BOOK REVIEW
Grappling with Quantum Weirdness
Peter Woit
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 mid1920s 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 atomicscale
physical phenomena that had until then been mysterious. Since its
discovery, the basic quantummechanical 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 infinitedimensional vector space
(the familiar quantummechanical "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 statevector.
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 socalled EPR (EinsteinPodolskyRosen)
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 statevector of a physical system evolves in
time according to the Schrödinger equation and does not
typically have a welldefined value for classical observables like
position and velocity. When the system interacts with an
experimental apparatus, the statevector "collapses" into
a state with a welldefined 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 statevector, but
this approach runs up against the problem that one usually expects
quantum statevectors to be superpositions of simpler states with
different values of observables. This point was most clearly made by
Schrödinger in his famous thoughtexperiment 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 welldefined 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 quantummechanical fashion, together with
possible revolutionary applications of such systems in quantum
cryptography and quantum computation. The longstanding
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
wellthoughtout introduction to this timely topic.
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