that even suggests the interpretation that we now associate with his name. Rather, it was another former assistant of Born's, Wolfgang Pauli, with eyes as sharp as his tongue, who saw in Born's work the idea that |Ψ(q)| represents the probability distribution for position.