The quantum measurement problem

How does one assess the merit of a scientific theory? Obviously, an "acceptable'' theory has to be empirically adequate and internally consistent. While quantum physics has been extraordinarily successful on the empirical front, it curiously suffers from an intrinsic conceptual lacuna within its internal structure.

For if one tries to describe a measurement process by applying quantum mechanics to the observed system and the measuring apparatus, the end result ineluctably implies that each member (comprising system plus apparatus) of the final ensemble is in the same state (meaning a homogeneous ensemble). This is clearly inconsistent with the obvious fact that different outcomes are macroscopically distinguishable (meaning that the final ensemble should be heterogeneous). It is thus a logical non sequitur to speak of probabilities of various outcomes when the very occurrence of an individual outcome is not consistently accommodated within standard quantum mechanics. This in essence is the quantum measurement problem.

Recent years have seen a plethora of books on the conceptual problems of quantum mechanics. While most are for a lay audience, this book is strictly for professional physicists who have more than a passing interest in the foundational issues of quantum mechanics. One advantage is that the book is sharply focused on the quantum measurement problem and does not get distracted by delving into other fundamental issues such as those related to quantum non-locality and wave-particle duality. Though its formal content overlaps largely with The Quantum Theory of Measurement (1991), also by Peter Mittelstaedt (with P. Busch and P. J. Lahtti), this new book is improved, more concise and, in particular, delineates clearly the key elements of the approach Mittelstaedt and his co-workers subscribe to - the minimal interpretation of quantum mechanics.

Mittelstaedt categorises the so-called standard interpretation of quantum mechanics ( à la Niels Bohr) as one that assumes that the macroscopic measuring instruments are subject to the laws of classical physics and that the measuring process itself is "unanalysable'' by means of quantum mechanics. The minimal interpretation goes beyond it by assuming quantum mechanics to be applicable to the macro-apparatus as well. But the minimal interpretation differs from other non-standard interpretations such as the realist ones by refusing to assign any observer-independent reality to the objective dynamical properties of individual systems; instead it regards the measurement outcomes (pointer values) as the only objectively real quantities in the theory. Thus the minimal interpretation may be viewed as the "weakest'' departure from the standard interpretation.

The main upshot of all the sophisticated mathematical exercises and rigorous logical analyses discussed in this book is to reinforce what one may call the "insolubility'' of the quantum measurement problem. But Mittelstaedt does not mention anywhere a crucial assumption underpinning the minimal interpretation; that a wave function is regarded as providing the "complete description'' of the state of an individual microphysical entity. So Mittelstaedt's demonstration in effect shows that if the mathematical formalism of quantum mechanics is left unmodified, a plausible recourse in confronting the quantum measurement problem is to renounce the assumption of the "completeness'' of a wave function.

Surprisingly, Mittelstaedt evades mentioning David Bohm's model of quantum mechanics that seeks to resolve the measurement problem by supplementing "incompleteness'' of the wave function with the putative ontological reality of the position of an individual particle. Non-standard approaches (other than the minimal interpretation) discussed in this book are the environment-induced decoherence scheme, the dynamical model of wave-function collapse and the many-worlds interpretation. The criticisms of the decopherence scheme and the many-worlds approach, pointing out why they fail to address the measurement problem, are essentially correct. But one wishes for more elaboration, particularly as these criticisms are not properly understood by a number of researchers working on this topic.

The other, more serious, qualm is that the Ghirardi-Rimini-Weber model of wave-function collapse is discussed in a rather sloppy way. Mittelstaedt does not emphasise the stochasticity inherent in this approach that allows it to escape the Gisin argument, which shows that superluminal signalling follows from any deterministic non-linear modification of quantum dynamics in the case of Einstein-Podolsky-Rosen (EPR) correlated pairs. But Mittelstaedt may draw comfort from the fact that even Steven Weinberg misinterpreted Gisin's demonstration as indicating that it was not possible "to change quantum mechanics by a small amount without wrecking it altogether'' (in Dreams of a Final Theory ), overlooking the possibility of appropriate non-linear stochastic corrections to the Schrodinger equation ( à la GRW type models). Mittelstaedt should have clarified properly that the GRW model seeks to address at the same time both the measurement and the classical limit problems of quantum mechanics by ensuring consistency with all quantum effects experimentally verified to date. But one must note the most curious feature of the GRW model (not mentioned by Mittelstaedt) that it allows for energy non-conservation in principle, though the effect is ensured to be experimentally unobservable.

Towards the end, Mittelstaedt tries to argue for the possible relevance of Gödel's theorem to the "insolubility'' of the quantum measurement problem. This is a comforting thought for those who accept the finality of the standard formalism and the "completeness'' of a wave function. But for those not already familiar with Gödel's theorem, Mittlestaedt should have given a more detailed account of the theorem, at least as an appendix.

To sum up, the usefulness of this book lies in providing an exposition of the "insolubility'' of the quantum measurement problem using the standard formalism, with the arguments couched in a systematic axiomatic approach using the probability calculus within the Boolean algebraic framework. It may serve to attract the attention of the formally minded physicist to the measurement problem.

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