Consistent Quantum Theory [Paperback]

Robert B. Griffiths (Author)

Book Description

Publication Date: December 8, 2003

This volume elucidates the consistent quantum theory approach to quantum mechanics at a level accessible to university students in physics, chemistry, mathematics, and computer science, making this an ideal supplement to standard textbooks. Griffiths provides a clear explanation of points not yet adequately treated in traditional texts and which students find confusing, as do their teachers. The book will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.

Editorial Reviews

Review

"Students, teachers and researchers familiar with or interested in issues of interpretation of quantum mechanics will enjoy this book." Choice

"The book is systematic and clear. The conceptual framework of the consistent histories approach is sharply delinerated, there is an abundance of examples, open questions are honestly identified, and there are references to more detailed studies. I think it is the best book on consistent histories thus far, indispensable for those who want to understand this interpretation of quantum mechanics." Mathematical Reviews

Book Description

This book presents what is known as the consistent quantum theory approach to quantum mechanics at a level accessible to university students in physics, chemistry, mathematics, and computer science, and can be used as a supplement to standard textbooks. It provides a clear explanation of points not yet adequately treated in traditional texts and which students find confusing, as do their teachers. The book will also be of interest to physicists and philosophers working on the foundations of quantum mechanics.

See all Editorial Reviews

Product Details

• Paperback: 408 pages
• Publisher: Cambridge University Press (December 8, 2003)
• Language: English
• ISBN-10: 0521539293
• ISBN-13: 978-0521539296
• Product Dimensions: 9.9 x 7.3 x 1 inches
• Shipping Weight: 1.9 pounds (View shipping rates and policies)
• Average Customer Review: 3.7 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #1,303,679 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

19 of 19 people found the following review helpful:

5.0 out of 5 stars Highly recommended for everyone interested in quantum mechanics, April 9, 2006

By 

Roger Berlind (NY, USA) - See all my reviews
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This review is from: Consistent Quantum Theory (Paperback)

This is a very interesting, clearly written introduction to the consistent histories (CH) interpretation of quantum mechanics that addresses many of the short-comings of the traditional Copenhagen interpretation. The book is self-contained and should be easy to understand for anyone with some prior exposure to quantum physics, linear algebra, and probability. While people curious about quantum mechanics and its interpretations could read this book by itself, physics students should read it as a supplement to standard textbooks.

After laying out the basic principles of quantum theory, Griffiths introduces consistent families of quantum histories and illustrates how they can be applied to quantum phenomena. He argues convincingly that applying CH principles avoids the confusion that many people feel when learning quantum mechanics. He then introduces a key principle called the "single-framework rule" which prohibits combining conclusions from inconsistent families of histories. The second half of the book discusses measurements in the context of quantum physics and explores many of the famous paradoxes of quantum theory, showing that they all result from violations of the single-framework rule.

One of the strengths of the CH interpretation is that it addresses the measurement problem of quantum mechanics in a way that applies the same quantum principles to all physical processes including measurements. Griffiths interprets the so-called "collapse" of the wave function introduced by von Neumann as a mathematical procedure for calculating probabilistic correlations rather than as an actual physical phenomenon. This approach avoids non-local effects and eliminates the need to assign any special role to conscious beings.

One thing did bother me about the CH approach: in many situations a physicist can select multiple incompatible frameworks of consistent histories to describe physical phenomena and derive contradictory conclusions from them. While Griffiths argues that incompatible frameworks cannot lead to contradictory results if they share the same initial data, a physicist is free to ignore some or all of the initial data available to him (via measurements) when constructing a family of consistent histories. The CH interpretation could benefit from some additional rules that would restrict the choice of frameworks.

Despite this objection, I enjoyed this book very much and encourage everyone interested in quantum mechanics to read it.

26 of 28 people found the following review helpful:

5.0 out of 5 stars non-measurement QM, March 30, 2002

By 

Mircea (LEESBURG, VA USA) - See all my reviews

This review is from: Consistent Quantum Theory (Hardcover)

Ab initio development of the "consistent-histories" formulation of QM, which avoids the classical, measurement-related paradoxes. Could be used at upper undergrad level, but I think one should be at least at grad level to appreciate this book. Great examples ("toy models") for building intuition, comprehensive review of mathematical machinery. Best textbook, IMO, for someone who wants to advance their *understanding* of QM (forget the Copenhagen interpretation!).

32 of 36 people found the following review helpful:

5.0 out of 5 stars Quantum mechanics is a local theory!, November 11, 2004

By 

Jill Malter ([e-mail]) - See all my reviews

This review is from: Consistent Quantum Theory (Paperback)

This book is not so much about doing practical quantum mechanical calculations as with the interpretation of quantum theory. As Griffiths says, you can't use it alone as a primary text to learn quantum mechanics: you'll need a separate text to cover blackbody radiation, the photoelectric effect, atomic spectra, the hydrogen atom, harmonic oscillators, perturbation theory, and the like.

When quantum mechanics was developed, it gave such good results that people often overlooked the difficulties with connecting the theory to physical reality. Reality to them consisted of actual measurements. And so the notion grew that measurements were an integral part of the theory, and that measurements affected what was thought of as physical reality, even non-locally. When students looked puzzled, their teachers merely reminded them that reality is weird! Well, sure, reality is a little strange, but there is never a need to describe reality in a self-inconsistent manner.

The problems came with concepts such as "collapse of the wavefunction." That is, we'd measure a property (say, the x-polarization) of some particle. And the nature of a faraway linked particle would appear to change, instantly. That's a non-local effect: it travels faster than light. And if that effect were genuine, it would permit sending signals backwards in time.

The associated problem was with measurement: the existence of an observer appeared to change reality.

Worse, these complaints struck right at the core of quantum mechanics, whose proponents boasted about the importance of "looking at the fundamental laws" in a way "which makes their self-consistency obvious" (quoting from Dirac's quantum mechanics book).

Those of us who read the excellent text, "The Feynman Lectures on Physics," were taught that the following statement is false: "you can not alter the physical nature of" (faraway) "photons by changing the kind of observation you make on your photons." And that just did not help. In some sense, that statement must be not false, but true, to avoid the problems we just stated.

Part of the reason for the confusion is that in most cases, making a measurement on a particle really does change the state of that particle. But not always: repeated measurements of x-polarization simply verify the state rather than changing it.

Now we have a book that explains how to make quantum theory self-consistent so we can avoid these problems. It explains that wave function collapse is simply a calculational device, rather than a physical effect produced by a measurement. It explicitly solves many famous quantum mechanics "paradoxes," including the "Schrodinger cat," the "Einstein-Podolsky-Rosen paradox," the "delayed choice paradox," and the "Hardy paradox." It discusses Bell's inequalities, showing that actual quantum mechanics is indeed a local theory (yay!) while "hidden variable" alternatives are non-local!

The key concept Griffiths introduces is the "consistent quantum framework" or "consistent quantum family." The idea is that there are multiple such frameworks, but accurate statements can be made only by choosing one of them and staying with it.

Griffiths explains that the following are true both of classical and quantum mechanics: measurements play no fundamental role in either, both are local theories, and both are consistent with the notion of an independent reality. However, there are some differences as well. Quantum theory shows that physical objects never have completely precise positions or momentums. The theory is stochastic, not deterministic, so we can't infer a unique future or past from the present. And finally, and most important, there is no unique exhaustive description of a physical system or process. "Instead, reality is such that it can be described in various alternative, incompatible ways, using descriptions which can not be combined or compared."

This is a valuable book for every physics graduate student.