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Optics and Photonics News

Werner Heisenberg’s Path to Matrix Mechanics

Barry R. Masters

Published Jul 3, 2014• 1 citation
Publisher

Abstract

In 1925, Werner Heisenberg—through a combination of intuition and sometimes brilliant guesswork, and strongly influenced by the previous works of Einstein, Ladenburg and Kramers—created his inchoate version of quantum mechanics.
DOI
10.1364/opn.25.7.000042

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Abstract Driven by the idea that a physical theory should only deal with observable quantities, Werner Heisenberg, a young post-doc working with Max Born in Göttingen, who had earlier done his Ph.D. work under Sommerfeld in Munich, was led to introduce a new type of object which represented the transitions between Bohr-Sommerfeld orbits. Max Born realized and recognized these objects as matrices. Together with Pascual Jordan, another post-doc, they worked out a complete theory, matrix mechanics. They completed this work in a few months. We discuss the role of matrix mechanics in the development of quantum mechanics.
In July 1925, exactly one century ago, Werner Heisenberg created Quantum Mechanics (QM) as an invariant-operational formalism by taking as a standpoint the intensive patterns that had been already observed by experimentalists in the lab. One of the few drawbacks of this proposal was the impossibility to conceptualize it in classical terms. Attempting to restore a somewhat classical spatiotemporal representation, six months later, Erwin Schrödinger would present a formalism grounded on a wave equation in configuration space. Taking as a standpoint Schrödinger’s wave mechanics together with the methodological guide of Bohr and logical positivists, Dirac would present in 1930 an axiomatic re-formulation of the theory of quanta that would become known as the “standard” version of QM (SQM). This new version of the theory, that is still today taught in physics classrooms all around the world, would become accepted regardless of its inconsistent narrative as a “recipe” intended (but unable) to predict (binary) measurement outcomes. After pointing out some of the many problems of SQM, in this work we propose to go back to Heisenberg’s matrix mechanics (and also to his understanding of physical theories). We will argue that his matrix mechanics, as an operationally-invariant standpoint, opens the door to a tensorial enlargement of the mathematical formalism capable to account for new phenomena.
Abstract In addition to recounting some contemporary scientific history, Chapter 6 describes the hypothesis that matter, like light, can display wavelike properties, and the creation of the various formulations of quantum mechanics. That matter could have a wavelength was proposed in 1924 by Louis de Broglie, who presented a specific formula for calculating it, one that was verified experimentally in 1927. However, de Broglie’s hypothesis was overshadowed by the creation of three versions of quantum mechanics in 1925/26. The first, denoted matrix mechanics, was proposed by Werner Heisenberg. It was quickly and successfully applied by Wolfgang Pauli to the hydrogen atom. Paul Dirac introduced the next version, which was followed by that of Erwin Schrödinger via a wave equation whose solutions, denoted wave functions, were soon interpreted byMax Born to be related to the probability that certain outcomes or events will occur: classical-physics determinism was thereby removed from quantum mechanics.
Abstract The breakthrough to quantum mechanics was, as we have seen in Episode 37, achieved by Heisenberg in the summer of 1925 and the theory, in the form now known as matrix mechanics, was completed a little later by Born, Heisenberg, and Jordan. From his first days as a student Heisenberg had belonged to groups which worked on quantum theory. He was, so to speak, totally immersed in the field and reached his solution at the age of twenty-three. At the turn of the year 1925/26 quantum mechanics was created again, now clad as wave mechanics [1], by Schrödinger, who did not belong to an active research group in the field and who was then thirty-eight. As soon as it appeared wave mechanics was popular with physicists, because it was based on familiar differential equations and not on matrix formalism which was practically unknown.