Quantum mechanics is much more than just a "theory"; it is an entirely new way of looking at the world. Unlike other theories in science, quantum mechanics is not concerned with how events take place, but with what we can predict. Dynamical variables of a system described by quantum mechanics have no definite values unless they are measured. A radical revision of the usual notion of objective reality is required.

In classical mechanics, the state of a system is described in terms of its dynamical properties such as position and velocity. But in quantum mechanics, the state is described by a complex mathematical object (called the wave function) that is not an observable quantity. How this quantity changes with time is described by Schrodinger's equation, which replaces the Newtonian equations of motion for particles. The wave function can be related to the probability of finding particles within a given region. In quantum mechanics, such predictions are irreducibly probabilistic, in striking contrast to the determinism inherent in Newtonian mechanics.

Quantum mechanics has been spectacularly successful in accounting for an enormous variety of empirical facts. It is an indispensable tool for just about every branch of physics. While the past few years have seen a plethora of books on quantum mechanics for a wider audience, fuelled by the emerging possibilities of quantum communications and computation, the present book occupies a special position. To convey the flavour of quantum mechanics almost non-mathematically, while avoiding misleading simplification is a daunting task. The way Tony Hey and Patrick Walters have accomplished this is a remarkable feat.

Their book is an updated and enlarged version of their earlier book, * The Quantum Universe * (1987). The target readership remains the same, starting with advanced high-school students and undergraduates. A major addition is a thorough discussion of basic concepts of frontier areas such as nanotechnology. Hey and Walters succeed in capturing the excitement of the breakthroughs being made by manipulating single atoms, creating artificial molecules and developing devices called "quantum dots", which are, in a sense, designer atoms whose sizes and shapes can be tuned to create new types of materials. This discussion is motivated by Moore's law (that the number of transistors that can be fitted on a chip doubles in every 18 to 24 months) and the question of to what extent quantum tunnelling limits the size of a transistor.

Hey and Walters explain the essence of quantum cryptography and quantum teleportation in quite a succinct way while remaining fairly accurate. In comparison, the discussion of quantum computing appears somewhat uneven.

While the historical evolution of some of the crucial ideas is well told, and the major difficulties impeding its practical realisation are indicated, the authors do not try to explain "how", in principle, a typical quantum algorithm may be able to perform an operation (such as factorising a large number) more efficiently than a conventional computer.

A highlight of the book is its perceptive discussion of the foundational issues of quantum mechanics, for instance the measurement problem and quantum nonlocality. For some years now, these issues have no longer been merely conceptual but amenable to experimental study. Both originate from quantum entanglement. In classical physics, if two systems get separated after interacting, they become mutually independent. But according to quantum mechanics, even after the interaction between two systems ceases, their individual states remain coupled - involving action at a distance - no matter how large the spatial separation between them.

Hey and Walters deal deftly with quantum entanglement and locality (no action at a distance) while discussing the Einstein-Podolsky-Rosen (EPR) thought experiment of 1935. EPR implied that unless quantum theory was completed by ascribing "objective reality" to the pre-measurement values of dynamical variables, quantum correlations between them for separated systems could not be explained without violating the locality condition.

But John Bell showed 30 years after the EPR paper that even if quantum mechanics were "completed" by an "objectively real" theory that satisfied the locality condition, the theory would necessarily imply an incompatibility with the verifiable predictions of quantum mechanics. The authors deserve a special compliment for their lucid "intuitive proof" of Bell's theorem - widely regarded as the "most profound conceptual discovery in quantum physics since the early years of its advent", whose far-reaching ramifications concerning quantum nonlocality continue to unfold.

The quantum measurement paradox is that although quantum mechanics predicts the probabilities of measurement results, the theory in its standard form cannot ensure how a definite outcome, distinguishable from other possible outcomes, occurs during an individual measurement. This is because the states of the system and the macroscopic apparatus become entangled after a measurement process. Consequently, the final ensemble comprises members that are all described by the same entangled state. Thus no separate state can be ascribed to denote the "objective reality" of an individual outcome that is "out there" and can be inspected at will at any instant. It is therefore not specified by the theory how a particular outcome (such as a pointer reading on a measuring instrument) is actualised from the various possible outcomes.

* The New Quantum Universe * is one of the few accessible books on quantum theory that highlights the acuteness of the quantum measurement paradox.

Both the orthodox solution ( * a la * Bohr and Heisenberg) and its criticisms are mentioned. Among the various possible solutions, the decoherence and the many-worlds interpretation are explained, along with their inadequacies. But surprisingly, no mention is made of the two other major approaches - the Bohm model and the dynamical model of wave-function collapse. The Bohm model was crucial in motivating Bell's discovery of his theorem.

The authors do not touch on the issue that, since the quantum measurement paradox originates from extrapolating the quantum superposition principle to the level of macro-systems, it is important to verify its validity in the macro-domain. Recent experimental studies verifying quantum interference effects using large molecules (C60 molecules known as buckyballs) and superconducting quantum interference devices are of particular interest in this context and should have been mentioned.

The afterword provides a lively discussion of the science-fiction stories, plays and novels centred on some of the profound enigmas and applications of quantum theory. Richard Feynman once lamented that the "awe and mystery of science" remained "unsung" by artists. He would definitely have been pleased to read this chapter. Thus, * The New Quantum Universe * has all the ingredients required to stimulate the imagination of young readers to take part in the grand adventure of chasing the truth of quantum mysteries and exploring the potentialities of quantum technology.

Dipankar Home is professor of physics, Bose Institute, Calcutta, India.

## The New Quantum Universe

Author - Tony Hey and Patrick Walters

Publisher - Cambridge University Press

Pages - 356

Price - £55.00 and £19.99

ISBN - 0 521 56418 2 and 56457 3

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