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Quantum Paradoxes: Quantum Theory for the Perplexed (Physics Textbook) [Paperback]

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Item description for Quantum Paradoxes: Quantum Theory for the Perplexed (Physics Textbook) by Yakir Aharonov & Daniel Rohrlich...

A Guide through the Mysteries of Quantum Physics!
Yakir Aharonov is one of the pioneers in measuring theory, the nature of quantum correlations, superselection rules, and geometric phases and has been awarded numerous scientific honors. The author has contributed monumental concepts to theoretical physics, especially the Aharonov-Bohm effect and the Aharonov-Casher effect.
Together with Daniel Rohrlich, Israel, he has written a pioneering work on the remaining mysteries of quantum mechanics. From the perspective of a preeminent researcher in the fundamental aspects of quantum mechanics, the text combines mathematical rigor with penetrating and concise language. More than 200 exercises introduce readers to the concepts and implications of quantum mechanics that have arisen from the experimental results of the recent two decades.
With students as well as researchers in mind, the authors give an insight into that part of the field, which led Feynman to declare that "nobody understands quantum mechanics".

* Free solutions manual available for lecturers at

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Item Specifications...

Pages   289
Est. Packaging Dimensions:   Length: 0.75" Width: 6.75" Height: 9.5"
Weight:   1.3 lbs.
Binding  Softcover
Release Date   May 6, 2005
Publisher   Wiley-VCH
ISBN  3527403914  
ISBN13  9783527403912  

Availability  0 units.

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Reviews - What do customers think about Quantum Paradoxes: Quantum Theory for the Perplexed (Physics Textbook)?

Highly Recommended  Aug 24, 2006
Understanding how to calculate quantum mechanics does not provide an understanding of quantum mechanics. This book addresses understanding quantum mechanics at a deeper level than calculations provide. Aharonov and Rohrlich organize "Quantum Paradoxes" not by examining progressively more complicated quantum systems to calculate as in conventional textbooks (i.e. first one dimensional potentials, later three dimensional, etc.) but by analyzing paradoxical phenomena to enhance understanding. Novel techniques for making nondisturbing measurement devised by Aharonov and collaborators are presented. These new types of measurements lead to sometimes surprising insights into what is essentially "quantum" about quantum mechanics and the many ways in which a quantum system can be probed. There are numerous subject areas covered throughout "Quantum Paradoxes", but I will review the Aharonov-Bohm (AB) effect, quantum measurement, and a particular type of measurement called weak measurement.

One might expect that if an electron passes through a double slit in which neither region after the slit has an electric or magnetic field, then there will be no effect on the electron. However, it turns out that there is an observable non-local quantum effect, which shifts the interference pattern. This remarkable prediction by AB is presented in Chapter 4 very clearly for two different cases. In one case there is a capacitor in the middle of the slits whereby there is an electric field inside the plates of the capacitor but there is no electric field where the electron emerges through either slit. In another case there is an inductor in the middle that causes a magnetic field again in a limited region but is zero where the electron moves through the slits. In both cases, it is shown why one sees an effect and this is explained by the necessity for use of potentials in the Hamiltonian as opposed to the EM field strengths. One can see the significance of potentials and understands the non-local effect on the electron. The AB effect turns out to extend to a grating of slits and incorporates the use of modular position and momentum and also the relation of AB to Berry's phase is shown.

Another important example where this book provides the reader understanding rather than just calculations is quantum measurement. Quantum measurement is covered in substantial detail; Chapters 7 through 16 examine various aspects of quantum measurement. "Quantum Paradoxes" utilizes a method proposed by von Neumann to analyze measurement by which an interaction Hamiltonian related to the observable being measured is used. The uncertainty principle is analyzed using this model and there is also a chapter devoted to non-canonical quantities such as velocity which can change during the measurement. A chapter on Schrödinger cats that examines the problem of superpositions is also developed within the von Neumann formalism. A related issue of whether quantum theory is complete in terms of the issue of Einstein,Podolsky Rosen (EPR) and its relationship to non-locality, entanglement, and Bells theorem is presented early on in Chapter 3. In Sec. 3.5 the authors conclude that Einstein may have been correct that quantum mechanics is incomplete but not in the EPR sense. A lucid account of the issue is given later in Sec. 9.2. Finally, there is an attempt to come to terms with the measurement problem by the use of the Aharonov-Bergmann-Lebowitz (ABL) formula. In this theory there is a forward vector in time as well as a backward vector that are used to describe quantum state evolution and understand the arrow of time. In the last chapter there is a discussion of this formalism and free will which are also very important from a philosophical point of view. The issue of final destiny states raises cosmological questions as well.

Most quantum measurements that are conventionally discussed deal with a sufficiently strong interaction between measurement device and the system being measured. However, it is possible to reduce the interaction to a regime called weak measurement. The authors consider whether this regime is useful when one considers that one will often destroy or collapse a wavefunction if one tries to learn about it using a strong interaction. In fact Bohr and others have made arguments that one cannot learn about the system without affecting it. Aharonov and Rohrlich succeed in showing quite the contrary--how to learn about a quantum system without disturbing it. They use weak measurement on multiple iterations of particles with the same wavefunction. Such new measurement techniques are now being employed in experiments to gain information about quantum systems.

There are numerous other paradoxes examined in this book including the Zeno effect, Interaction free measurement, Quantum walks, a quantum shell game, a quantum catalog, and even a quantum card trick. There are problems at the end of each chapter for use as a textbook or to become proficient. Although the organization of the material could probably be improved, I can see where this is difficult with so much interrelated material. In addition to the many paradoxes presented there is much more, including discussions on nearly all major fundamental quantum theoretical questions as well as methods and techniques. There is no other book that elaborates on fundamental issues in such detail.
"Paradox" may be in the eye of the beholder  Jul 22, 2006
I obtained this book through interlibrary loan, with the intention of buying it if it looked as if it would repay careful study. I decided against buying it for reasons described below.

