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arXiv:2308.04199 · WORLD SCIENTIFIC eBooks

A centennial reappraisal of Heisenberg’s Quantum Mechanics with a perspective on Einstein’s Quantum Riddle.

T. C. Choy

Published Jul 1, 2026• 0 citations
arXivHTMLPDF

Abstract

Heisenberg's breakthrough in his July 1925 paper that set in motion the development of Quantum Mechanics through subsequent papers by Born, Jordan, Heisenberg and also Dirac (from 1925 to 1927) is reexamined through a modern lens. In this paper, we shall discuss some new perspectives on (i) what could be the guiding intuitions for his discoveries and (ii) the origin of the Born-Jordan-Heisenberg canonical quantization rule. From this vantage point we may get an insight into Einstein's Quantum Riddle (Lande1974,Sommerfeld1918,Born1926) and a possible glimpse of what might come next after the last 100 years of Heisenberg's quantum mechanics.

DOI
10.1142/9789819827572_0004

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Heisenberg's breakthrough in his July 1925 paper that set in motion the development of Quantum Mechanics through subsequent papers by Born, Jordan, Heisenberg and also Dirac (from 1925 to 1927) is reexamined through a modern lens. In this paper, we shall discuss some new perspectives on (i) what could be the guiding intuitions for his discoveries and (ii) the origin of the Born-Jordan-Heisenberg canonical quantization rule. From this vantage point we may get an insight into Einstein's Quantum Riddle (Lande1974,Sommerfeld1918,Born1926) and a possible glimpse of what might come next after the last 100 years of Heisenberg's quantum mechanics.
High Resolution Image Download MS PowerPoint Slide In July 1925, Werner Heisenberg submitted a paper to Zeitschrift für Physik entitled ‘On quantum-theoretical reinterpretation of kinematic and mechanical relationships’, thus giving birth to quantum mechanics. In the following year, building on de Broglie’s wave-particle duality, Erwin Schrödinger developed wave mechanics, and soon, Max Born provided a probabilistic interpretation of the wave function. The theory was further enriched by the exclusion principle of Wolfgang Pauli and the uncertainty principle of Heisenberg, which ultimately led to the development of relativistic quantum mechanics by Dirac. The Copenhagen Interpretation created a probabilistic framework for understanding the theory. Over the past century, quantum mechanics has paved the way for advances in quantum field theory, computing, and modern technologies. This historical narrative provides insights into the complex discovery process that led to the development of quantum mechanics, which can potentially guide novel breakthroughs amid challenging conceptual struggles, as seen in the field of artificial intelligence today.
The aim of the famous Born and Jordan 1925 paper was to put Heisenberg’s matrix mechanics on a firm mathematical basis. Born and Jordan showed that if one wants to ensure energy conservation in Heisenberg’s theory it is necessary and sufficient to quantize observables following a certain ordering rule. One apparently unnoticed consequence of this fact is that Schrödinger’s wave mechanics cannot be equivalent to Heisenberg’s more physically motivated matrix mechanics unless its observables are quantized using this rule, and not the more symmetric prescription proposed by Weyl in 1926, which has become the standard procedure in quantum mechanics. This observation confirms the superiority of Born–Jordan quantization, as already suggested by Kauffmann. We also show how to explicitly determine the Born–Jordan quantization of arbitrary classical variables, and discuss the conceptual advantages in using this quantization scheme. We finally suggest that it might be possible to determine the correct quantization scheme by using the results of weak measurement experiments.
The 1925 paper “On quantum mechanics” by M. Born and P. Jordan, and the sequel “On quantum mechanics II” by M. Born, W. Heisenberg, and P. Jordan, developed Heisenberg’s pioneering theory into the first complete formulation of quantum mechanics. The Born and Jordan paper is the subject of the present article. This paper introduced matrices to physicists. We discuss the original postulates of quantum mechanics, present the two-part discovery of the law of commutation, and clarify the origin of Heisenberg’s equation. We show how the 1925 proof of energy conservation and Bohr’s frequency condition served as the gold standard with which to measure the validity of the new quantum mechanics.