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A formidable and intelligent account of the (partial) Hilbert-space formalization of quantum mechanics and the inevitable philosophical ambiguities that result...A marvelous book. -- P.D. Skiff Choice The power and elegance of the quantum-mechanical arguments are excellently portrayed and the reader...could not help being impressed by the sheer intellectual beauty of the subject. -- Alastai R. Rae Times Higher Education Supplement [This book] complements the material covered in standard textbooks on quantum theory, in which the issue of interpretation of the theory is too often neglected. -- Eduardo Sanchez Velasco Science Books And Films Hughes has written the best self-contained introduction to the foundations of quantum mechanics yet to appear...Hughes is clearly a gifted teacher, and a casual look at the book may suggest that it is primarily a textbook. In fact, a definitive interpretive perspective is developed throughout the book. -- Allen Stairs Synthese
Product Description
This work provides an account of the philosophical foundations of quantum theory that should become a text for scientists and nonscientists alike. Hughes offers a detailed and accessible analysis for the Hilbert-space models used in quantum theory and explains why they are so successful. He goes on to show how the very suitability of Hilbert spaces for modelling the quantum world gives rise to deep problems of interpretation, and makes suggestions about how they can be overcome.
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Most Helpful Customer Reviews
5 of 5 people found the following review helpful
Format:Hardcover
An extremely clear discussion of the structure of quantum mechanics. Most undergraduate textbooks can leave people feeling lost in a strange world. This book shows very clearly that this strange world makes perfect sense mathematically, and also emphasises the interpretive aspect of the subject. It amuses me that although much of the material covered in this book is usually considered unnecesssarily mathematical for an introductory text, the book ends up being more accessible than most textbooks. In fact, the only background it expects of the reader is high-school maths. I would recommend this book to anyone who to whom quantum mechanics feels strange and counter-intuitive. To anyone who is new to the subject and is willing to spend time getting a feel for the quantum mechanics as a whole before obtaining practical results, I would strongly recommend reading this before reading a standard textbook.
Most Helpful Customer Reviews on Amazon.com (beta)
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12 reviews
43 of 47 people found the following review helpful
Great book on quantum theory for the ambitious reader
26 Aug 2003
Format:Paperback
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.
20 of 21 people found the following review helpful
Most Comprehensible of the Substantive Non-Specialist Books
3 Jan 2001
Format:Paperback
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.
9 of 9 people found the following review helpful
In depth analysis
23 Aug 2005
Format:Paperback
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.
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.
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