Relativity: The Special and General Theory

Einstein wrote this book for the general reader, warning at the outset that it demands some patient thought but no specialist mathematics. He begins by showing that geometry itself must be treated as a physical science: the propositions of Euclidean geometry are 'true' only to the extent that rigid bodies in nature obey them, and this is an empirical question, not a logical certainty.

Part I builds the special theory from two postulates: the principle of relativity (no uniformly moving frame is preferred) and the constancy of the speed of light. Using a railway embankment and a passing train as his running example, Einstein demonstrates that simultaneity is relative. Two lightning strikes that appear simultaneous to a stationary observer do not appear simultaneous to an observer moving toward one of them. From this it follows that time intervals and distances between events differ between observers, and that the classical rule for adding velocities breaks down. The Lorentz transformation provides the correct relationship between measurements in two uniformly moving frames.

Part II extends the principle to all frames of reference, including accelerating ones. Einstein's key argument is the thought experiment of a man in a sealed chest being pulled through empty space by a rope: he is unable to distinguish his situation from sitting in a gravitational field. This equivalence of inertial and gravitational mass, long known but never explained, becomes the physical foundation of the general theory. Because clocks run at different rates in a gravitational field and measuring rods are shortened, Euclidean geometry fails on a rotating disc and, more generally, wherever matter is present. Gaussian co-ordinates, which label events without presupposing any particular geometry, provide the mathematical language needed to state physical laws in a form valid for any frame.

Part III turns to the universe as a whole. Einstein identifies two difficulties with classical Newtonian cosmology: Newton's theory requires the universe to have a centre, and it predicts an unbounded build-up of gravitational potential that cannot be made finite. General relativity suggests a different picture. If space is spherical (analogous to the surface of a sphere in two dimensions), it is finite in volume yet has no edge or boundary. A traveller moving in any direction would eventually return to the starting point without ever passing a wall. The universe is, in this sense, finite and yet has no limits.

Throughout, Einstein is careful to explain not just conclusions but the reasoning behind each step, and to point out where classical intuitions must be surrendered. The book closes by noting that general relativity, combined with the observed near-uniformity of matter in the universe, permits tentative conclusions about the overall geometry of space, a question that observation had previously left entirely open.