The Interpretation of Quantum Mechanics
Omnes (Roland)
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Author’s Preface
  • Almost all of physics now relies upon quantum mechanics5. This theory was discovered around the beginning of this century. Since then, it has known a progress with no analogue in the history of science, finally reaching a status of universal applicability.
  • The radical novelty of quantum mechanics6 almost immediately brought a conflict with the previously admitted corpus of classical physics, and this went as far as rejecting the age-old representation of physical reality by visual intuition and common sense. The abstract formalism of the theory had almost no direct counterpart in the ordinary features of the world around us, as, for instance, nobody will ever see a wave function when looking at a car or a chair. An ever-present randomness also came to contradict classical determinism. This was really troublesome because determinism not only was a dominant philosophy among scientists but also is something whose existence is necessary for our understanding of the world. Such trivial and basic features as remembering the past from memory or recalling it from a record or a photograph, as well as the fact that a laboratory apparatus or a mechanical device is going to work in a predictable fashion, are altogether essential features of our understanding of reality and our relation to it. They are fundamentally linked with determinism, and as such, one could wonder whether they hold in a world obeying quantum laws.
  • When a theory is so strange that it must be interpreted, whether it be relativity or quantum mechanics7, the aim of this interpretation is to reconcile the fundamental, outrageously abstract concepts with plain empiricism: the kind of ordinary situation met in a laboratory or anywhere else. Interpretation must also reconcile the theory with the cornerstones of physics — namely, the existence of facts and their agreement with common sense together with its everyday determinism, at least as far as large-scale phenomena are concerned. This endeavour could define the main purpose of this book.
  • The following text does not consist of a commentary upon the writings of Bohr and Heisenberg and what they said, as was often the case for interpretative books in the past. Neither is it a new, formal, axiomatic approach, nor is it pleading for forthcoming incomplete theories purporting to replace quantum mechanics8. It is essentially a fresh approach to the older interpretation we all owe to Bohr, though putting it upon new and firmer foundations. It was found on several occasions that the traditional Copenhagen views, though essentially correct for the vast majority of experimental or natural conditions, should be modified in order to obtain better consistency. This does not mean that it was fundamentally wrong, but it needed some trimming after more than seventy years.
  • This renewal of the conventional interpretation is the outcome of a recent change of emphasis in the general strategy of research in this domain, which has rapidly given many new and significant results. It came after a rather long episode during which the main interest was the question of existence or nonexistence of hidden variables, following the discovery of a corresponding test by John Bell. A new effort aiming, on the contrary, at a clarification and a justification of Bohr’s interpretation has now followed, though some of its actors may elicit strong criticisms of various excesses in the nebula known as the Copenhagen interpretation.
  • This change began in the period 1975-1982 with the discovery and understanding of the decoherence effect, which is responsible for breaking quantum linear superpositions of different macroscopic properties. The existence of these superpositions, which seemed to follow directly from the basic theory, had been plaguing interpretation since the beginning, because it meant that different classical data could not be understood as clearly distinct events. This is also known as the problem of Schrodinger's cat. Soon after this breakthrough, one learned (in 1984) how to describe correctly the properties of a quantum system by narrating its history in detail, and this was to lead, in 1988, to a sound logical description of the behaviour of a quantum system. This might look like a much more modest achievement, but quantum mechanics9 has always defied logic — stating, for instance, that a unique photon must follow both arms of an interferometer. It became possible to firmly control such apparent aberrations, to make clear what makes sense and what does not in quantum mechanics10, and to make this soundness the basis and the unique assumption of the whole of interpretation. The fruitfulness of this new approach became clear when it allowed a complete derivation of classical physics, explaining why and when determinism can hold under large-scale conditions, though the basic theory underlying it is purely probabilistic. It became at last possible to understand quantum mechanics11 by resorting to a basic inversion in the process of understanding: rather than starting from common sense to try fitting it with a physical theory obviously foreign to it, the trick was to understand what principles of a logical nature stand at the bottom of physics itself and to derive from them when and how common sense is valid.
