Customer Reviews

Consistent Quantum Theory

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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.

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!).

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.

I doubt that even at the time it was formulated anyone really considered the Copenhagen interpretation of quantum mechanics to be fundamental. I would guess that even then it was looked at as a provisional point of view that was good enough to allow work to continue. Among its problems are the assumed existence of a classical world, that there are external observers (since quantum mechanics applies to the universe this is clearly a problem) and that these external observers play some sort of fundamental role in quantum mechanics. One unfortunate consequence of this is that it is easy to get the impression that there are two kinds of dynamical processes in quantum mechanics, unitary evolution and wavefunction collapse, the latter of which seems to violate the spirit of special relativity. This book provides important material that will help students avoid these misconceptions.

This book presents the consistent histories formulation of quantum mechanics. This approach has the advantage of not requiring external observers and that wavefunction collapse is seen a calculatingly tool.

It begins with an overview of many quantum mechanics concepts, most of which would be familiar to what I believe to be the intended audience, people already familiar with quantum mechanics at least at the level of a good undergraduate course. This includes things like wavefunctions, Schrodinger's equation, Dirac notation, observables and Hermitian operators, probability and more.

The concept of consistent histories is then introduced. Consistent histories are used in the book to analyze the common paradoxes of quantum mechanics such as Schrodinger's cat and the EPR paradox. In addition, some less common ones are considered. One strength of the book is that it clarifies concepts with toy models (usually quantum systems with a finite number of states) that simplify the physics as much as possible. There is also some material that I do not recall seeing elsewhere, such as a nice discussion of counterfactual arguments. One quibble is that I would have like to have seen an expanded discussion of decoherence, but he may have omitted that because such discussions appear elsewhere.

What is the audience? It won't help you calculate scattering cross sections or the energy levels of a hydrogen atom, but it should help you understand the concepts of quantum mechanics better.

If you are a student of quantum mechanics (for the first time) you will learn nothing from this book. It does not contain anything of practical value. If you are interested in philosophy, or an amateur of science, this book is for you. If you are an experienced physicist, this book is pretty useless. How can one talk about histories without using the path integral? You are better off reading Feynman, Kleinert, Thirring and other authors who do understand quantum field theory deeply.

As a physicist in training, I think it's important to put in some distinctions between science and philosophy. The distinct position of science is due mainly to the power to predict or calculate future outcomes of an isolated event based on laws of physics. For example, based on Newton's Law, we can calculate the trajectory of a speeding bullet. Of course, as we refine our theoretical and experimental physical understanding, we encounter predictions that are counter-intuitive. This is where science differs greatly from philosophy - explainations and interpretations in sciences are only meaningful if and only if it implicates further physical predictions. Therefore, however bizzare physical results or theory maybe, further explainations are considered only when it provides additional predictions. I cannot say today that there won't be experiments in the future that can help us resolve all these "quantum mysteries", i.e., physically show us which interpretation is correct. The beauty of mathematics is that one can dream up infinite different ways of representing something consistently. But one has to remember that mathematics in physics is an abstraction of reality. Multiple representation of reality might be useful computationally or conceptually, but if it adds to neither, than it is a mere philosophy. That all being said, while the theory of Consistent Quantum History might be interesting, it is as of now untestable. It is not untestible in the sense of String Theory, where testible results are not within our experimental reach. It is the framework of quantum mechanics that prevents us from distinguishing the various interpretations, and therefore rendering CQT only a slight bit more than a carefully composed philosophy.