Preface. Part I: Gathering the Tools. 1. Introduction to Quantum Physics. 2. Quantum Tests. 3. Complex Vector Space. 4. Continuous Variables. Part II: Cryptodeterminism and Quantum Inseparability. 5. Composite Systems. 6. Bell's Theorem. 7. Contextuality. Part III: Quantum Dynamics and Information. 8. Spacetime Symmetries. 9. Information and Thermodynamics. 10. Semiclassical Methods. 11. Chaos and Irreversibility. 12. The Measuring Process. Author Index. Subject Index.

Quantum Theory: Concepts and Methods

Criticism and the Growth of Knowledge. Edited by I. Lakatos and A. Musgrave. Pp. viii, 282. £3·50, paperback £1. 1970. (Cambridge University Press.)

Classical mechanics was first envisaged by Newton, formed into a powerful tool by Euler, and brought to perfection by Lagrange and Laplace. It has served as the paradigm of science ever since. Even the great revolutions of 19th century phys icsnamely, the FaradayMaxwell electro-magnetic theory and the kinetic t h e o r y w e r e viewed as further support for the complete adequacy of the mechanistic world view. The physicist at the end of the 19th century had a coherent conceptual scheme which, in principle at least, answered all his questions about the world. The only work left to be done was the computing of the next decimal. This consensus began to unravel at the beginning of the 20th century. The work of Planck, Einstein, and Bohr simply could not be made to fit. The series of ad hoc moves by Bohr, Eherenfest, et al., now called the old quantum theory, was viewed by all as, at best, a stopgap. In the period 1925-27 a new synthesis was formed by Heisenberg, Schr6dinger, Dirac and others. This new synthesis was so successful that even today, fifty years later, physicists still teach quantum mechanics as it was formulated by these men. Nevertheless, two foundational tasks remained: that of providing a rigorous mathematical formulation of the theory, and that of providing a systematic comparison with classical mechanics so that the full ramifications of the quantum revolution could be clearly revealed. These tasks are, of course, related, and a possible fringe benefit of the second task might be the pointing of the way 'beyond quantum theory'. These tasks were taken up by von Neumann as a consequence of a seminar on the foundations of quantum mechanics conducted by Hilbert in the fall of 1926. In papers published in 1927 and in his book, The Mathemat ical Foundations of Quantum Mechanics, von Neumann provided the first completely rigorous

The mathematical foundations of quantum mechanics

The interpretational problems of quantum mechanics are considered. The way in which the standard Copenhagen interpretation of quantum mechanics deals with these problems is reviewed. A new interpretation of the formalism of quantum mechanics, the transactional interpretation, is presented. The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereby consistent with recent tests of the Bell inequality, yet is relativistically invariant and fully causal. A detailed comparison of the transactional and Copenhagen interpretations is made in the context of well-known quantum-mechanical Gedankenexperimente and "paradoxes." The transactional interpretation permits quantum-mechanical wave functions to be interpreted as real waves physically present in space rather than as "mathematical representations of knowledge" as in the Copenhagen interpretation. The transactional interpretation is shown to provide insight into the complex character of the quantum-mechanical state vector and the mechanism associated with its "collapse." It also leads in a natural way to justification of the Heisenberg uncertainty principle and the Born probability law ($P=\ensuremath{\psi}{\ensuremath{\psi}}^{*}$), basic elements of the Copenhagen interpretation.

The transactional interpretation of quantum mechanics

Preface Prologue 1. Introduction 2. On sets and kinds in IR 3. Vector and Hilbert spaces 4. Linear transformations, operators and matrices 5. Conditional logic in IR 6. The geometry of IR Appendix I. Linear algebra Appendix II. Quantum mechanics Appendix III. Probability Bibliography Index.

The Geometry of Information Retrieval

Paramagnetic resonance in solids

General relativity and matter

In my view, the most curious section in this book is Chapter 3, Sec. 19: ’An Apology for Having Been Controversial’. The title and discussion of this section of Sir Karl Popper’s book indeed strikes against his own philosophy of science-the idea that (responsible) controversy is indeed at the heart of any real scientific progress (whether or not the leaders of the ongoing views [normal science] are happy or unhappy about this controversy!). Thus, I do not believe

Quantum Theory and the Schism in Physics

Sir Karl R. Popper has published a very interesting and provocative set of three books, Postscript to the Logic of Scientifc Discovery, intended as a sequel to his well-known Logic of Scientific Discovery.1 This is the first of two of the books that I will review, the other one to follow: Quantum Theory and the Schism in Physics, is related to the subject of this book in their discussion of the philosophy of the quantum theory and its possible extension to a general philosophy of physics. The third book of the set, Realism and the Aim of Science, deals with Popper’§ view of the philosophy of science, per se, particularly his meaning of the term ’realism’ in science, which I will discuss in this review. The Open Universe puts forward Pbpper’s main arguments in support of his notion of indeterminism, as an underlying concept of the physical world. At the outset, he makes clear a distinction between three kinds of indeterminism: religious, scientific, and metaphysical. But his thesis in this book deals mainly with what he calls ’scientific determinism’, which he claims to refute once and for all. Popper asserts that one cannot conclusively refute religious or metaphysical determinism because they are based on faith rather than having a rational, logical basis. But he does present arguments that try to make these forms of determinism less believable than his (opposite) belief in indeterminism. ’Religious determinism’, to Popper, refers to the existence of a higher spirit, God, outside of the universe, who is aware of the entire predetermined future of the universe, as it evolves in time according to His divine law. In Popper’s view, this form of determinism (as the other forms) rejects the view of human free will, and is therefore unacceptable as a truth, in view of his ’common sense’ awareness of free will. ’Scientific determinism’ compares with religious determinism by replacing ’God’ with ’nature’, and replacing ’divine law’ with ’natural law’. Butitis crucial in Pbpper’s argument that this form of determinism also includes the human being’s predictive capacity-his ability to predict the future from the natural laws with absolute certainty. ’Metaphysical determinism’ then removes the human being’s predictive ability from the scene, asserting that all events in the world are predetermined, though not all of them are necessarily known or predictable by the human species. Thus, the adjectives, ’metaphysical’ (or ’scientific’) in the notion of determinism refer to predetermined laws of the universe in all of its manifestations, though in the absence (or in the presence) of human involvement regarding his awareness of the universe and its future. That is, the metaphysical view is purely ontological while the scientific view of

The Open Universe: An Argument for Indeterminism:

Maxwell's equations are formulated in a number of different representations: (a) As a single four‐component spinor equation whose transformation properties are almost identical with those of the Dirac equation. (b) As a pair of uncoupled two‐component spinor equations, in two different representations. One of these is similar to the Weyl equation for the neutrino field and the other to the two‐component spinor form of the Dirac equation. (c) As a single equation in which the field variables are 2 × 2 matrices. In terms of these new field variables corresponding conservation laws are derived. Identification of these conservation laws with the standard ones is made. The transformations that are appropriate to the maintainance of covariance of the field equations are discussed.

Mendel Sachs

Papers

Paramagnetic resonance in solids

General relativity and matter

Quantum Theory and the Schism in Physics

The Open Universe: An Argument for Indeterminism:

On Covariant Formulations of the Maxwell‐Lorentz Theory of Electromagnetism