To Copenhagen and far beyond

"The most incomprehensible thing about the world is that it is comprehensible," Albert Einstein once remarked. Ever since Isaac Newton showed that the same physical laws can be used to calculate the motions of both the apple falling from the tree and the Moon orbiting the Earth, it has been an article of faith among scientists that the whole physical universe can be described in a similar way. However, when it comes to quantum physics, there are good reasons to believe that the limits of Einstein's maxim may have been reached and exceeded. If so, and if we cannot rely on calculation to take us forwards, we are likely to need the guide promised in the subtitle to Jim Al-Khalili's book.

This volume has two main aims. The first is to give an account of how quantum physics has succeeded in explaining a wide range of physical phenomena, many of which underlie what are now everyday technologies such as computing and communication. The reader learns how quantum physics is crucial to the understanding of the microchips that play an essential role in our computers, the principles of lasers and the generation of nuclear power. Modern developments, such as scanning tunnelling microscopes, which allow us to see individual atoms and have opened up the whole field of nanotechnology, are explained, and future possibilities are explored, such as quantum computers with power that would be unbelievably greater than anything we know today. The almost complete absence of mathematics, combined with clear explanation and lavish illustration, enables the interested reader to share the pleasure and excitement that scientists gain from their understanding of the modern universe. The interspersed essays by a number of leading physicists add to this.

The second aim is to bring the reader to an understanding of the underlying perplexities of quantum physics and the suggestions that have been made to guide us through them. Nearly half the book is devoted to an exposition of the features of the quantum world that are surprising and counterintuitive. We are introduced to wave-particle duality, apparently "spooky" connections between physically separated objects and of course Schrödinger's ubiquitous cat. Quantum physics has been developed as an attempt to understand these, and the resulting philosophical basis of the subject is still a matter of great controversy.

What is now the orthodox view is the "Copenhagen interpretation", developed in the 1930s by Niels Bohr and others who worked in that city. This is based on a form of positivism which states that the only role of scientific theory is to explain the results of measurements, so that any description of unobservable phenomena is meaningless. Al-Khalili quotes James Cushing's suggestion that the Copenhagen interpretation is today's orthodoxy mainly because it "got to the top of the hill first", and encourages us to look seriously at alternatives, such as hidden variable theories and "many worlds". The resulting description of the conceptual problems of quantum physics and their possible resolution is clear and balanced, although his own viewpoint, summarised in the introduction as "I am not a supporter of any particular interpretation... but I do have clear views on the issue" is somewhat perplexing in itself. I have two technical queries with what he says about the Copenhagen interpretation: in Bohr's view, at least, it is based on the nature of the measuring apparatus rather than any particular property of the observer; and it does not necessarily imply any physical non-locality.

Robert Griffiths' book is aimed at a completely different readership. He invented what is known as the "consistent histories" interpretation of quantum physics about ten years ago, and much recent work in the field has been based on this idea. Although aware of this for some time, it is only after reading his own account that I have begun to appreciate the power and importance of these ideas, which aim to develop "a rational approach to quantum theory that is not based upon measurement as a fundamental principle". His exposition uses a formal, mathematical approach, which would challenge many physics graduates, never mind the general reader.

However, the basic concept of a consistent history can be understood reasonably simply. If we consider a beam of light consisting of a number of quantum particles (photons) passing through a screen containing two slits, we can describe it as a wave passing through both slits; when it is projected on a second screen mounted behind the slits an "interference pattern" of light and dark bands is produced. Or we can insert detectors within the slits and detect through which slit each photon passes, in which case the interference pattern disappears. Either model constitutes a set of consistent histories, but any combination of parts of each (for example, any attempt to tell through which slit a photon passed before forming an interference pattern) is inconsistent and not allowed by this interpretation. Griffiths discovered that the formalism of quantum physics provides both a test for consistency and a procedure for calculating the probabilities of the various histories in a consistent set (for example, the probability of detecting a photon in one or other of the slits). Which set of consistent histories is valid in a particular situation depends on the experimental context (for example, the presence or absence of the detectors in the slits determines which history we should use in the above example). When the experimental context changes, we must use a different set of histories to describe the system, but this does not imply any physical change in the quantum system. Although the Copenhagen interpretation is not mentioned in this book, the consistent histories model can be seen as developing from it and attempting to generalise it and make it more objective.

In summary, the perplexed general reader should certainly seek guidance from Al-Khalili and specialists should read Griffiths' book. Consistent histories merit only a brief mention from Al-Khalili, but if the idea stands the test of time, we can expect it to feature more prominently in future guides for the perplexed.

Alastair Rae is reader in quantum physics, University of Birmingham.