Heisenberg's Quantum Mechanics

Seyyed Hedayat Sajadi

Heisenberg is one of the founders of quantum mechanics, and one of the pioneers and intellectual leaders of the Copenhagen interpretation of quantum mechanics. He proposed in two seminal papers in 1925 and 1927, the fundamentals of matrix mechanics (1925) as the first formalism of quantum mechanics, and then the uncertainty relations (1927) as one of the essential components of the Copenhagen interpretation. The purpose of this paper is to formulate Heisenberg's philosophical approaches during the formation of quantum mechanics and its Copenhagen interpretation. The main question of the paper is whether philosophical approaches can be formulated in the development of quantum mechanics through Heisenberg's works? To answer this question, two seminal papers by Heisenberg (1925 and 1927) are examined. The research method of the paper is based on the content analysis of the text (physics) of Heisenberg's papers. The findings of this study show that three crucial principles - observability, correspondence, and analogy-can be formulated from Heisenberg's 1925 paper, which has played a key role in the formation of the fundamentals of matrix mechanics. Moreover, from his 1927 paper, some issues are addressed including interpretation, understanding and classical-quantum relation, the role of experience and measurement, the subject of causality, as well as reality. Finally, it is concluded that through these works of Heisenberg, four philosophical approaches can be formulated including empiricism, Unificationism, indeterminism, and anti-causality, as well as anti-realism, which themselves include other sub-approaches.

Luis de la Peña, Ana Marı́a Cetto, Andrea Valdés Hernández

Caio Lima Firme

This chapter introduces Heisenberg’s trajectory from old quantum mechanics towards his quantum matrix mechanics. It shows his partnership with Born and for the study of the helium atom and molecules under the old quantum theory and his work on the core model to account for the anomalous Zeeman effect in collaboration with Landé. The collaboration between Heisenberg Kramers to present the treatment between matter and radiation under the scope of the old quantum mechanics is also displayed. Then, afterwards, it is shown the birth of the matrix mechanics by its three initial papers in 1925: the Heisenberg’s paper where he replaced the motion of the electron into its transition; the Born and Jordan’s paper where they placed Heisenberg equation into matrices and found the corresponding equation of motion and the commutator between linear momentum and position of the electron; the Heisenberg, Jordan and Born’s paper where they obtained the diagonal elements of the Hamiltonian matrix (the energy of a quantum state) and its application to one-electron harmonic oscillator. Dirac’s contribution to matrix mechanics is also introduced followed the application in the quantum angular momentum (184 words).

Arkady Plotnitsky

This article considers a revolutionary transformation – physical, mathematical, and philosophical – of modern physics brought about by Heisenberg’s invention of quantum mechanics (QM). While physical and mathematical aspects of Heisenberg’s invention have been extensively commented on, and while they are essential for this article, considering the transformative philosophical aspects of Heisenberg’s thinking is rare. This article fills this lacuna through the concept of reality without realism (RWR) and the corresponding interpretations of QM, and philosophical implications of this concept.

Daniel R. Bes