Statistical interpretation of various formulations of quantum mechanics

John Hasbrouck Van Vleck

Max Born

Guido Bacciagaluppi

At the 1927 Solvay conference Born and Heisenberg presented a joint report on quantum mechanics. I suggest that the significance of this report lies in that it contains a ‘final’ formulation of the statistical interpretation of quantum mechanics that goes beyond Born’s origi-nal proposal. In particular, this formulation imports elements from Heisenberg’s work as well as from the transformation theory of Dirac and Jordan. I suggest further a reading of Born and Heisenberg’s position in which the wave function is an effective notion. This can make sense of a remarkable aspect of their presentation, namely the fact that the ‘quantum mechanics’ of Born and Heisenberg apparently lacks wave function collapse.

Max Born

Jeffrey Alan Barrett

Abstract The book starts with a description of classical mechanics then discusses the quantum phenomena that require us to give up our commonsense classical intuitions. We consider the physical and conceptual arguments that led to the standard von Neumann-Dirac formulation of quantum mechanics and how the standard theory explains quantum phenomena. This includes a discussion of how the theory’s two dynamical laws work with the standard interpretation of states to explain determinate measurement records, quantum statistics, interference effects, entanglement, decoherence, and quantum nonlocality. A careful understanding of how the standard theory works ultimately leads to the quantum measurement problem. We consider how the measurement problem threatens the logical consistency of the standard theory then turn to a discussion of the main proposals for resolving it. This includes collapse formulations of quantum mechanics like Wigner’s extension of the standard theory and the GRW approach and no-collapse formulations like pure wave mechanics, the various many-worlds theories, and Bohmian mechanics. In discussing alternative formulations of quantum mechanics we pay particular attention to the explanatory role played by each theory’s empirical ontology and associated metaphysical commitments and the conceptual trade-offs between theoretical options.

Gary E. Bowman

This chapter first discusses statistical techniques and concepts — including probability, probability distribution, average and expectation value, and uncertainty — that are relevant to quantum mechanics. The physical interpretation of probability in quantum mechanics is then discussed. It is argued that by adopting the statistical interpretation, one can think clearly about quantum mechanics without committing to any of the various physical interpretations, and without tackling the conceptual hurdles that they present. The history and substance of interpretational issues in quantum mechanics is then briefly discussed, the point being to introduce these profound, unresolved questions without taking sides in ongoing scientific debates. The chapter closes with a personal reflection on Albert Einstein, the most revered and fascinating figure in physics, and the one most famously at odds with the conventional interpretation of quantum mechanics.