The Everett interpretation of quantum mechanics. Collected works 1955--1980 with commentary. Edited by Jeffrey A. Barrett and Peter Byrne (Q2889185)

In modern language the von Neumann measurement of a non-degenerated observable \(A\) with discrete spectrum may be considered as a channel whose input is quantum information and whose output is classical information, given by a point \(\lambda_i\) in the spectrum of \(A\). Let \(\{\phi_i\}\) denote the basis of normalized eigenfunctions of \(A\) and the input be given by \(\psi = \sum_ia_i\phi_i\), with probability \(|a_i|^2\) the output will be \(\lambda_i\) and the quantum system will be left in the state \(\phi_i\). This, so called, collapse of the wave function is considered as a discontinuous and stochastic ingredient to quantum dynamics aside of the Schrödiger equation. Considering the measurement channel as a quantum operation without observing the result, the transition \(\psi \mapsto \sum_i|a_i|^2|\phi_i\rangle\langle\phi_i|\) is called decoherence. Collapse and decoherence are the source of many controversial discussions and criticisms from then up to now.NEWLINENEWLINEIn his dissertation thesis under supervision of J. A. Wheeler, Hugh Everett in 1957 proposed to understand quantum mechanics to be based only on wave mechanics, without external observers, without collapse and without decoherence. A central point in his attempt is the fact that a pure state of a bipartite system may be represented as \(\psi = \sum a_{ij}\phi_i\chi_j\), where \(\{\phi_i\}\) and \(\{\chi_j\}\) are arbitrary orthonormal bases in the respective Hilbert spaces. By the hypothesis of \(\phi_i\) to be the state of the first system \(\frac{1}{c_i}\sum_ja_{ij}\chi_j\), \(c_i\) being the normalization constant, is the \textit{relative state} of the second system. If \(\{\phi_i\}\) are the eigenfunctions of \(A\) and the relative states are pairwise orthogonal, entanglement arises in which the states \(\phi_i\) are strictly (one-to-one) correlated to their relative states, as it is considered in the usual description of the measurement process. The point is now that H. Everett assumes observers to be quantum systems endowed with a memory. Considering a multipartite system which consists in many object systems in the same state \(\psi = \sum_ia_i\phi_i\) and such an observer in a pure state with empty memory, a sequence of consecutive interactions with the object systems, one after another, leads to a superposition of multipartite states s. t. the observer part in each component of this superposition gets a series of results into his memory and the states of the object parts are the respective eigenfunctions of \(A\), i.e. \(\phi_{i_1}\otimes \phi_{i_2}\otimes\dots\otimes \phi_{i_N}\otimes \Psi_{i_1,i_2,\dots,i_N}\) after \(N\) interactions, where \(\Psi_{i_1,i_2,\dots,i_N}\) is the (relative) observer state. The clue is that H. Everett shows that the frequency rates of the eigenvalues of \(A\) in the memory of the observer part in each component of the superposition converges to \(|a_i|^2\) for \(N\to \infty\). So the probability distribution of measurement results in the memory of the observer part of each component of the superposition is (more precisely: converges to) the same and just as quantum mechanics predicts. This has been concluded without external observers, collapse, or decoherence. Hence the cosmos might be a quantum system in a pure state, the universal wave function, which develops continuously and causal due to the Schrödinger equation. Non-zero entropies and irreversible processes can arise only in subsystems of the universe. This picture of the world has opened the door for deep philosophical discussions among Everett and leading physicists of the second half of the last century. Most popular is the Many Worlds Interpretation, strongly suggested by Bryce DeWitt, which proposes the world to split after each quantum measurement into as many worlds as there are components of the superposition arising. These worlds are assumed to be strictly separated one from the other and identical up to the different results of the measurement. Collapse and decoherence are omitted, but possibly different outcomes of a single measurement are recognized and become real events in the different splits of the world.NEWLINENEWLINEThe present book presents on 390 pages reprints of writings, publications, correspondences of Hugh Eveverett including personal notes, several in form of facsimiles. \textit{J. A. Wheeler}'s ``Assessment on Everett's ``Relative State' Formulation of Quantum Theory'' [Rev. Mod. Phys. 29, No. 3, 463--465 (1957)] is also reprinted. All te reprints are endowed with short comments by the editors. Moreover, the editors give in part I on the first 90 pages a general, a biographical, and a conceptual introduction. Part II contains writings by H. Everett belonging to the evolution of his thesis including the first ``long'' version and the final ``short'' version of it as well as Wheeler's Assessment. Part III contains correspondences of Everett and Wheeler with the Copenhagen school and chapter IV other correspondences. Part V contains the personal notes of Everett. The book has a detailed index, which is very helpful since proposals to given problems are distributed in several essays. The texts are mainly philosophical in character. This book will be very useful for historians as well an philosophers working on the development of interpretations of quantum theory.NEWLINENEWLINEFor recent opinions, statements, and discussions among philosophers and physicists see a collection of contributions to two conferences on occasion of the fiftieth anniversary of Hugh Everetts thesis [\textit{S. Saunders} (ed.) et al., Many worlds? Everett, quantum theory and reality. Reprint of the 2010 hardback ed. Oxford: Oxford University Press (2012; Zbl 1243.81022)].