Did Werner Heisenberg and Carl Friedrich von Weizsäcker compromise with the Nazis? The story begins with Albert Einstein, who became a target for conservative physicists like Philipp Lenard and Johannes Stark who could not follow Einstein’s physics, and the early Nazi Party that rejected Einstein as a Jew as well as his pacifism and internationalism. When Hitler came to power, Lenard and Stark gained great influence. Stark in particular tried to accumulate power but steadily lost influence through conflicts with other Nazis. When Stark’s nemesis, the theoretical physicist Arnold Sommerfeld, was going to retire and be succeeded by Werner Heisenberg, Stark launched a vicious attack on Heisenberg in the SS newspaper. Heisenberg appealed to SS Leader Heinrich Himmler and thanks to support from the aeronautical engineer Ludwig Prandtl was eventually rehabilitated by the SS. The established physics community then launched a counterattack against the “Aryan Physics” of Lenard and Stark, which included writing Einstein out of the history of relativity theory. This was arguably Heisenberg’s greatest compromise with Nazism.

This monograph is about the change in meaning and scope of human rights rules, principles, ideas and concepts, and the interrelationships and related actors, on moving from the physical domain into the online domain. The transposition into the digital reality can alter the meaning of well-established offline human rights to a wider or narrower extent; it can turn positivity into negativity and vice versa. The digital human rights realm has different layers of complexity in comparison with the offline realm.

This project uses the procedure of root-finding to resolve the eigenvalue problem of a rectangular quantum well. The procedure is applied to determine the first two to three energy levels of a simplified model of a hydrogen atom, represented by the rectangular quantum well. The project also explores the eigenvalue problem within various physics fields. While the project involves simple mathematical operations, it is rooted in complex physical concepts like quantum mechanics, often unfamiliar to first-year students. The fundamentals of quantum mechanics are introduced, providing enough understanding for successful project execution. The project initially focuses on the central object, the quantum state, and its probabilistic nature in quantum mechanics. The Schrödinger equation, an eigenvalue problem, is used to find state functions. This project explores eigenenergies and eigenfunctions within a rectangular finite quantum well, treating the well as a simplistic 1D model of the hydrogen atom.

Quantum field theory (QFT) provides us with one and almost only suitable language (or mathematical tool) for describing not only the motion and interaction of particles but also their “annihilation” and “creation” out of a field considered a priori in a sophisticated way, whose view seems to be suited for describing dislocations, as a particle or a string embedded within a crystalline ordered field. This chapter concisely overviews the method of QFT, emphasizing distinction from the quantum mechanics, conventionally used for a single and/or many particle problems, and its equivalence to the statistical mechanics. The alternative formalism based on Feynman path integral and its imaginary time representation are reviewed, as the foundation for our use in Chapter 10.

Basic concepts of quantum mechanics: Schroedinger equation; Dirac notation; the energy representation; expectation value; Hermite operators; coherent superposition of states and motion in the quantum world; perturbation Hamiltonian. Time-dependent perturbation theory: harmonic perturbation. Transition rate: Fermi’s golden rule. The density matrix; pure and mixed states. Temporal dependence of the density operator: von Neuman equation. Randomizing Hamiltonian. Longitudinal and transverse relaxation times. Density matrix and entropy.

In this chapter, we review basic concepts from quantum mechanics that will be required for the study of superconducting quantum circuits. We review the fundamental idea of energy quantization and how this can be formalized, using Dirac's ideas, to develop a quantum mechanical description that is consistent with the classical theory for a comparable object. We review the notions of quantum state, observable and projective and generalized measurements, particularizing some of these ideas to the simple case of a two-dimensional object or qubit.

Here we discuss the possible relation ofour generalconjecture on global attractors ofnonlinear Hamiltonian PDEs todynamicaltreatment of Bohr's postulates and of wave--particle duality, which are fundamental postulates of quantum mechanics, in the context of couplednonlinear Maxwell--SchrödingerandMaxwell--Dirac equations. The problem of adynamicaltreatment was the main inspiration for our theoryof global attractors ofnonlinear Hamiltonian PDEs.

