Dusted off to revive its gleam

Einstein's general theory of relativity is the bedrock supporting numerous areas of physics. In extreme astrophysical objects such as pulsars, supernova explosions, quasars and black holes the action of the gravitational force is completely dominant. General relativity encroaches onto the new discipline of astroparticle physics. Embedded in great clusters of galaxies are gravitational lenses that act as telescopes giving distorted views of matter in the remote universe. Instrumentalists continue to develop interferometers and spacecraft that should allow detection and observation of gravitational waves. Cosmology provides the intellectual space where relativists confront the universe.

It is almost a century since the publication of the general theory. In that time, it has made a steady transition from the obscurity that followed its confirmation to a central position in high-energy astrophysics and cosmology.

Jean Eisenstaedt tells of the historical events surrounding general relativity and the techniques Einstein employed to construct this almost impenetrable theory. Einstein began with the special theory in which the laws of physics are written in an invariant form that holds for any reference frame in uniform motion. His 1905 paper showed that length and time are not intrinsic magnitudes: they depend on the motion of the frame of reference with respect to which they are measured. The same paper set out the relativistic version of the Doppler effect, and the way in which frequency and energy are transformed by a change of frame. Later that year, he introduced his famous equation E=mc² to establish the equivalence of mass and energy.

Einstein next turned to gravitation, although few of his colleagues supported him. Mass-energy equivalence implied that energy is a source of gravitation. Thus, he sought a generalisation of Newton's theory of gravitation to accommodate the new relativistic mechanics. Eisenstaedt gives a compelling account of Einstein's thinking style and his approach to theory. His success with the special theory stemmed from his adoption of principles such as the constancy of the velocity of light. He then used mathematical tools to explore the consequences of the principles. For the general theory, he adopted the principle that gravitational mass (how bodies fall) and inertial mass (how bodies resist force) are identical: the principle of equivalence. To this, he added the principle of covariance, which expresses the idea that physical laws are intrinsic and therefore have the same inherent form that is independent of the co-ordinate system in which we choose to work. Finally, he dismissed Newton's concept of absolute space.

To understand the structure of space-time and the behaviour of matter within it, Einstein used mathematical tools that had never featured before in theoretical physics. In particular, he used tensor calculus to handle the transformations between reference frames. By late 1915, he had the field equations in the now classical form and could write to his friend Heinrich Zangger that "the theory is beautiful beyond comparison", adding:

"Only one colleague has really understood it."

Now the theory could be put to the test. Einstein correctly accounted for the motion of Mercury's perihelion, the first fundamental success of the theory. The second success concerned the deflection of light rays by a massive body. At the total eclipse of the Sun on May 29, 1919, a team led by the Cambridge astrophysicist Arthur Eddington validated Einstein's theory. Eddington had been the first scientist in Britain to receive Einstein's paper, and he immediately recognised its significance. The eclipse result brought worldwide fame overnight. Eddington also had a hand in the third test, which states that clocks run more slowly in a gravitational field. In 1925, at his suggestion, the Mount Wilson Observatory observed the spectrum of the white dwarf companion of the star Sirius, finding that it had a redshift caused by the large gravitational field of the collapsed star.

After the 1920s, Einstein spent little time on general relativity. His revolutionary ideas were eclipsed by an even more startling theory, quantum mechanics, in which uncertainty and chance featured significantly, and to which Einstein also made brilliant contributions. Relativity theory moved into obscurity. Newton's much simpler theory explained almost everything concerning motion in the solar system. It must have seemed pointless to expend so much effort on a difficult theory when the divergence at the level of measurable results was so small.

The discovery of pulsars in 1967 rescued general relativity from its small niche in an ivory tower. Once theorists had identified pulsars with rotating neutron stars, it was a small step to posit the existence of black holes, the physical behaviour of which could be explored only through general relativity. Cosmology was transformed, the quest for quantum gravity launched, and relativistic astrophysics burst on the scene.

This book is a treasure from a world expert. It offers a deeper understanding of Einstein's theory and, above all, it is an inspiring account of his unique scientific style.

Simon Mitton is a fellow of St Edmund's College, Cambridge.