The loan period was only ten days, and I was only able to read the first eight chapters (about half the book) in this time. However, I did look over the rest, and its flavor seemed typical of the chapters that I did read. Most of the authors' arguments are exceedingly vague.

The preface begins:


"*Quantum Paradoxes* is a series of studies in quantum theory. Each chapter begins with a paradox motivating the study ... of a fundamental aspect of the theory. ...
The studies, taken together, set out a new interpretation of quantum theory.''


Before continuing, I should remark that the precise content of the "new interpretation of quantum theory" escaped me. Indeed, I wouldn't have guessed that the book contained such an interpretation had it not been for the above quote. Perhaps the "new interpretation" is implicitly contained in the chapters which I didn't have time to read carefully.

The authors seem to use the word "paradox" in the sense of "any unexpected result of a calculation" (my interpretation, not a quote from the book). Most of their "paradox"-yielding calculations are of the hand-waving variety. None of them seemed to me to justify the term "paradox".

For example, the Aharanov-Bohm effect demonstrates that a magnetic field can have an observable effect on electrons even when the field is confined to a region which the electrons never enter. However, the observable effect is a statistical quantum effect (an interference pattern), not an effect which would make sense for a single electron within the conceptual framework of classical electrodynamics. The Aharonov-Bohm effect is surely a striking effect unanticipated by classical electrodynamics, but it seems a stretch to call it a "paradox".

Chapter 2 is largely devoted to a description of a thought experiment devised by Einstein to convince Bohr that the time-energy uncertainty relation (see below) need not hold. The authors report that after considerable effort,
Bohr resolved this "paradox".

But the time-energy uncertainty relation is not a fundamental part of the logical structure of quantum mechanics---it is a kind of assumed generalization of the Heisenberg uncertainty relations
(which *are* rigorous consequences of most axiomatizations of quantum mechanics such as those of Von Neumann and Mackey). Why should it be considered a "paradox" if the time-energy uncertainty relation did not hold (as seems quite conceivable to me)?

In Chapter 2, the reader is never advised that there is a fundamental logical difference between the time-energy uncertainty relation and the position-momentum Heisenberg uncertainty relation. The authors do finally recognize this in an extended discussion in Chapter 8. It begins with the following quote from Section 8.1, p. 106,
in which "\Delta" stands for the uppercase Greek letter "Delta",
and \nu for the lowercase Greek "nu":


``Numerous books and papers claim that a measurement of energy cannot take an arbitrarily short time. They interpret the energy-time uncertainty relation

[equation (2.10), \Delta E \Delta T >= h ] as follows:

the faster the energy measurement, the more uncertain the result.
Let us examine some arguments for this interpretation.

i) A simple argument starts with Einstein's equation relating energy and frequency [equation (2.3), E = h \nu ]. Suppose a quantum wave takes a time T to pass through a measuring device. Since the wave lasts a time T, its Fourier transform is large for frequencies in a range that includes 0 <= \nu <= 1/T.
Then \Delta E = h \Delta \nu >= h/T . ii) ... "


If you find this clear and convincing, then you may get more out of the book than I did. To see the difficulties, try to formulate the authors' assertions as a rigorous theorem for a wave function \psi = \psi(x,t) satisfying the Schroedinger equation, and then try to prove it. None of my formulations were trivial, either mathematically or physically. Proofs, if any exist, seem probably difficult. (No proof, or reference to a proof, is given in the book.)

Chapter 7 develops a "model for the measurement of an observable" which is used throughout the rest of the book. It attributes this model to von Neumann, but if it is in fact due to von Neumann, it must be in some different form, because the book's development of it is largely mathematical fantasy. The mathematical details can be found on my web site.

The above makes clear that I think the book has serious flaws. But I would hesitate to say that it is totally without merit for the following reasons.

Aharonov apparently used reasoning of a style similar to the text
to suggest the possibility of the striking Aharonov-Bohm effect.
(I do not know the details of the history of this effect). The text's motivation of this effect seems to me not sufficiently convincing to bet on the effect before it was observed. Nevertheless, it *was* observed, and it was Aharonov-type thinking which led to its observation. There may be something to be learned from this.

It may be that the accepted logical structure of quantum mechanics will eventually be recognized as too limited. Perhaps it will be enlarged to encompass and make rigorous the hand-waving kind of arguments presented in this book.

This is the sort of book which I might recommend for purchase by a well-stocked university library with excess funds for acquisitions. Though I did not buy it because my best judgment is that its careful study would be unlikely to repay the effort,
it is a book which I might like to have available for browsing.

It seems well edited and professionally produced, with good diagrams.
For example, its description of the Bohr-Einstein controversy over the time-energy uncertainty relations includes an elaborate diagram of an antique clockwork mechanism to measure the time of an energy emission. I enjoyed reading about this even though
it seems to me an irrelevant historical curiosity.

The book is subtitled "Quantum Theory for the Perplexed". This seems to hold the promise that reading the book may make the subject clear and obvious. I would be very surprised if a significant number of readers came away with this hope fulfilled.

In particular, the Preface's claim that "students can use the book even during a first course in quantum mechanics" seems wildly optimistic. I can imagine this book being of interest to mature physicists, but I think it would be a disservice to recommend it to someone learning quantum mechanics. I think it would only heighten the usual perplexity experienced not only by new learners, but by almost everyone who has thought carefully about how quantum mechanics can possibly be consistent with our everyday experience.


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