7. Geometry of the physical world

Abstract

‘Geometry of the physical world’ reviews Euclidean geometry, which provided a framework for interpreting empirical observations and making accurate predictions for over two millennia. However, as measuring apparatus improved, the geometry of the Universe is not that of Euclidean space. There were a number of 20th-century theories of physics which are based on geometries different to Euclidean geometry. These describe the Universe more accurately. The most basic of these is Minkowski geometry, which replaces Pythagorean distance by a space-time interval. The theory of gravitation is based on a curved version of the Minkowski distance and the electromagnetic and strong nuclear interactions are manifestations of curvature.