Understanding Quantum Mechanics by Roland Omnès (PDF)

Description

Here Roland Omnès offers a clear, up-to-date guide to the conceptual framework of quantum mechanics. In an area that has provoked much philosophical debate, Omnès has achieved high recognition for his Interpretation of Quantum Mechanics (Princeton 1994), a book for specialists. Now the author has transformed his own theory into a short and readable text that enables beginning students and experienced physicists, mathematicians, and philosophers to form a comprehensive picture of the field while learning about the most recent advances. This new book presents a more streamlined version of the Copenhagen interpretation, showing its logical consistency and completeness. The problem of measurement is a major area of inquiry, with the author surveying its history from Planck to Heisenberg before describing the consistent-histories interpretation. He draws upon the most recent research on the decoherence effect (related to the modern resolution of the famous Schrödinger’s cat problem) and an exact formulation of the correspondence between quantum and particle physics (implying a derivation of classical determinism from quantum probabilism). Interpretation is organized with the help of a universal and sound language using so-called consistent histories. As a language and a method, it can now be shown to be free of ambiguity and it makes interpretation much clearer and closer to common sense.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I enjoyed Omes’ previous publication, The Interpretation of Quantum Mechanics (Princeton University Press). If you have read the earlier book, you do not need this one. The earlier book provides more detail.Additionally, the earlier publication is more satisfying. Allow me to focus on this later “understanding” :(1) I note an unfortunate typo, page five: for units of Planck’s constant (it is “energy times time,” not the “energy divided by time” where the book reads “Joules/second”). Omnes: “there is nothing better than the papers by the pioneers.” So, keep a copy of the Wheeler & Zurek compendium (1983) handy.(2) You get historical insight in the initial chapters (30 pages): “Harmonic oscillators were central…” (page 10). Read: “The Bohr-Sommerfeld theory was a bridge over a chasm…” (page 21) and “in quantum mechanics simplicity is often more or less an illusion.” (page 22). The third chapter is useful, Heisenberg’s matrix mechanics surveyed.(3) Regards Max Born and probability: “Born’s introduction of probabilities in quantum mechanics reveals an essential feature…that had been practically ignored until then.” (page 35). In my opinion, Max Born remains underappreciated to this day.(4) Here read: “The aim of the interpretation of quantum mechanics…must involve, in one way or another, a radically new manner of thinking and understanding.” (page 49). You read of the so-called reduction of the wave-function (pages 52-54). The best is yet to come in chapter six, with John Von Neumann.(5) Read: “The wave-function is not an objective physical quantity, but a compendium of information” and “perhaps the fuzziest idea of quantum mechanics is the concept of ‘object’ .” (page 71).Read Isham for more (1995).(6) John von Neumann appears time and time again. Ninth chapter, Neumann’s Projection Postulate. Nice. I do find ambiguity in this: “a moment later, its wave-function is divided into two parts.” (page 104).That is, I question the interpretation that the ‘wave-function’ is ‘divided’ into two parts.(7) Meet Wigner and Weyl (distributions, page 112). More from them in Esposito, Marmo and Sudarshan (2004). There you see where “it shows the sense in which quantum mechanics is non-local.” (page 544).(8) A central theorem, due to Egorov, will be referred to often (pages 125-131). This will be new to many a reader even if they have had a first course in quantum mechanics. This chapter, eleven, is too brief.(9) Next, Histories. Read: “they are as intuitive as quantum physics can tolerate.” (page 140) and read “but sense versus non-sense is a matter of logic.” Now, press on to the excellent thirteenth chapter: “the state of a system.” Max Born is again given advertisement (page 145) and learn of “state preparation.”John von Neumann is reintroduced (page 150). Gleason is introduced (“the most abstract one”). I refer the reader to Isham: “Gleason’s Theorem places strong constraints on any attempts to modify the standard quantum formalism.” (1995, page 211). Histories keep you occupied for another three chapters.(10) Now read: “reality can certainly not be defined.” Decoherence keeps you occupied for three chapters. Learn of the close relation between dissipation and decoherence (“macroscopic interferences”). Read: “by the word ‘real’ I mean that the measurement devices are macroscopic and that they show decoherence.” (page 221). Notes and comments concludes the publication.(11) Concluding: This is a thoughtful and well written exposition, within grasp of its intended audience,an audience of beginning students. It will not replace–nor was it intended to replace–a standard course.It should be followed-up with a few others (Omnes’ earlier monograph or Isham’s lectures-text).Well worth the investment in time and effort. Not the final word, yet, an encouraging word.

⭐I bought this book a long time ago and have finally gotten around to reading it after much time spent on actually learning the subject of quantum mechanics, for which I remain a student. It should most certainly not be the first book one reads on quantum mechanics. I don’t think anyone who thinks that understood much in this book. This book is really difficult and covers both philosophy and physics. The level of philosophy is approachable, the level of physics is that of someone with 1 year + of a QM course if not more.The author breaks the book into three parts with most of the content in the third. The first part of the book the author discusses aspects of the history of quantum mechanics, the relevance of Plancks constant, the emission lines in hydrogen and most importantly aspects of the framework for thinking in both wave mechanics terms as well as matrix mechanics terms. Core ideas of quantum mechanics are discussed extremely briefly, like the non-commutativity of matrices and Schrödinger’s equation as well as the Hydrogen eigenvalue equation. The author moves onto the real subject with the assumption of a pretty full understanding of both wave as well as operator methods in quantum mechanics; hence as a light first introduction to quantum mechanics one without prior knowledge of the math behind QM there is little to really hold on to. Nonetheless with assumed background the author mainly gets into discussing several major topics. The author spends time on concepts of reality in quantum mechanics, the relationship between classical ideas and quantum mechanics and the bridge between the two framings of reality. The reader should understand the difference between the Heisenberg and Schrodinger interpretations and very familiar with unitary transformations. The author spends a lot of time on projection operators and diagonal matrices as they are needed to understand consistent histories. One of the hardest parts of the book, but most important is the discussion on decoherence. This was a weak part of the book, decoherence is not discussed in quantum mechanics classes to undergraduates to any real extent so the author, with a supposed audience of students, should have discussed the ideas from a more elementary level. Instead the author was speaking to the expert on a matter which was the most important part of the book. This was a missed opportunity and a major oversight in my opinion. The author discusses how decoherence can solve paradoxical hypothetical phenomenon like Schrodinger’s cat, but in practice it is not easy to follow the main arguments as they are not discussed from close to a first principles basis. The author discusses measurement theory which is pretty enjoyable to read and then ends with a chapter on measurement which is very abrupt and there is no conclusion to the book.Understanding Quantum mechanics attempts to bring quantum mechanics back to the realm of human understanding and intuition. From that as a goal it doesn’t really succeed as its mainly a discussion of making sense of decoherence which is a rather unexplained topic to a student of quantum mechanics. There is much of the material that can be loosely followed by knowing wave and matrix mechanics and knowing some functional analysis, but when it gets to the core ideas of quantum mechanics I think the target audience is really for PhD students and professors. This is not broadly readable and the explanations for the main ideas are not comprehensive.

⭐This book is the first book you should read if you haven’t had much exposure to quantum theory. This is a must have for any person interested in physics, Hell get this book just to read to the kids or Grampa when he gets confused about 1/2 spin particles. you won’t be crunching unified fieled theory equations, but your brain will be not dumb no more.

⭐This book is sooooo good!!! If your mind is stuck in a classic point of view, this book will help you develop a more quantic perspective, with very few equations!

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