Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2603.15638

The Birth of Quantum Mechanics and the Dirac Equation

Volodimir Simulik·Denys I. Bondar
View original source ↗Read source document ↗Export metadata ↓

Abstract

The year 2025 marked the centennial of quantum mechanics, inaugurated by Heisenberg's matrix formulation and the foundational contributions of Pauli, Schrodinger, and Dirac. Concurrently, 2026 marks the centennial of the Klein - Gordon equation, the second-order relativistic wave equation from which both the Schrodinger and Dirac equations were derived. This article supplements the recent review published in J.Phys. A: Math.Theor.,58 (2025) 053001 by providing a more detailed examination of the formative period 1925 - 1928, with particular attention to contributions that have received insufficient recognition in the standard narrative. We reconstruct Kramers' independent derivation of the Dirac equation - obtained essentially simultaneously with Dirac's own result yet unpublished for seven years - and discuss its relation to Van der Waerden's group-theoretical approach. The role of Charles Galton Darwin in elucidating the physical content of the Dirac equation is also highlighted. In addition, we present two modern derivations not catalogued in the earlier review: one based on Operational Dynamical Modeling, which deduces the Dirac equation from relativistic Ehrenfest relations and the canonical commutation algebra, and one rooted in the Madelung hydrodynamic formulation. Three broad periods of quantum theory development -- foundational, consolidation, and the modern era of quantum information -- are briefly surveyed.

Explore related subjects

physics.hist-phmath-phmath.MPquant-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Volodimir Simulik, Denys I. Bondar. 2026-04-18. The Birth of Quantum Mechanics and the Dirac Equation. https://arxiv.org/abs/2603.15638

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Deriving Ontological Statements from the Unnatural Higgs Mass

We provide novel, metatheoretical arguments strengthening the position that the naturalness problem of the light Higgs mass is a pseudo-problem: Under one assumption, no physics beyond the standard model of particle physics is needed to explain the small value of the Higgs boson. By evaluating previous successes of the guiding principle of technical naturalness, we restrict its applicability to non-fundamental phenomena in the realm of provisional theories within limited energy scales. In view of further breaches of autonomy of scales in apparently fundamental phenomena outside particle physics, the hierarchy problem of the Higgs mass is instead reinterpreted as an indication of the ontologically fundamental status of the Higgs boson. Applying the concept of robustness of theoretical elements under theory changes by Worrall and Williams justifies this seemingly contradictory attribution within the effective theories of the standard model of particle physics. Moreover, we argue that the ongoing naturalness debate about the Higgs mass is partly based on the adherence to the methodology of effective theories (often claimed to be universally applicable), for which there is no justification when dealing with presumably fundamental phenomena such as the Higgs mechanism, even if it is embedded into an effective theory.

physics.hist-ph↗
arXiv2026

Stagnant Lakatosian Research Programmes

We propose an extension of the classical dichotomous categorization of research programmes into progress and degeneration according to Lakatos in the form of a neutral third category: the stagnant research programme. First, a critical examination of the primary literature with its often criticized definitional gaps justifies such a category. Through a generic derivation of criteria for stagnant programmes, a clear demarcation from progressive and degenerative ones is achieved. An empirical cross-check is subsequently employed for support: Both a series of examples from fundamental physics and a general analysis of today's research landscape also suggest on an empirical level the need to go beyond the traditional Lakatosian conception. Attributing stagnation is entirely in line with Lakatos' original intentions, which aimed not to hastily discard promising research but to exercise patience until the lifting of certain external constraints potentially enables progress once again.

physics.hist-ph↗
arXiv2026

A not-too-simple solution to Goodman's New Riddle of induction

I review the works of Gärdenfors (1990) and Scorzato (2013) and show that their combination provides an elegant solution of Goodman's new riddle of induction. The solution is based on two main ideas: (1) clarifying what is expected from a solution: understanding that philosophy of science is a science itself, with the same limitations and strengths as other scientific disciplines; (2) understanding that the concept of complexity of a model's assumptions and the concept of direct measurements must be characterized together. Although both measurements and complexity have been the subject of a vast literature, within the philosophy of science, essentially no other attempt has been made to combine them. The widespread expectation, among modern philosophers, that Goodman's new riddle cannot be solved is not defensible without a serious exploration of such a natural approach. A clarification of this riddle has always been very important, but it has become even more crucial in the age of AI.

physics.hist-ph↗