American Scientist

Sneaking a Look at God's Cards: Unraveling the Mysteries of Quantum Mechanics. Giancarlo Ghirardi. xxii + 488 pp. Princeton University Press, 2005. $35.

The discovery of quantum mechanics in the mid-1920s by Werner Heisenberg, Erwin Schrödinger and others was a truly revolutionary development in the history of physics. The new theory was an immediate success, explaining a wide range of atomic-scale physical phenomena that had until then been mysterious. Since its discovery, the basic quantum-mechanical formalism has survived more or less unchanged and has become the very foundation of modern physics. But from the earliest days of the theory, confusion about its interpretation engendered a continuing series of debates, and these are the subject of Italian physicist Giancarlo Ghirardi's new book, Sneaking a Look at God's Cards.

As a mathematical formalism, quantum mechanics is remarkably simple. It postulates that the state of a physical system is completely characterized by a vector in an infinite-dimensional vector space (the familiar quantum-mechanical "wavefunction"), and observable quantities correspond to linear operators on this space. What is not so simple is the relation of this formalism to the standard ideas about physical reality used both in everyday life and in experimental physics laboratories. These describe reality in terms of objects with definite positions and velocities, something which doesn't correspond to any quantum mechanical state-vector.

Ghirardi begins by describing in detail the conceptual setup of quantum mechanics, focusing on certain simple physical systems for which the interpretational issues are as clear as possible. He then recounts the history and content of the interpretational debates that began immediately after the formulation of the theory, the most famous of which pitted Niels Bohr against Albert Einstein. Einstein believed that quantum mechanics was an incomplete theory, because in many cases it was only capable of giving statistical predictions. His arguments were most sharply made in his work with Boris Podolsky and Nathan Rosen on the so-called EPR (Einstein-Podolsky-Rosen) paradox. Ghirardi carefully explains the EPR paradox, which is a real challenge to encapsulate in a way that makes sense.

The general consensus of the physics community is that Bohr's point of view triumphed, enshrined in what became known as the "Copenhagen interpretation" of quantum mechanics. According to Bohr, the state-vector of a physical system evolves in time according to the Schrödinger equation and does not typically have a well-defined value for classical observables like position and velocity. When the system interacts with an experimental apparatus, the state-vector "collapses" into a state with a well-defined value of the observable being measured. In general, Bohr's interpretation works perfectly well operationally, but it is conceptually incoherent and leaves important questions unanswered. How exactly does this "collapse" take place?

A more coherent interpretation would describe both the system under study and the experimental apparatus in terms of a state-vector, but this approach runs up against the problem that one usually expects quantum state-vectors to be super-positions of simpler states with different values of observables. This point was most clearly made by Schrödinger in his famous thought-experiment that leads to the impossible notion of a cat being in a superposition of a state in which it is alive and one in which it is dead.

Ghirardi and collaborators have investigated modifications of the Schrödinger equation involving nonlinear and stochastic terms, such that their versions of quantum mechanics agree with the standard theory in regimes for which they have been tested but evade the "collapse" problem. These new versions of quantum mechanics are nonrelativistic and encounter severe problems at relativistic energies, so Ghirardi wisely avoids making too much of them, noting just that they suggest new directions for future research.

Most physicists generally believe that quantum mechanics, in its relativistic version as a theory of quantum fields, is a complete, consistent and highly successful conceptual framework. They assume that there must be some well-defined way of describing the entirety of a physical system, experimental apparatus and human observer, appropriately dealing with the confusing interpretational issues. As a result, the study of the sorts of questions examined in this book has often been considered somewhat of a backwater. Recent years have seen great progress in constructing macroscopic systems that behave in characteristically quantum-mechanical fashion, together with possible revolutionary applications of such systems in quantum cryptography and quantum computation. The long-standing interpretational problems of quantum mechanics may be significantly clarified as they become directly relevant to this important new technology. Ghirardi's book provides a careful, evenhanded and well-thought-out introduction to this timely topic.