The flip side of universal equations

Symmetries in Physics

January 7, 2005

2005 is the World Year of Physics, and in the UK it will be known as Einstein Year. While commemorating the centenary of the three groundbreaking papers Einstein wrote in 1905, the year will also provide an opportunity to reflect on the wealth of Einstein's legacy. For many physicists, one word might sum it up: "symmetry". Symmetry played a key role in most of the major advances in physics during the 20th century, and it continues to dominate attempts to go beyond existing theories; Einstein was the first fully to see and exploit its power.

Einstein's 1905 theory of special relativity, in a mathematical formulation by Hermann Minkowski of 1908, revealed a remarkable and unexpected symmetry between space and time, in the absence of gravitating matter. (It need hardly be emphasised how contrary such a symmetry is to our everyday experience: we can turn around in space but not in time.) Still grasping the golden thread, Einstein was led to a monumental new theory of gravity, published in 1916. He showed how the presence of gravitating matter allows a more general space-time symmetry to operate: by postulating this larger symmetry, the origin and properties of gravity are explained. Thus, for the first time, the existence of a force could be understood in terms of a space-time symmetry principle. The theory has become established experimentally, and it forms the basis of all work in areas such as black hole physics and cosmology.

Einstein spent his last 30 years trying unsuccessfully to find a unified description of electromagnetism and gravity in terms of more space-time symmetries. With the discovery of quantum mechanics in 1925, the line of advance changed and, for a while, the Einstein vision faded. Quantum mechanics was combined with special relativity and Maxwell's electromagnetic theory to produce quantum electrodynamics (QED), still the most thoroughly tested physical theory. But two new fundamental forces also appeared: the "weak" force responsible for certain radioactive processes, and the "strong" force that holds the constituents of nuclei together. How were they to be understood? Symmetry supplied an answer.

QED is built on a symmetry called "gauge symmetry", which involves simultaneous operations on the electromagnetic and charged matter fields.

In the 1950s, the exploration by Chen Ning Yang, Robert Mills and others of generalisations of such symmetry turned out to be fruitful, leading in the 1960s and 1970s to a unified description of electromagnetism and the weak force, and to an understanding of the strong force. These three gauge theories constitute the successful Standard Model of particle physics. But the nature of a symmetry that could link these three to Einstein's gravity still eludes us.

It is little wonder that philosophers of physics have begun to take a keen interest in symmetry. Indeed, I was surprised to learn that the first philosophy of physics workshop on symmetries in physics was held no earlier than 2001. The success of that workshop convinced the organisers, Katherine Brading and Elena Castellani, that the time was ripe for a collection of papers about the issues that dominate discussions in philosophy of physics on the subject of symmetry. Some of the 21 articles originate from papers presented at the workshop, but most were specially commissioned; all are by philosophers working in the philosophy of physics.

The book has four sections. The first, "Continuous symmetries", occupies nearly half the book and is concerned with gauge theories. The second, "Discrete symmetries", deals with a different kind of symmetry, principally permutation symmetry and parity. The third tackles a vital area in condensed-matter physics and particle physics - namely "Symmetry breaking", and the crucial idea of "spontaneously" broken symmetry. A short final part covers "General interpretative issues". Each part begins with extracts from authors such as Gottfried Leibniz, Immanuel Kant, Pierre Curie, Hermann Weyl and Eugene Wigner. Each also contains a review of literature and issues. The book begins with a fine introduction by the editors.

The contributions are diverse. Some involve quite sophisticated mathematical ideas, such as constrained Hamiltonian systems, fibre bundles and C* algebras. No less technical, but in a philosophical sense, is an exploration of the origins of Weyl's gauge theory in Edmund Husserl's transcendental phenomenological idealism. Several authors carry forward traditional philosophical arguments, in the light of advances in physics; for example, there are discussions of the impact of parity violation on the substantivalist-relationist debate about the nature of space, and of quantum indistinguishability on the metaphysics of identity and individuality.

More general themes are taken up in an essay by Peter Kosso on "Symmetry, objectivity and design". In our everyday world, we say that an object, such as a flower, has some symmetry if there is something we can do to it (a rotation, for example) so that afterwards it looks the same as it did before. Similarly, the use of symmetry in physics brings into focus what remains the same - or invariant - under mathematical transformations. Kosso argues that such invariance represents something objective about reality, much as there is a fact about nature that guarantees the truth of the sentence "the Moon is closer to the Earth than is the Sun" when translated into any human language. This was Einstein's view. His 1905 paper on "relativity" provided precisely the tools for identifying observer-independent physical laws, and thus reaching an objective reality.

For Kosso, symmetry is profoundly natural. By contrast, he suggests, broken symmetry requires "intervention", or "design". In this context, physicists speak of "putting things in by hand", a practice to which they have a strong aversion. Here lies the significance, which Kosso seems to miss, of the concept of "spontaneous" symmetry breaking, for it can and does occur naturally. An example is provided by the rotational symmetry possessed by a volume of water in a tank, which is reduced to a more restrictive crystalline symmetry when the water freezes. Crucially, the intermolecular forces do not change, but the symmetry does. Here the "intervention" is simply a change in temperature. In a similar way, the highly successful "electroweak" part of the Standard Model unifies electromagnetism and the weak force in a symmetrical theory, and attributes the differences observed between them to a kind of "freezing" that occurred some milllion millionths of a second after the Big Bang. The dream of many physicists today is of showing how, from a fiery and perfectly symmetrical beginning, the diversity of forces now observed may have evolved naturally, via a succession of such freezings as the temperature dropped. Thus Einstein's vision might be finally realised.

Brading and Castellani's book will be a useful resource for students and researchers in the philosophy of physics and the philosophy of science, and for physicists with an interest in philosophy.

Ian Aitchison is emeritus professor of physics, Oxford University.

Symmetries in Physics: Philosophical Reflections

Editor - Katherine Brading and Elena Castellani
Publisher - Cambridge University Press
Pages - 445
Price - £65.00
ISBN - 0 521 82137 1

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