Helmut Rechenberg

Planck's Half-Quanta: A History of the Concept of Zero-Point Energy

Max Planck introduced the concept of zero-point energy in spring 1911. In the early struggles to establish the concept of the energy-quantum, it provided a helpful heuristic principle, to guide as well as supplement the efforts of some leading physicists in understanding the laws that applied in the atomic domain. The history and growth of this concept, and its application in the general development of quantum theory during the past many decades are studied under three principal headings: (1) The Birth of the Concept of zero-Point Energy; (2) Does Zero-Point Energy Really Exist? and (3) The Ground State of Quantum Systems.

Quantum field theories, nuclear forces, and the cosmic rays (1934--1938)

During the 1930s, cosmic rays were the most important source of data on the high‐energy behavior of both quantum electrodynamics and nuclear forces. In the period 1934–1938, with which this article is concerned, the dominant fundamental theory of nuclear forces was that of the Fermi field. In sorting out the various cosmic‐ray phenomena in the atmosphere, it was found that the less penetrating components were associated with electromagnetic cascade showers, and that the more penetrating component contained a new ‘‘elementary’’ particle, the mesotron. However, there remained puzzling features of the cosmic rays that left adequate room for other interpretations.

Nuclear structure and beta decay (1932–1933)

Before the discoveries of the neutron and the positron in 1932, the only known fundamental material particles were the electron and the proton (referred to sometimes as ‘‘negative and positive electricity’’), which were also thought to be the only constituents of all matter, including the atomic nucleus. Well‐known nuclear phenomena, especially β decay, seemed to require that nuclei contain electrons, even though their presence violated accepted principles of microscopic physics. During 1932 and 1933, however, the picture changed considerably and the foundation was laid for a future theory of nuclear structure and β decay, with the nucleus composed of only neutrons and protons as fundamental building blocks.

The Probability Interpretation and the Statistical Transformation Theory, the Physical Interpretation, and the Empirical and Mathematical Foundations of Quantum Mechanics 1926–1932

Contents-Part 1.- 1 The Probability Interpretation and the Statistical Transformation Theorythe Physical Interpretationand the Empirical and Mathematical Foundations of Quantum Mechanics (1926-1932).- I The Probability Interpretation and the Statistical Transformation Theory.- II Uncertainty, Complementarity, and Quantum Fields.- III The Empirical and Mathematical Foundations of Quantum Mechanics.

The Conceptual Completion and the Extensions of Quantum Mechanics (1932–1941)

The invention of quantum and wave mechanics and the great, if not complete, progress achieved by these theories in describing atomic, molecular, solid-state and—to some extent—nuclear phenomena, established a domain of microphysics in addition to the previously existing macrophysics. To the latter domain of classical theories created since the 17th century applied—principally, the mechanics of Newton and his successors, and the electrodynamics of Maxwell, Hertz, Lorentz, and Einstein. The statistical mechanics of Maxwell, Boltzmann, Gibbs, Einstein, and others indicated a transition to microphysics; when applied to explain the behaviour of atomic and molecular ensembles, it exhibited serious limitations of the classical approach. Classical theories were closely connected with a continuous description of matter and the local causality of physical processes. The microscopic phenomena exhibited discontinuities, ‘quantum’ features, which demanded changes from the classical description.

P.A.M. Dirac (1930) and J. Von Neumann (1932), books on quantum mechanics

Publisher Summary This chapter discusses P.A.M. Diracs and J. Von Newmanns works on classical mechanics. These works are the classic physicists treatise on the quantum mechanical transformation theory, which is a generalization of the matrix-mechanical and wave-mechanical quantum theories of Werner Heisenberg and Erwin Schrodinger, respectively. These works formulated an alternative mathematical theory of quantum mechanics, known as quantum algebra. Dirac generalized the matrix formulation of quantum mechanics, in which he called the non-commuting quantum variables q-numbers, distinguishing them from the classical commuting quantities that he called c-numbers. In 1927, Dirac published a quantum theory of the electromagnetic field interacting with electrons, the so-called quantum electrodynamics (QED). Diracs first chapter considers the principle of superposition, which is different from the classical notion of superposition of waves. While Hilbert had shown in 1906 that every bounded symmetrical bilinear form possessed a unique representation with a unique set of eigenvalues, this was not yet clear for the unbounded symmetrical operators occurring in von Neumanns space H for quantum mechanics. Nature agrees with quantum mechanics as the proper description of atomic processes, and preserves the important contributions contained in von Neumanns Mathematical foundations.