The interest taken by Surrealists in alchemy has been well known since the late 1940s, but knowledge of their preoccupation with modern science is more recent. This chapter observes the Surrealist penchant for premodern, occultist epistemologies before focusing on their take up of modern physics in the early 1920s. The theory of relativity (1905 and 1915–16) and developments in quantum mechanics (1922–7) were then undergoing popularization. Apart from popular articles in newspapers/journals, this occurred partly through physicists’ own writings and partly through the philosophy of science. This chapter indicates the importance to Surrealism of the writings of the French philosopher of science, Gaston Bachelard. It also features a case study of the work of German physicist Pascual Jordan whose attempt to extend the findings of quantum mechanics to biology was known to Max Ernst and used by the Surrealists to justify the rejection of positivism. So modern physics became a means of retrospectively comprehending the Surrealists’ turn towards automatism and Ernst’s own natural history incursions. His response to Jordan’s writings offers an alternative way of reading his work.

This chapter examines Cassirer's view on contemporary science. It revisits Cassirer's lesser-known work Determinism and Indeterminism in Modern Physics and argues that it harbors a significantly new stage of his philosophy of physical science. On the one hand, this work presents the quantum formalism as a limiting pole of the Bedeutungsfunktion, the highest mode of symbolic formation according to Cassirer’s “phenomenology of cognition.” Inspired by Paul Dirac, Cassirer understands quantum mechanics as a symbolic calculus for deriving probabilistic predictions of measurement outcomes without regard to underlying wave or particle “images” – or, as an exemplar of abstract symbolic thought. On the other hand, Cassirer recognizes the philosophical significance of the use of group theory in quantum mechanics as advancing a purely structural concept of object in physics. Hence, Ryckman reveals that Cassirer drew epistemological consequences from the symbolic character of contemporary physical theory that retain relevance for philosophy of science today.

In this first capstone chapter we aim to set classical mechanics in context. Classical mechanics played a key role in developing modern physics in the first place, and in turn modern physics has given us deeper insights into the meaning and validity of classical mechanics. Classical mechanics, even extended into the realm of special relativity, has its limitations. It arises as a special case of the vastly more comprehensive theory of quantum mechanics. Where does classical mechanics fall short, and why is it limited? The key to understanding this is Hamilton’s principle. We begin with the behavior of waves in classical physics, and then show results of some critical experiments that upset traditional notions of light as waves and atoms as particles. We proceed to give a brief review of Richard Feynman’s sum-over-paths formulation of quantum mechanics, which describes the actual behavior of light and atoms, and then show that Hamilton’s principle emerges naturally in a certain limiting case.

Chapter 6 covers the internal energy E, which is the first term in the free energy, F = E – TS. The internal energy originates from the quantum mechanics of chemical bonds between atoms. The bond between two atoms in a diatomic molecule is developed first to illustrate concepts of bonding, antibonding, electronegativity, covalency, and ionicity. The translational symmetry of crystals brings a new quantum number, k, for delocalized electrons. This k-vector is used to explain the concept of energy bands by extending the ideas of molecular bonding and antibonding to electron states spread over many atoms. An even simpler model of a gas of free electrons is also developed for electrons in metals. Fermi surfaces of metals are described. The strength of bonding depends on the distance between atoms. The interatomic potential of a chemical bond gives rise to elastic constants that characterize how a bulk material responds to small deformations. Chapter 6 ends with a discussion of the elastic energy generated when a particle of a new phase forms inside a parent phase, and the two phases differ in specific volume.

This chapter extends the discussion of waves beyond the longitudinal oscillations with which we began.Here, we look at the wave equation as it arises in electricity and magnetism, in Euler's equation and its shallow water approximation, in ``realistic" (extensible) strings, and in the quantum mechanical setting, culminating in a quantum mechanical treatment of the book's defining problem, the harmonic oscillator.