Understanding Quantum Mechanics
Omnes (Roland)
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BOOK ABSTRACT:

Back Cover Blurb


Preface
  • The aim of this book is to explain the interpretation of quantum mechanics2, simply and completely if possible. It is addressed to beginners with some elementary knowledge of quantum theory3 and also to physicists wishing to refresh their memory and see what the present state of interpretation is.
  • There are many textbooks on quantum mechanics4, but most of them do not give much space to interpretation and a book such as this one might be a useful complement to them. One of the meanings of “interpreting” is “understanding,” and we all know that this is the main difficulty of quantum mechanics5. Can it really be understood? I think now it can.
  • Bohr, Heisenberg, and Pauli laid the foundations for interpretation long ago, and nothing that has since been discovered really undermines that groundwork. Some portions of their work have been revised, however, and others were found to be incomplete. Rather than replicate the writings of the founding fathers here, it would certainly be more faithful to their spirit by updating them rather than by repeating them. Two important discoveries led to a revision of the old interpretation. The first one was the notion of decoherence, an effect explaining why no quantum interference can be seen at a macroscopic level and removing the perennial difficulty known as the Schrodinger cat problem. Decoherence was proposed in 1954 and was seen experimentally in 1996. It is now essential to an understand of quantum measurements. The second advance came in the last two decades from a full insertion of classical physics into the framework of quantum physics. Classical determinism was thereby found to be the direct consequence of a fundamental quantum probabilism, whose only remaining effect at our macroscopic level is that every causal prediction has a tiny probability of error. These results, the outcome of work by many people, shed a completely new light on interpretation.
  • A third important idea, consistent histories, was put forward in 1984 by Robert Griffiths and was not always clearly understood. Some people believed that it was an attempt (necessarily doomed to failure) for reintroducing a simple-minded realism into the quantum world. Histories have nothing to do with that. They rely directly on the basic principles of the theory and they give us a method, the means for clarifying and organizing interpretation, which can so easily turn into a quagmire, or a maze. Histories are also the foundations of a new language. One can do without them if one does not wish to change old habits, just as one can dig out the foundations of a building with a shovel rather than an excavator.
  • I wished to provide the reader with a convenient textbook and not a detailed treatise, and this aim entails a few consequences. I avoided difficult proofs and long calculations, replacing them as far as possible, by simple arguments. I refrained from recounting some trends of research, however deep or brilliant, that would be too speculative. The commentaries at the end of the book provide some recommendations for supplementary reading as well as for more technical information.
  • Physics will remain at the center of this book, but there will be little foray into epistemology. Philosophical issues cannot be completely ignored, however. I will not enter upon the difficult (or perhaps too trivial) question of realism because my emphasis will bear on the pragmatic aspects of physics. Even so, quantum mechanics6 requires a new way of understanding, as Bohr, Heisenberg, and Pauli knew, and if one is so bold as to take issue with Richard Feynman’s famous saying — “nobody understands quantum mechanics!”7 (1965c, p. 129) — one must say not only how quantum mechanics8 can be understood, but also why, and what perspectives this understanding reveals.
  • I wrote another book on a similar topic a few years ago ("Omnes (Roland) - The Interpretation of Quantum Mechanics", Princeton University Press), and I owe the reader an explanation for why a new one is proposed. First, there is a significant difference in emphasis: the present book is much less technical and more explanatory. A fair number of people kindly told me that something more accessible would be useful for students as well as for physicists with a cultural interest in interpretation and I tried to answer the request. A second reason is that research is active in this field and quite several significant results could be added.
  • Five important new features appear in this new book.
    1. The first one originates in a reading of the pioneers of interpretation and their commentators. I learned particularly from Dugald Murdoch and Catherine Chevalley of the inquiries by Bohr, Heisenberg, and Pauli on the language of interpretation. I realized better on this occasion the true nature of consistent histories and the existence of a wider frame for them. They are effectively a language for interpretation. This language has two faces, two versions: a direct one that can be expressed in plain English (or any other vernacular language) and an abstract one relying on mathematics and rooted in the basic principles of quantum mechanics9. The second is a universal language: it can deal with atoms, particles, and also with experimental devices as well as with any ordinary object we can see or touch. It is also a rational language with a clear and explicit logical framework. When seen in that light, there is no possible confusion concerning the nature of histories. They are part of the universal language of interpretation. No language defines reality: it can only say what we know of reality. And we know much.
    2. The second feature involves recent progress concerning decoherence. It has been observed, and more powerful theories now exist for it. Decoherence now appears to be an irreversible process, the strongest one in existence, and thus sheds a new light on time, logic, and irreversibility.
