Thus, neither space nor time by itself can exist in the real phenomenal world which the physicist explores. Space and time appear as mere modes of perception, mere relations, varying and changing according to the conditions of relative motion existing between the observer and the observed. With the disappearance of the objectivity of space and time regarded as absolute and universal forms of our perception, the objectivity of the entire physical world seemed to sink into a mist. If, then, any kind of objectivity was to be retained, it was necessary to effect a synthesis of all the individual points of view of all the different observers, to mould into one sole representation the multiplicity of individual spaces and the multiplicity of individual durations. Could this result be accomplished, the relativity of practical congruence for both space and time would give way to some universal definition of practical congruence holding for all observers regardless of their relative motion, and connoting, therefore, the existence of some absolute continuum no longer a mere shadow. In place of the individual point of view varying with the relative motions of the observers, we should obtain an impersonal and hence common objective understanding of nature. The achievement of this supreme synthesis of the points of view of all observers was accomplished by Minkowski in 1908. He succeeded in obtaining an invariant definition of congruence by combining any given observer’s definitions of practical congruence for space and for time, and by showing that this combination possessed an invariant value holding equally for all other observers. Of course, the type of congruence obtained was one neither of space nor of time. It was a combination of both. But its existence showed us that, transcending space and time, there existed an impersonal and fundamental four-dimensional metrical continuum which Minkowski called space-time. The definition of congruence obtained by him for this mysterious continuum proved it to be Euclidean (more properly, semi-Euclidean). The elusiveness of space and time, or rather the ambiguity of these concepts, depending as they do on the observer who measures and senses them, is replaced by the common objectivity of this fundamental continuum, which is the same for all and transcends the particular conditions of motion of the observer. This continuum, though of itself neither space nor time, yet pertains to both in that the observer is able to carve it up into that particular space and that particular time which are characteristic of the frame of reference in which he is stationed, and which constitute the space and time in which he lives and experiments. [Pg 192]