Space and Time
By Hermann Minkowski in Göttingen.
Gentlemen! The concepts about time and space, which I would like to develop before you today, have grown on experimental physical grounds. Herein lies their strength. Their tendency is radical. Henceforth, space for itself, and time for itself shall completely reduce to a mere shadow, and only some sort of union of the two shall preserve independence.
I
I would like to show you at first, how we can arrive – from mechanics as currently accepted – at the changed concepts about time and space, by purely mathematical considerations. The equations of Newtonian mechanics show a twofold invariance. First, their form remains unaltered when we subject the underlying spatial coordinate system to any change of position, second, when we change the system in its state of motion, i. e., when we impress upon it any uniform motion of translation; also the null-point of time plays no role. We are accustomed to look upon the axioms of geometry as settled, when we feel ready for the axioms of mechanics, and therefore the two invariants certainly are seldom mentioned in the same breath. Each one of these denotes a certain group of transformations in itself for the differential equations of mechanics. We look upon the existence of the first group as a fundamental characteristics of space. We always prefer to punish the second group with content, so as to get over the fact with a light heart, that we can never decide from physical considerations whether the space, which is supposed to be at rest, may not finally be in uniform motion. So these two groups have quite separate existences besides each other. Their totally heterogeneous character may scare us away from the attempt to compound them. Yet it is the whole compounded group which as a whole gives us occasion for thought.
We wish to picture to ourselves the whole relation graphically. Let x, y, z be the rectangular coordinates of space, and t denote the time. Subjects of our perception are always places and times connected. No one has observed a place except
