Minkowski: The Universe Is a 4-Dimensional Manifold

In 1908 in a lecture Minkowski gave a brilliant reformulation of Einstein’s theory. He views the World as a 4-dimensional manifold that can be observed from reference systems with three space-axes and a time-axis. The transitions between the systems are determined by the Lorentz transformations. About space and time Minkowski said: “Space in itself and time in itself will be completely reduced to shadows and only a kind of union of the two will maintain independence”. In this chapter we sketch a part of Minkowski’s lecture. We conclude our discussion of the twin-paradox.