Customer Reviews

The Structure and Interpretation of Quantum Mechanics

5 star:		(6)
4 star:		(1)
3 star:		(2)
2 star:		(1)
1 star:		(0)

 

 

This is a superb teaching book for taking your understanding of quantum mechanics to the next level. Much of the book is devoted to understanding a good deal of the underlying math and mathematical formalism, such as Hilbert spaces, Hermitians, eigenvalues and eigenvectors, Cantor's calculus of infinities, the analysis and representation of spin properties, and other very cool stuff which I didn't have a very good grasp of before. And yet the previous math required is minimal, really only high school algebra, and Hughes defines new concepts as he goes along. Actually, there is some calculus here and there, but not a whole lot, which is fine, as my advanced calculus is pretty rusty at this point. So Hughes keeps the advanced math to a minimum. This doesn't mean the book is easy reading, as the algebra of Hilbert spaces includes such things as the logical properties of inner products, spectral decomposition, vector projections, the analysis of different vector operators, and so on, and that's only one small section in the book, not to mention the fact that Cantor's ideas in number theory about the ordinality or sizes of inifinite series is pretty mind-boggling stuff. Basically, Cantor established the improbable and surprising fact that certain infinities are "bigger" than others. One way he did this was to show that some infinities are "countably infinite" and others are not. Fun stuff.

All this is just preparation for understanding the quantum mechanics, however, and the author does a fine job of linking the mathematical concepts with the applied ideas in quantum theory. This is important, since quantum mechanics is basically a purely mathematical theory. Unlike Einstein's Special and General theories of Relativity, which, although pretty mind-boggling theories in themselves, can still be explained by using more or less intuitive and easy to understand spatial concepts and illustrations. You've probably encountered these in some of the books on the subject, such as doing the fun thought experiment of having two observers, with one travelling at the speed of light and the other stationary, to demonstrate the relativistic effects on space, time, and matter in the case of the Special Theory. But unfortunately those kinds of entertaining and informative thought experiments are difficult to do in quantum mechanics, which is why a book like this that explains the concepts at a relatively high level clearly and concisely is such a great find. Overall, this is an excellent "upgrade" book written by a gifted teacher on a very difficult subject. There are very few books like this that bridge the gap between the purely popular presentations of quantum theory and the very difficult technical quantum physics books.

I used this text in a tutorial with a distinguished philosopher of science at Queens College, New York. It's outstanding. The mathematical formalism is difficult for non-specialists, but no so much as to be out of reach. Advice: be patient--the understanding will come. The part on the interpretation of QM is exceptionally valuable to anyone interested in understanding modern physics without falling for dishonest notions like "quantum healing", "quantum chi", and "quantum dieting". In short: if you're a serious student, this is probably the best book of its kind.

This book provides an excellent analysis of relevant and interesting points raised by quantum physics in philosophy as well as detailed and useful explanations of the physics itself - something many books cannot do. The explanation of the physics, the experiments and their results provide material to think on. Simple, arbitrary conclusions leave no room for thought - analysis of real life experiments provoke thought.

The math is not easy for an inexperienced student, though the subject in general tends to preclude those. I had just taken a class on matrix mechanics and I was so greatful I had, as it let me actually visualize the equations rather than simply read the letters and symbols.

An excellent launching pad for those who are already familiar with EPR, the slit experiment and quantum spin, etc. and want to know what it all means.

This book was recommended to me as a very nice introduction to quantum mechanics for the mathematically-inclined. It looks like I'll be awaiting the publication of the new edition of Sudbery's text instead, because, at least for me, this book didn't quite end up filling the bill. It's true that, unlike so many popular introductions to quantum theory, Hughes' book doesn't shy away from mathematics. The mathematics for me was fine (although I wonder what a person who'd had "only high school algebra" would make of the derivatives and integrals that show up unannounced). It's in trying to make sense of what the mathematics is supposed to be modelling that I felt that this book lost a star. (How much of the problem is due to the author's exposition and how much is due to my shortcomings as a reader is something I'm not prepared to judge.)

Again, this is a good book, but I have no idea where people are coming from when they write "this is not only the best book ever written, but also the best book that ever will be written".