Conclusion: Four Generations of Quantum Physicists

Looking back now on one hundred years of quantum theory, we recognize that the foundations were laid essentially by four generations of pioneers. The first one consists of Max Planck (born 1858), Arnold Sommerfeld (born 1868), and the younger Albert Einstein (born 1879), who—though deeply rooted in the concepts of the 19th century—accomplished the transition from the classical to the quantum-theoretical description of a set of new physical phenomena. The second generation began with Max Born (born 1882) and included Niels Bohr (born 1885), Erwin Schrodinger (born 1887), and finally Louis de Broglie (born 1892), who built on the already existing quantum concepts and applied them to various fields of physics, notably, atomic theory. Although not in age, but rather through his crucial contribution, Schrodinger broke into the third generation, younger by about 15 years—consisting of Wolfgang Pauli (born 1900), Werner Heisenberg (born 1901), Paul Dirac (born 1902), Eugene Wigner (born 1902), and John von Neumann (born 1903)—which created quantum and wave mechanics. The fourth generation we have in mind enlarged the use of quantum mechanics and extended the formalism to treat adequately the new levels of physical phenomena. This generation also extended the limits beyond the European (especially Central European) continent to the whole scientific world; it included the Japanese Hideki Yukawa and Sin-itiro Tomonaga (both born in 1907), the Russians Lev Landau and Nikolai Bogoliubov (both born in 1908), the Indian Subrahmanyan Chandrasekhar (born 1910), and finally the Americans John Bardeen (born in 1908), Julian Schwinger, and Richard Feynman (both born in 1918). The lifetimes and activities of these four generations spanned nearly the entire century of quantum theory, as can be seen from the many contributions of the above-mentioned pioneers, their collaborators and disciples, discussed in Volumes 1–6. It is therefore fitting to end the last volume of this series by completing the stories of their lives and activities.

Epilogue: Aspects of the Further Development of Quantum Theory (1942–1999)

In an ‘Historical Overview of the Twentieth Century in Physics,’ Philip W. Anderson praised the first half of the century as ‘the triumph of physics’ (Anderson, 1995, p. 2020). Without going into detail—we may say that he indeed had essentially quantum theory and its applications, which we have discussed in these volumes, in mind—he made a note of the popular appreciation of this science which ‘attracted increasing support for the research from private philanthropy,’ such as the Nobel or the Rockefeller Foundations, while governmental funding was just starting.1114

The electron in physics - selection from a chronology of the last 100 years

The crucial role of the electron in the history of physics over the past hundred years is documented in a selected, four-part chronology: 1. The early electron - conductivity, -rays and relativity theory; 2. The electron and the old quantum theory of atomic structure; 3. The electron in quantum and wave mechanics; 4. The electron in nuclear and elementary particle physics. Zusammenfassung. Die beherrschende Rolle des Elektrons in der Physikgeschichte der letzten hundert Jahre wird anhand einer vierteiligen Chronologie (1. Das fruhe Elektron - Leitfahigkeit, -Strahlen und Relativitatstheorie; 2. Das Elektron und die altere Quantentheorie des Atombaues; 3. Das Elektron in der Quanten- und Wellenmechanik; 4. Das Elektron in der Elementarteilchenphysik) aufgezeigt.

Über die Anfänge der neuzeitlichen Wissenschaft (1974)

Wir wollen nun noch einen weiteren Auszug aus der Korrespondenz von Walther Gerlach und Werner Heisenberg abdrucken, namlich einen Brief, in dem Gerlach zu einer entscheidenden physikhistorischen Frage Stellung nimmt.