Non-specialists who have tried to make sense of what is actually happening in the exotic world of quantum phenomena by delving into the textbooks on quantum mechanics soon find themselves lost in a morass of formalism, some of it quite intimidating. Is it possible to get to the heart of the matter without having to master all this mathematical detail?

Good question. I once thought it could be done, but after trying for many years to find a simple way to describe what is "really going on", it became clear that we still do not fully understand the quantum world. We just do not have the non-mathematical concepts to express ourselves clearly. Why else can we find ten or more "interpretations" of the formalism, each with its own group of advocates, some of whom defend "their" interpretations like religious zealots ?

Daniel Styer tries to reach an audience of non-technical readers and to take them straight to the remarkable discoveries of the last two or three decades without getting into all these problems. In fact, the bulk of this short book is concerned with quantum non-locality, a subject in which I have had more than a passing interest since the 1960s. As he wants to get to the heart of things quickly, he rejects the much-favoured historical approach, preferring to leave this discussion to an appendix.

Lying at the centre of these surprising non-local effects is the "entangled" quantum state involving two or more particles. It was the debate in the mid -1930s between Einstein, Podolsky and Rosen, Schrödinger and Bohr that first drew to our attention the implication of these entangled states, states that seemed to imply some kind of non-local connection. Indeed as Einstein later put it, there appeared to be some kind of "spooky action-at-a-distance" operating between two entangled particles.

This seemed to be such an outrageous idea that many concluded that Einstein’s objections must be flawed and subsequent discussions were confined to small isolated groups. Indeed, I grew up wondering why so many of my contemporaries did not even want to discuss the issues and why they did not take the trouble to explain to me why these implications of non-locality were incorrect. Certainly almost all physics majors were totally unaware of the existence and importance of this debate. The critical physicists were convinced that Bohr had had the last word and there was nothing here to be concerned about. The quantum formalism was correct, so do not worry. Get on with your scattering perturbation calculations. It is only now, seven decades later, that some, but by no means all, physics students are being exposed to these ideas.

With the recent discoveries of quantum cryptography and quantum teleportation and their potential applications, it is all the more important that these remarkable ideas reach a wider audience. Styer’s book is a very commendable effort to do just that. In explaining its aims, he draws an analogy with the motor car. One does not have to be an expert motor mechanic to understand the principles of how the engine functions, so why can we not explain the principles of these exotic quantum effects without insisting on going through a long and difficult apprenticeship first? Thus Styer wants "to strip away the machinery of the edifice and bare the raw ideas in their naked form". The trouble with stripping is that it often reveals embarrassing blemishes. Fortunately the author is well aware of the difficulties and that is why I think this book is a valuable contribution to the subject. He is open about these things. He also realises the difficulty of his task and immediately gets the profession al physics community on his side by claiming he is using the "standard interpretation". In fact, it relies very heavily on the probability amplitudes approach as outlined in Feynman’s book, * Q.E.D: The Strange Theory of Light and Matter * .

I know what a probability amplitude is, but what will the general reader make of it? We are asked to stop thinking about particles and instead to imagine rotating "two-dimensional arrows", one associated with each path. Of course, he explains that these vectors are not physical entities, they are just mathematical tools. But having carefully set this all up, he then concludes:"The best approximate phrase is 'the atom goes through both branches'. This conclusion seems patently absurd. Actually, it is correct and seems absurd only if one thinks of an atom as being like a marble, only infinitely smaller and infinitely harder."

OK, if the classical ideas are wrong, what do we put in their place? Here comes the difficulty: we do not have a physical image of what is actually going on and for some reason we do not want to admit it. Bohr was very clear on this point. He insisted we can never find a pictorial representation of a quantum process. Why? Because of the indivisibility and uncontrollability of the quantum of action that links the observed system to measuring apparatus. This implies the impossibility of making a sharp separation between observer and the observed, and no sharp separation means that we cannot give an unambiguous description of what the observed system is actually doing. All we can do is to provide a mathematical algorithm from which we can calculate the probable outcome of a given experiment. That is what the probability amplitudes allow you to do and that is all they can do.

I do not understand why we cannot say unequivocally that "pictures" of the underlying process are not possible in the standard approach. T hen at least the reader will not waste time trying to make sense of statements like "the atom goes through both branches". If you desperately want a picture of what is going on, then the best consistent approach is the Bohm approach. But mentioning that approach will still bring down the wrath of many profession al physicists.

I think Styer is aware of these problems because early in the book he takes the trouble to explain the distinction between an explanation and a description. By insisting that he is only giving a "description" of quantum effects, not an "explanation", he hopes to avoid these awkward questions. He argues that explanation in physics always relies at some stage on a concept or concepts that must be taken to be basic. For example, the presence of a magnetic field will explain the precession of a magnetic needle, but there is no explanation of the magnetic field. Thus since these probability" amplitudes" are supposed to be analogous to the magnetic field, we should not look for an "explanation" of them. Analogous they may be, but they clearly are n o t the same. We can generate magnetic fields, but I know of no amplitude generator.

It sounds as if I am very unhappy with this book. Actually I am not. I am merely pointing one of the blemishes intrinsic to discussing quantum processes, namely that no matter how hard you try to bring out the physical principles of quantum phenomena, you are always forced to rely on a mathematical algorithm which has no physical counterpart. Once reader s grasp this point then t he y can devote their whole attention to learning how to use probability amplitudes in simple experiments. In fact, t he simple way in which traditionally difficult calculations are presented in this book is much to be praised. The problems at the end of each chapter help the reader master these rules and once they are mastered, the reader will begin to see the richness of the physical ideas that emerge from quantum processes.

The order of presentation is also interesting. After an explanation of the Stern-Gerlach experiment, we are taken almost immediately into a simple explanation of the Einstein-Podolsky-Rosen paradox and its implications. This is based on the beautiful account presented by David Mirmin, that brings out in a very direct way the stark contrast between the implications of the entangled state and those obtained by assuming locality. The Greenberger-Horn-Zeilinger variation of the EPR, which for me is the icing on the cake, is also presented. It is only after these topics have been analysed that interference is discussed and the roll of the probability amplitude is explained further. Then, to re-enforce the importance of the notion of a probability amplitude, the amplitude techniques are applied to the EPR paradox. There is a short chapter on quantum cryptography and the use of probability amplitudes, for a quantum bouncing ball rounds off the presentation of some of the more fascinating properties of the quantum domain.

It is all very stimulating stuff. I hope the non-technical reader will get a lot out of this book as it clearly highlights a radically different structure underlying the macroscopic world of classical physics.

Basil Hiley is professor of physics, Birkbeck College, University of London.

## The Strange World of Quantum Mechanics: First edition

Author - Daniel F. Styer

ISBN - 0 521 66104 8 and 66780 1

Publisher - Cambridge University Press

Price - £40.00 and £14.95

Pages - 154

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