The math parts of this book are rather nice, but (as Hughes, to his credit, acknowledges) the book has the same problem as many other books written in the philosophy of science: in trying to neatly summarize the 'structure' of the subject, you get only a lifeless corpse of something that in fact is somewhat bloody and raw. Quantum mechanics, if you would take the word of philosophers for it, is a neat, self-contained bit of science from which all other science flows. The problem is, even if that were in some sense correct (an assertion I'm not entirely convinced of), then you'd have some tough explaining of how the other, extravagantly successful theories in physics come from it. Books like this skew away from that sort of practical consideration. Hughes, in later chapters, seems to think that the language of quantum mechanics is terribly important, but doesn't come to grips with the ways in which QM is actually used. You don't get the raw, bloody results of perturbation theory, the messy approximations that constitute the major part of the usage of QM in real-life scientific situations.

Perhaps these criticisms shouldn't strictly apply to this book. After all, the title is 'The Structure and Interpretation of Quantum Mechanics,' and, indeed, the first part of the book discusses the mathematical formalism (the 'structure'), and the second part of the book describes the way that different people have thought about QM (the 'interpretation'). So if I were to be absolutely fair in my review of the book, I'd have to say that Hughes succeeds in his main intentions. But at the same time, I can't give the book a wholehearted reccomendation, because I feel that in describing a the 'theory' in a setting entirely divorced from its experimental applications, it gives a very misleading understanding of what the whole enterprise is actually about. For instance, in the later sections of the book when Hughes argues against the view that QM is about matter waves, this seems to me to be very wrongheaded; if one of the historical justifications of a topic is the whole de Broglie idea, then why should we give it up, just because it isn't hardwired into the formalism?

It's not so much that I don't like this book as that I think that if one read it without quite a bit of physics background, he might end up more confused than he started. If you divorce 'physics' from describing actual, concrete physical systems, of course it'll seem strange. Do yourself a favor, and read a book describing some actual quantum mechanics, as it's used. Principles of Quantum Mechanics is a nice place to start.

When I first took a serious interest in quantum mechanics, I systematically searched through my university's entire section on quantum mechanics (a very sizable section) for a book that would help a novice non-scientist to systematically achieve a rigorous understanding of quantum mechanics, mathematical foundations and all. The instant I came across Hughes' book, I recognized it for the treasure it is. This is not only the best book ever written, but also the best book that ever will be written.

This is one of the most lucid accounts of a subject famous for its obscurity.

Hughes is one of a precious few who has one foot firmly planted in the science and the other in the broader philosophical tradition.

His text, a contemporary classic, sits comfortably on the shelf in the company of Jammer, Cushing, Shimony and D'Espangnat. Everyone from beginners to seasoned professionals can profit from this work. I heartily recommend it to anyone keen to understand the foundations of quantum theory -- a timely subject, now stirring to life after 60 years of slumber.

Before reading von Neumann or Akhiezer, go through this book first, PLEASE. It's not only a good introduction to QM, but also an interpretation or philosophy book. The contents are balanced and understandable for even a high-school student, which usually is not expected from a great thinker like Hughes. The book making is good as well -- cover design, editing, binding, etc. An interesting and decent treatment of quantum physics. Probability a must for any phys and math thinker. (I got the paperbound)

This is basically a Philosophical/Logical Analysis of the
fundamental assumptions of Quantum Mechanics. What it comes
down to in the end is that it decides, for example, the
adoption of Hilbert Space to work in is (philosophically/
logically)justifiable for the development of the
mathematical underpinning of Quantum Mechanics! So, what
else is new?
What other Infinite Dimensional Space, other than Hilbert's
would improve matters? For example, could QED have been
developed on a more promising basis using a different Space assumption than Hilbert's? This book does not provide an answer.

I bought this text when I was first interested in learning the math behind quantum mechanics. I was attracted to the exposition of the mathematical formalism of spin. That part of the book did not disappoint. But the remainder was almost unreadable: longwinded, pretentious pontifications on the "meaning" of quantum mechanics. The author could have saved many pages by substituting the following: "I really don't know what the "meaning" of quantum mechanics is". No shame there. As Richard Feynman once said: "Nobody understands quantum mechanics." And he should know.