From the Bohr model to Heisenberg's quantum mechanics

Arkady Plotnitsky

Helge Kragh

Failed attempts to understand the anomalous Zeeman effect contributed to the feeling of crisis that by 1924 characterized parts of the physics community. The solution proposed by W. Heisenberg’s ‘core model’ only raised other problems. Another indication was the state of radiation theory and the uncertain relationship between wave theory and the light quantum, a problem that resulted in the controversial BKS (Bohr–Kramers–Slater) theory of 1924. In the wake of this theory, H. Kramers and Heisenberg constructed a formal theory of dispersion that did not rely on electron orbits but only on observable quantities, in agreement with the ‘quantum mechanics’ programme of M. Born. The development culminated with Heisenberg’s paper of August 1925, which marks the end of the Bohr model and the beginning of quantum mechanics. The chapter reconsiders the crisis and the reasons for it, in particular the role of experimental anomalies.

Daniel R. Bes

Mohsen Razavy

Jan-Åke Larsson

The Heisenberg microscope provides a powerful mental image of the measurement process of quantum mechanics (QM), attempting to explain the uncertainty relation through an uncontrollable backaction from the measurement device. However, Heisenberg's proposed backaction uses features that are not present in the QM description of the world, and according to Bohr not present in the world. Therefore, Bohr argues, the mental image proposed by Heisenberg should be avoided. Later developments by Bell and Kochen-Specker show that a model that contains the features used for the Heisenberg microscope is in principle possible but must necessarily be nonlocal and contextual. In this paper we will reexamine the measurement process within a restriction of QM known as Stabilizer QM (SQM), that still exhibits, for example, Greenberger-Horne-Zeilinger nonlocality and Peres-Mermin contextuality. The reexamination will use a recent extension of SQM, the Contextual Ontological Model (COM), where the system state gives a complete description of future measurement outcomes reproducing the quantum predictions, including the mentioned phenomena. We will see that the resulting contextual Heisenberg microscope backaction can be completely described within COM, and that the associated randomness originates in the initial state of the pointer system, exactly as in the original description of the Heisenberg microscope. The presence of contextuality, usually seen as prohibiting ontological models, suggests that the contextual Heisenberg microscope picture could perhaps be enabled in general QM.