Spacetime and Four-Vectors

Abstract

Einstein taught us to regard events as the basic data of physics. He showed us the full significance of inertial frames and inertial observers. It was he who found that every inertial observer has his own privately valid time, and, correspondingly, his own “instantaneous three-spaces” consisting of all events (x, y, z, t) with fixed time coordinate. But it was the mathematician Minkowski (in 1908) who taught us to think of the totality of events in the world as the “points” of an absolute four-dimensional manifold called “spacetime.” Different inertial observers draw different sections through spacetime as their “instants.” In fact, each inertial observer, with his standard x, y, z, and t, coordinatizes all of spacetime, just as a choice of x and y axes coordinatizes the Euclidean plane. Figure 2.3 represents spacetime with two dimensions suppressed, but that suffices to illustrate how two observers make different instantaneous sections (for example, the x and x’ axes) and how they have different time axes. Certain lines in spacetime correspond to the history of material particles, and are aptly called “particle worldlines.” They are straight if the particles are free. Extended bodies have “world tubes” in spacetime.