Quantum theory: a very short introduction

By John Polkinghorne

Quantum physics is hard. And weird. There's just no getting around it. It takes Plus a lot of tea and biscuits to write anything about the quantum world. But since discovering John Polkinghorne's book, Quantum Theory, it thankfully has become a little bit easier.

Polkinghorne's book is part of the Very Short Introductions series produced by Oxford University Press. These books intend to give an accessible (both in level and length) introduction to a wide range of subjects. Titles currently include Buddhism, Globalisation, Russian literature, and Cosmology. They are all written by experts in the given subject; the Mathematics: a very short introduction is written by the Fields Medallist and recently knighted Tim Gowers.

In this deceptively slim volume Polkinghorne gives us a tour of one of the strangest areas of modern science. He starts with old quantum theory: the first hints of the wave/particle duality of light discovered by Max Planck, Albert Einstein and Niels Bohr and others in the early days of the twentieth century. Polkinghorne then guides us through the rush of discoveries in the 1920s – including Hiesenberg's uncertainty principle, the probabilistic nature of quantum theory and superposition – as new quantum theory begins to chart these landmarks of the unknown quantum world. He reveals the controversies and confusions these discoveries wrought and the ongoing conundrums still unresolved today.

Quantum physics often seems to fly in the face of our own experience of the world. But as well as equipping you with the vocabulary of the area Polkinghorne also gives surprisingly accessible and convincing accounts of the key ideas. The main text manages to cleverly reveal the twists and turns of quantum physics but in a non-technical way. And if you are hungry for the technical details many of them are there in the appendices. I found the appendix outlining a mathematical argument behind Heisenberg’s uncertainty principle very reassuring – two properties can only be simultaneously observed if their corresponding matrices commute – now that's something my brain can get to grips with! And I continue to dip in and out of the book, when I need a reminder of the history or science, thanks to the useful glossary, list of further reading and index.

The book not only gives us an introduction to the physics, it also gives a lovely glimpse of the human face of the quantum world. Polkinghorne learned quantum physics from one of its pioneers, Paul Dirac, when he attended a famous course of lectures Dirac gave in Cambridge. He describes them as enthralling for their "clarity and the majestic unfolding of their argument". And he recounts the theatrical way Dirac illustrated the concept of superposition at the start of his lectures, by breaking a piece of chalk in two and placing the pieces on either side of his lecturn: classically the chalk is either "here" or "there", but "replace the chalk by an electron and in the quantum world there are not only states of 'here' and 'there' but also a whole host of other states that are mixtures of these possibilities".

Polkinghorne has a colourful turn of phrase, writing about "wraithlike wave functions" and describing entropy in terms of untidy desks (very applicable here in my office). This writing style definitely helps you hold on to some of the more complicated discussions. Describing different interpretations of the measurement problem (one of the biggest outstanding issues in quantum theory), he describes one approach stating that it's enough that quantum theory works in practice: "It is simply inappropriately intellectually greedy to ask for more." But he then goes on to give the opposing argument, describing the previous approach as "abhorrent to the mind of the scientist, whose ambition is to gain the maximum understanding of what is happening in the physical world. To settle for less would be treason of the clerks."

Polkinghorne has managed not only to write a concise clear introduction to one of the most complicated areas of knowledge, he has also written an enjoyable story of human discovery. He passes on his admiration for the people, his wonder at the mysteries and his appreciation for the beauty of the theories that describe them. The very final part of the book is an appendix on the Dirac equation, engraved on Dirac's memorial in Westminster Abbey. It is fitting that, due to the depth of the mathematical concepts involved, Polkinghorne can't decipher the equation for us but he still thinks it's important to share it with all readers: "…whether on paper, on the page, or on a stone in the Abbey, the onlooker should have the opportunity to pay respect to what is one of the most beautiful and profound equations in physics." And Polkinghorne's little book allows us all the chance to glimpse the beauty and profundity of the quantum world.

You can hear more from John Polkinghorne in our podcast Does quantum physics really describe reality?

Book details:

Quantum Theory: A Very Short Introduction

John Polkinghorne

paperback — 128 pages

Oxford University Press (2002)

ISBN: 978-0192802521

About the author

Rachel Thomas is the editor of Plus.