Hertha Sponer’s (1894-1968) early years in physics were spent at the center of the quantum revolution. Training as an experimentalist under Debye, then heading the spectroscopy labs in Göttingen uniquely situated her to contribute to the development of quantum theory and the emergence of quantum chemistry, by novel interpretations of hitherto unexplained spectrographic data using quantum mechanics, and suggesting new applications of the theory to atoms and diatomic molecules. Sponer’s name has nevertheless been largely written out of scientific accounts of these years. When mentioned in the context of quantum theory, it is usually as Franck’s “assistant” (incorrect) and second wife – descriptions that obscure her status as a world-renowned scientist who’d contributed importantly to physics and chemistry over a long and illustrious career. Extant accounts of Sponer’s life and work almost exclusively concern her postwar years as a professor at Duke. But by then quantum theory was well established, and her research had pivoted in other directions. This chapter aims to introduce Sponer into the history of early quantum theory, with appropriate attention to her achievements.

This chapter shows how particles arise naturally as an effect of waves, known as “resonance,” and that the particle concept, properly understood, is not somehow incompatible with the existence of waves. The definitions of “fermion” and “boson” fields, often associated with “matter” and “energy” particles, are introduced. The solidness of objects in our experience is a direct consequence of fermion wave properties.

This chapter presents some basic calculations that show counterintuitive or unexpected results. First, it is shown that the Planck spectrum of light, which played an important role in the history of quantum mechanics, doesn’t say anything about the existence of indivisible particles. Second, a brief discussion of “chaos theory” shows that jumpy and unpredictable behavior can occur in classical systems. Last, the concept of “entanglement” is introduced as a basic property of quantum systems.

After having shown in previous chapters that wave-particle duality is not a fundamental problem for quantum mechanics, this chapter introduces the really strange effect of quantum mechanics, namely “nonlocal correlations” that appear to act over long distances faster than the speed of light. The “Copenhagen” interpretation of quantum mechanics is introduced, which puts human knowledge in a special role, and some of the philosophical objections to it.

This chapter explains what we mean by “fields” and “waves” in physics, and argues that quantum waves are just as “real” as other waves we experience in daily life, such as water waves and sound waves.

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.