Getting back to fundamentals

Quantum State Diffusion - Testing Quantum Mechanics on New Ground
March 10, 2000

Fundamental physics is no longer just about particle physics. Driven by a subtle mix of social and technological developments in the past 20 years, the foundations of quantum mechanics have emerged from the ghetto of "mere philosophy" to be a vibrant and empirically based branch of physics. The subject is fundamental not because it deals with the spatially small but because it addresses the meaning and interpretation of physical concepts.

Metaphysical issues have often occupied the greatest physicists. It is Einstein's perception of the incompleteness of the quantum description through his analysis of nonlocality, for example, that set the agenda for much of the current activity. Through the perseverance of a few, ways have been found to make metaphysics an experimental subject. The foundations of quantum physics are becoming professionalised - it is no longer a hobby to be fitted in when one takes time off from more serious science.

It is de rigueur nowadays to reprove Niels Bohr for obscurity, but one of his great insights was that the language we employ to express theories should itself be subject to scientific investigation. We do not need to accept Bohr's own proposal for interpreting quantum theory (retain but limit the applicability of classical discourse) to recognise that the failure to address the issue of language adequately is one of the principal obstacles to comprehending quantum mechanics. Mathematics alone cannot solve this. The way we use language may not appear to have empirical implications, which is why it is felt safe to ignore it, but it is implicit in Partha Ghose's timely and valuable book that experimental discrimination in this difficult area may be attainable. An example is the various approaches that have been proposed to the concept of transit time, a notion that is difficult to formulate consistently within standard quantum theory. As Ghose shows, although not yet testable, the coherent set of concepts embodied in the pilot-wave interpretation implies unambiguous predictions about transit times. It is a case where an interpretation is more than just another view, but extends the predictive base of quantum mechanics. We have come a long way; the pilot wave was dismissed as "Marxist physics" when David Bohm proposed it during the United States's brush with McCarthyite fascism but now appears in university examination papers. Who says that scientific knowledge is independent of social context?

Ghose reviews the current experimental basis of this emergent field, a blend of tests of classic quantum phenomena and specific interpretations. As far as I know it is the first book to attempt this comprehensively, with full technical details. The endeavour draws on a lot of physics, particularly advances in atomic, optical and nuclear physics. It is remarkable how rich the compendium of tests of basic quantum mechanics now is, comprising self-interference and quantum jumps for single atoms, "Schrödinger cat" states in micromasers, the quantum Zeno effect and geometric phase effects. Experiments are planned to test certain collapse models. The foundations are a crucial ingredient in other fields, too - in seeking to monitor displacements of 10-19cm, gravitational wave detectors are macroscopic quantum objects.

A topic where the author might have given a more critical assessment is the use of language in the debate on tests of complementarity, the trade-off between knowledge of the path an object takes and its contribution to coherence effects. How, for instance, do the various mathematical functions that express the notion of "which path" correspond to intuitive notions of objects moving in space that could have a "path"? As Ghose recognises, the foundations are a fast-moving field - no reference is made, for example, to the recent demonstration of nonlocality over 10km or to the self-interference of "buckyballs". But the book contains a wealth of results and techniques that will remain basic for some time, and it is highly recommended as a resource for graduate students and researchers.

Ian Percival addresses a similar audience in his survey of a field he has helped create: quantum-state diffusion. The idea is to emulate for quantum states the classical analysis of Brownian motion. That is, the objects of study are open quantum systems, those that are separately discernible but which are entangled with their environment, whose states evolve stochastically.

Many will see this as an unnecessary complication of standard quantum mechanics, but that would be rash. The conceptual incompleteness of quantum theory has to be addressed somehow, and daring to enrich the formal framework should not be a basis for criticism. Simplicity is not a virtue if a theory is unclear. One should judge the exercise not by counting axioms but in terms of what is gained in understanding. For example, in contrast to the standard formalism, state-diffusion theory attempts to treat measurement as one of its applications rather than invoking extraneous assumptions.

The author adopts a terse style that can make the narrative opaque to outsiders. For example, the master equation on which the approach is based, the Lindblad equation (describing the evolution of the density operator of a system interacting with its environment), is stated without proof. Just a few lines of motivation for the non-Hamiltonian terms in this equation would have clarified the subsequent analysis, particularly the key demonstration that reasonable conditions lead to a unique unravelling of the linear-density matrix evolution into nonlinear evolution of the component pure states. Using computer modelling, the theory has been applied to an impressive range of problems.

A canonical problem of 20th-century physics is how to reconcile the classical theory of individual substantive systems with the quantum-statistical description, given that the latter applies at the classical scale. Percival presents with clarity the issue of the classical-quantum boundary and how this should be a derived concept in a fundamental theory, and makes an honest assessment of his theory's record in this regard. A popular modern mechanism for the emergence of classicality is to use entanglement with the environment to generate localisation of states through decoherence. The state-diffusion theory is an example where the environmental method is particularly successful. But in themselves, peaked-probability distributions have nothing to do with localised states of matter, or with the classical limit, so additional assumptions must be made. Close attention is needed here to what one is trying to achieve in deriving the "classical limit" from quantum mechanics. What, for example, is the ontological status of the wave function? Percival asserts that matter waves are "real". The hope is that evidence for the reality of quantum waves will follow from the state-diffusion theory in the way that the reality of atoms was asserted on the basis of observations of Brownian motion. Percival points to possible tests of the idea in atom interferometry.

Percival makes reference to some previous stochastic models. To judge more fully the status of the state-diffusion programme it would have been helpful to review its achievements and open up problems in the context of the many other contemporary theories that address similar problems, especially those which employ decoherence to achieve localisation. Although this book describes work in progress, it is recommended as a very good introduction to stochastic methods in contemporary physics.

Peter Holland is professor in the foundations of physical sciences, University of the West of England, Bristol.

Quantum State Diffusion

Author - Ian Percival
ISBN - 0 521 62007 4
Publisher - Cambridge University Press
Price - £30.00
Pages - 184

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