This is the first ever English translation of Heisenberg’s unpublished response to the EPR paper. In this chapter, Heisenberg uses his famous cut argument to argue against the possibility of hidden variables.

The famously controversial 1935 paper by Einstein, Podolsky, and Rosen (EPR) took aim at the heart of quantum mechanics. The paper provoked responses from leading theoretical physicists of the day, and brought entanglement and nonlocality to the forefront of discussion. This book looks back at when the EPR paper was published and explores those intense. conversations in print and in private correspondence. These offer significant insight into the minds of pioneering quantum physicists, including Bohr, Schrödinger and Einstein himself. Offering the most complete collection of sources to date – many published or translated here for the first time – this text brings a rich new context to this pivotal moment in physics history.

This is a translation of an anonymous report published about Einstein’s seminar in Berlin in November of 1931 dicussed in detail in Chapter 1. The report describes Einstein discussing the meaning of Heisenberg’s uncertainty relations and describing his famous photon-box thought experiment.

This chapter presents a collection of letters between the main protagonists in the EPR debate as analysed in the present volume. Among many other letters, it includes the first ever complete English translation of the correspondence Schrödinger held concerning the EPR paper with, e.g., Einstein, Bohr, Pauli, Born and Teller. He kept these letters in a special folder labelled ‘The Einstein Paradox’, only a small portion of which has previously been discussed in the foundations literature. These historical documents, many of which are published here for the first time, form the basis of our analysis in the beginning chapters of this book.

This chapter introduces in more comprehensive fashion than elsewhere in the literature the interesting role of Heisenberg in the EPR debate. Although we have already published an analysis of Heisenberg’s posthumously published draft response to EPR, only now are we able to situate this excellent primary source in its fullest context, by contributing a chapter describing, for example, Heisenberg’s thinking prior to EPR about interacting systems and hidden variables, the crucial role of Grete Hermann for Heisenberg’s thinking about separability, completeness and observational context, and describing the correspondence between Heisenberg and Bohr discussing Heisenberg’s manuscript.

The topic of this chapter is the wave function – what it is, how it is to be interpreted and how information can be extracted from it. To this end, the notion of operators in quantum physics is introduced. And the statistical interpretation called the Born interpretation is discussed. This discussion also involves terms such as expectation values and standard deviations. The first part, however, is dedicated to a brief outline of how quantum theory came about – who were the key people involved, and how the theory grew out of a need for understanding certain natural phenomena. Parallels are drawn to the historical development of our understanding of light. At a time when it was generally understood that light is to be explained in terms of travelling waves, an additional understanding of light consisting of small quanta turned out to be required. It was in this context that Louis de Broglie introduced the idea that matter, which finally was known to consist of particles – atoms – must be perceived as waves as well. Finally, formal aspects such as Dirac notation and inner products are briefly addressed. And units are introduced which allow for convenient implementations in the following chapters.

This chapter provides a brief overview of the history of the development of quantum theory, with a critical focus on the antirealist tradition inaugurated by Niels Bohr. The distinction between “principle theories” and “constructive theories” is discussed, and it is noted that quantum mechanics is a “principle theory.” It is argued that quantum theory is amenable to a fully realist interpretation provided we let go of the demand that reality be classically picturable.

Our modern understanding of atoms, molecules, solids, atomic nuclei, and elementary particles is largely based on quantum mechanics. Quantum mechanics grew in the mid-1920s out of two independent developments: the matrix mechanics of Werner and the wave mechanics of Erwin Schrödinger. For the most part this chapter follows the path of wave mechanics, which is more convenient for all but the simplest calculations. The general principles of the wave mechanical formulation of quantum mechanics are laid out and provide a basis for the discussion of spin, identical particles. and scattering processes. The general principles are supplemented with the canonical formalism to work out the Schrödinger equation for charged particles in a general electromagnetic field. The chapter ends with the unification of the approaches of wave and matrix mechanics by Paul Dirac, and a modern approach, known as Hilbert space, is briefly described.