The formalisms of quantum mechanics. An introduction
The true paradox of quantum mechanics is well portrayed in the opening address of this interesting new book: despite being ``probably the most successful and complete physical theory that was ever proposed in the history of science,'' the debate about its principles, its interpretations and the explanation of its most surprising features is still with us well more than a century after its beginnings. It is true: the doubts about its foundations raised a few decades ago by a previous generation of physicists seem to have been overcome by the subsequent experimental confirmations. But strangely enough, from these very controversies several new research branches stemmed out (as quantum information and quantum computing) which, together with other experimental and theoretical advances (experimental tests on microscopic systems, quantum gravity, cosmology to quote just a few), ``have led to a revival of the discussions about the principles of quantum mechanics and its seemingly paradoxical aspects.'' This consequently seems to leave this body of theories in the somewhat weird position of being both ``(1) the unchallenged and dominant paradigm of modern physical sciences, (2) but at the same time a still mysterious and poorly understood theory, that awaits some (imminent) revolution.'' Apart, perhaps, from some overstatement about a ``revolution'' that does not seem to be currently boiling up, it is difficult not to agree with the author. As a matter of fact, even today, every thinking physicist which makes acquaintance with quantum mechanics asks himself some inescapable questions which still do not have answers that everyone agrees on (apart from not asking them at all). Everybody then either accepts one of the available explanatory schemes that he can live with, or continue his long conceptual quest, possibly in parallel with his other scientific pursuits. Admittedly however David's book is not mainly about this last issue of the foundations of quantum mechanics, but is rather devoted to explore ``why is quantum mechanics so consistent and successful'' and in so doing he chooses to present a synthetic view of its ``main formalizations'' along with ``their interrelations and ... their theoretical foundations'' because he wisely believes that ``discussing and comparing these various formulations is useful to get a better understanding of the coherence and the strength of the quantum formalism.'' This book however is neither designed to surrogate a handbook of mathematics or physics, nor to be a historical, sociological or epistemological essay, but across its 150 or so pages it leads the reader in a survey which, by keeping a sober distance from excessive details, proposes an integrated view of the different facets of the theory. The main exposition is organized in four, evenly distributed sections: after recalling the ideas and the notations of the Standard formulation (Section 2), the core of the book deals with the Algebraic formalism (Section 3), and mainly with the Quantum logic (Section 4) as conceptual settings that progressively generalize the standard formulation. As a matter of fact these last two points of view, which can be retrieved only in a more specialistic literature, are noticeably absent in most of the textbook or reviews about quantum mechanics, and David's commendable book is primarily intended to fill this gap. Naturally enough the ideas, the problems and the formal structures are just sketched with a few notable additional examples, without elaborating all the consequences which are left to the interested reader. The presentations however are often original in their style, while the added remarks are telling and constitute an inspiring guide for further insights. It is intriguing to remark, however, that the two previously quoted sections inescapably lead us to the last one on the more recently developed field of the Quantum information (Section 5) where the discussions about correlations and entropy display tight connections to the original ideas of entanglement and Bell inequality so popular in the 60's and 70's, and hence help to shed a new light on the older problems of hidden variables and local realism: the circle is hence completed bringing us back to the square one of the mysteries of quantum mechanics. The book is also provided with a rich, but necessarily far from exhaustive bibliography: many single quotations must be taken indeed just as clues to a further inquire.
scientific article; zbMATH DE number 6340797