    3. The third feature arose from a criticism of decoherence by John Bell and Bernard d’Espagnat. They said that decoherence cannot provide an explanation of the basic problems of interpretation but rather that it hides them by offering an answer valid “for all practical purposes,” that is, an answer agreeing with any possible experiment and thereby forbidding us to see more deeply beyond these experiments. I came to the conclusion that these so-called fundamental questions hinge on the meaning of extremely small theoretical probabilities. An interpretation of probability calculus must therefore stand at the entry to an interpretation of quantum mechanics10, and the most convenient one was proposed by Emile Borel: an event with too small a probability should be considered as never occurring. From an empirical standpoint, a very small probability is one which cannot be measured by any experimental device that can be realized, or even conceived, in the universe. One can then assert that decoherence cannot be bypassed and is really fundamental.
    4. The fourth feature is also essential. When I wrote the Interpretation of Quantum Mechanics11, the reader was left with a problem having no solution. This is the so-called objectification problem, which concerns the issue of the existence of a unique datum at the end of a quantum measurement. This looked like a big deficiency because many specialists claim that here lies “the” problem of interpretation. When looking at it, thinking of it, dreaming of it, I realized that it might be a false problem. It originates in a traditional line of thought that has no sure logical foundations. When decoherence is taken into account, one finds that the universal language of interpretation cannot encompass anything other than a unique datum, in agreement, of course, with observation. Said otherwise, there is no sound language in which the objectification problem might be stated, so therefore it may very well not exist. I must note that these ideas are an elaboration of previous insights by Robert Griffiths, Murray Gell-Mann, and James Hartle.
    5. The last feature has to do with the meaning of probabilities and the randomness of quantum events. Probabilities enter the language of interpretation by the back door: they are found necessary for providing this language with a logical backbone. The relation with empirical randomness looks rather far-fetched, and it was not clearly explained in my previous book (as a matter of fact, it was not yet clearly understood, either). Here again, one finds that the language we must use cannot deal with anything other than random events. This may be not an explanation, like one could also say of objectification, but it is a logical necessity.
  • Finally, I may add that no effort has been spared for keeping the present account of interpretation as close as possible to the Copenhagen interpretation. There are four good reasons for doing so. As a complement of standard textbooks, this book would have been useless if it contradicted what one usually learns. It does not. Furthermore, the Copenhagen rules are used everyday in the practice of physics, and because they are correct, my task was to explain why without undue rewriting. It turns out also that histories can be considered as a systematic use of imaginary measurements, as used in Heisenberg’s works. As to the last reason, I thought that showing another instance of two approaches, leading to the same conclusions through very different ways, is a beautiful example of the unity of physics.
  • To make the reader find his or her way more easily through this book, I may say how it is organized. There are three parts. The first one is a brief sketch of the early history of quantum mechanics12. I am aware of a fashion in modem books to proceed as if everything worth knowing in science was discovered in the last decade, but it would not work here. On the contrary, I decided to start with a history, because some questions are much better appreciated when one sees them developing from the beginning, as well as how deep they go. There is a strong continuity in quantum mechanics13 and its interpretation, and I felt that the historical dimension is not only useful but also illuminating. Even if not answering them completely, one cannot ignore such questions as: How came this splendid theory, which needs another theory for being understood? Could it be otherwise? On the other hand, the Einsteinian question, “Should not it be otherwise?” is answered in the two following parts, showing the consistency of interpretation and the completeness of standard quantum mechanics14.
  • The second part of the book is another brief history, this one of interpretation. Interpretation is often confusing and, I tried to provide an orientation.
  • There are three chapters in this second part.
    1. The first one is devoted to the Copenhagen interpretation, a name I propose reserving for the ideas expressed by Bohr, Heisenberg, and Pauli — and of nobody else.
    2. The second chapter is a summary of basic contributions, mainly by John von Neumann, that were not integrated in the standard Copenhagen interpretation. The most relevant criticisms by Einstein and Schrodinger are also discussed here. They had an essential role in keeping the question of interpretation alive and pointing out the most important questions. Other proposals and events, particularly around Bell’s contributions, are also mentioned, even if very briefly.
    3. The third chapter (Chapter 7 of the book) might be called a keystone, and the reader in a hurry might directly start from it. It is a nontechnical summary of the main aspects of a consistent interpretation of quantum theory15 establishing its completeness. It cannot be easily condensed, and I therefore will not describe it in this foreword.
  • The third part of the book is the longest one. It further develops the points indicated at the end of the second part. It does not refer to historical matters and gives a rather detailed and systematic account of interpretation.
  • The present book relies heavily on essential works, particularly by Murray Gell-Mann, Robert Griffiths, Serge Haroche, James Hartle, Jean-Michel Raimond, Hans Dieter Zeh, and Wojciech Zurek. It also relies on important ideas or advice from Roger Balian, Bernard d’Espagnat, and Lars Hormander. I benefited immensely from exchanges with these wonderful people. … [snip]

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