  • It became clear only recently that the various pieces of the puzzle that had been discovered more or less independently could be fitted together to make clear that no inconsistency had been left aside, no paradox unsolved, no well-known difficulty untouched. The overall result is an interpretation possessing the two major properties of consistency and completeness: consistent as being explicitly free from any logical self-contradiction or paradox, complete as providing a definite prediction for every experimental situation.
  • Quite a few of Bohr’s views had to be modified accordingly, though these are only minor changes as far as the practice of physics is concerned. The modifications of the underlying conceptual framework are much more significant, but they also often provide a more straightforward justification of some rules or notions that had been put forward by Bohr with no obvious or completely convincing argument. As an example of these changes, one may mention that the usual axioms of measurement theory can be reduced to a unique logical principle, that there exist macroscopic systems behaving in a quantum mechanical way and showing macroscopic tunnel effects; wave packet reduction, though undoubtedly very useful for practical purposes, is not a necessary assumption and in any case not a physical effect undergone by the measured object; old paradoxes such as that by Einstein, Podolsky, and Rosen, become almost trivial and in any case easily untied; many conventional or more philosophical ideas concerning objectivity and reality need serious reconsideration.
  • A satisfactory feature of the new approach is that the interpretation of quantum mechanics12 has now recovered the standard of a mature science, ie. a deductive construction relying upon clear-cut principles. One no longer needs to justify it by relying upon the word of past authorities, because its logical consistency as well as its agreement with experiment are now obvious. Another convenient feature is that interpretation is now easier to understand. These were also my two motives for writing the present book.
  • This is intended to be a book by which one can learn the interpretation of quantum mechanics13, not an interpretation. A reader who is not particularly interested in the most recent fashions and the latest results and who wants to learn what is the conventional Copenhagen interpretation will find this book useful, as will the reader who wants to keep in touch with research in this domain. This is because the older interpretation is given and also justified; rather than glossing over its difficulties as usual, I show how they can be avoided. Quite a few rather obscure recommendations by Niels Bohr become clear because they now follow from a consistent construction.
  • The interpretation of quantum mechanics14 is developed here by starting from what one can learn in a first-year course on the subject, and most of the book has been kept at that level. This is obtained by restricting the discussion to the main ideas, giving only the simplest proofs and the most important examples. When some theoretical results of a higher level were found to be necessary, they were explained, as far as possible, in an intuitive way rather than with elaborate proofs or difficult calculations. The proofs and the calculations, when they are really necessary for a deeper understanding or for practical applications, have been provided in a few technical appendixes.
  • The content of the present book is an extended version of lectures given at College de France in Paris during the winter of 1991, and I thank ... [snip]

“How to Read This Book”
  • It has become customary to tell the reader how to read a book, as if he were not able to browse through it by himself. I rarely understand this kind of introduction, except after having read most of the book. This is why I shall mention here what should not be read.
  • If you already know quantum mechanics15, don’t read the first chapter. It contains the usual preliminaries.
  • If you want to know what is new in the present approach, go immediately to the first part of the last chapter. After that you may wish to read what comes before. By all means, don't read the second part of the last chapter. It is more or less philosophical in nature and would lead you to believe that the rest of the book is like it. That would be misleading.
  • If, on the contrary, you are inclined toward the theory of knowledge and what quantum mechanics16 can add to it, read the second part of the last chapter and browse through the text containing no equations, particularly the end of Chapter 2, the interlude, and some parts of Chapter 8.
  • If you were looking for a novel and you found only this book in the library. you didn't make a complete mistake as, under another title such as "The murder of Professor Schrodinger's cat,” it contains an enigma with a solution at the end to exercise little grey cells. If you want to understand quantum mechanics17, I beg you to read a significant part of the text, and, from my heart, I hope you will be satisfied. If there is at least one such person, many years of work will not have been useless.
  • Finally, although the main text has been kept at a rather uniform level, it may be mentioned that the appendices are more mathematical. This is also true of a few sections, which are marked by an asterisk; I have tried my best that they might be skipped without breaking the line of argument. Similarly, a problem marked by an asterisk indicates that it is on the border of research or that it involves nontrivial calculations.


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