Friday, August 23, 2013

New Father-and-Son Quantum Text Book

Samarkand, Uzbekistan by Richard-Karl Karlovitch Zommer
Samarkand, one of the world's oldest inhabited cities, once prospered as a trading post on the Silk Road between China and Europe. During the Islamic Golden Age (750 AD -- 1258 AD) the city became a famous focus of Arab scholarship in astronomy, medicine and mathematics. In more modern times, there graduated from the State University of Samarkand a physicist Moses Fayngold, who with his son Vadim, also a physicist, has written a new text book on quantum mechanics, intended for advanced undergraduates and beginning graduate students. I found this book rich and unpredictable and, like the romantic Silk Road metropolis, offering something fresh and exotic around every corner.

Why does the world need yet another book about quantum mechanics? This question was raised by the father. "[The father], who by his own admission, used to think of himself as something of an expert in QM, was not initially impressed by the idea, citing a huge number of excellent contemporary presentations of the subject. Gradually, however, as he grew involved in discussing the issues brought up by his younger colleague, he found it hard to explain some of them even to himself. Moreover, to his surprise, in many instances he could not find satisfactory explanations even in those texts he had previously considered to contain authoritative accounts on the subject." (from the Preface).

Unlike most conventional quantum physics texts which merely explain things, this book also focuses on many of the loopholes, exceptions, imperfections, misunderstandings, man traps and pitfalls that exist in this complex field.

When you buy a new car, you will find an Owner's Manual in the glove compartment that tells you how to change the oil and how to replace the light bulbs. But if you are handy with tools you will also want to purchase the Mechanic's Manual to learn how to do things that only professionals should attempt. And, in particular, to learn things that YOU SHOULD NOT DO. (Never unscrew part A before releasing part B.)

This new quantum text book is the equivalent of a Mechanic's Manual that makes previous text books seem mere Owner's Manuals.

Most quantum text books tell you how to do things, but I have never run across a text book like Moses and Vadim's which tells you WHAT NOT TO DO. Over and over again in this text, I ran across comments to the effect that "The naive way to do this is B, but B will give you the wrong answer. Here's how to do things right." The authors seem to have anticipated many pitfalls that lie in wait for the quantum neophyte and have posted the appropriate warnings. My guess is that these pitfalls are those into which Moses and Vadim have themselves fallen. Niels Bohr once claimed that the definition of an "expert" in a field is a person who has made all the mistakes in that field. In this unusual book Moses and Vadim give you the advantage of that kind of street-smart expertise.

Their book begins by describing some major phenomena that classical physics could not explain (black-body radiation, photoelectric effect, low-temperature specific heats and atomic spectra), then show how one simple concept--the quantization of energy--could correctly reproduce these results.

Moses and Vadim then describe the origin of Louis DeBroglie's hypothesis--that matter possesses a wave-like nature whose wavelength DeBroglie could calculate. Altho this textbook confines itself to non-relativistic quantum mechanics, I was surprised (one surprise of many) to discover that DeBroglie's calculation was motivated by special relativity which means that his discovery is deeper than necessary and transcends its non-relativistic buddies such as the Schrödinger equation.

Using the DB hypothesis to physically justify energy quantization (similar to the way that resonance modes quantize the notes of stringed instruments), Moses and Vadim then use the Superposition Principle for waves to construct an "embryonic quantum mechanics" from which much more good physics can be derived without yet mentioning the Schrödinger Equation.

This book includes in-depth discussions (always accompanied by Moses and Vadim's dependable pitfall warning signs) of most of the conventional topics in quantum theory including Hilbert space, Dirac notation, angular momentum, scattering theory, band structure, quantum tunneling, density matrices, Kaon and neutrino oscillations, quantum entanglement, CHSH, POVMs, CNOT and XOR gates, the Bloch sphere, Zeno's paradox, Schrödinger's Cat, and much much more.

Moses and Vadim also introduce a novel topic they call "submissive quantum mechanics" in which they show how to manipulate potentials to create customized wave functions never before realized in nature--a useful skill that may prove profitable in the emerging field of nanotechnology.

Again and again while reading this book I got the feeling of a wise adviser at my side. The ratio of explanatory text to equations is large--resulting in a lucidity reminiscent of the classic Feynman Lectures as well as Quantum Theory by David Bohm.

Besides devising the shortest proof of Bell's theorem, Nick Herbert's main claim to physics fame is his FLASH (First Laser-Amplified Superluminal Hookup) proposal which purported to send signals faster-than-light using a "laser-like device" to clone single photons. The FLASH proposal was refuted by Wooters and Zurek who proved that "a single (unknown) photon cannot be cloned", a result which crucially limits what quantum computers can do--for instance, when quantum hard drives or quantum DVDs are built, the no-cloning theorem provides automatic copy protection courtesy of the laws of physics.

Naturally I was curious about how Moses and Vadim would deal with my FLASH proposal in their hyper-informative "Mechanic's Manual" style. In this I was not disappointed.

The authors agree that the W&Z "no perfect cloning of unknown states" proof definitively refutes my FLASH proposal. But what about "imperfect cloning"?, they ask. And what about the cloning of states that are not completely unknown but part of a small prearranged set of known states? Moses and Vadim carefully consider these loopholes (and a few more) to the standard FLASH refutation and definitively decide that FLASH won't work. But in the course of their detailed refutation the reader learns a lot about quantum cloning machines.

This book is a wonderful Mechanic's Manual crammed full of intimate details about the operation of one of the most elegant intellectual sports cars we possess--the theory of non-relativistic quantum mechanics. But in addition to this Mechanic's Manual, I urge you to also purchase an Owner's Manual of your choice, a book that you can use to solve everyday problems in simple ways. (My own favorite Owner's Manual is the classic text by Leonard Schiff from which I learned QM in those bygone days when the world's largest particle accelerator was the Berkeley Bevatron.)

But next to your trusted Owner's Manual, be sure to include this helpful Mechanic's Manual on your book shelf, both to deepen your knowledge of quantum mechanics and to help you avoid some of its more obvious pitfalls.

This book is perfect for those quantum mechanics who know how to fix Volkswagons and now want to go to work on Porsches.

New father-and-son quantum text book

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