"With the rejection of such classical absolutes as length and duration, our ability to conceive of an objective impersonal world, independent of the presence of an observer, seems to be imperiled. The great merit of Minkowski was to show that an absolute world could nevertheless be imagined, although it was a far different world from that of classical physics. In Minkowski's world the absolute which supersedes the absolute length and duration of classical physics is the Einsteinian interval. ... Thus suppose that, as measured in our Galilean frame of reference, two flashes occur at points A and B, situated at a distance l apart, and suppose the flashes are separated in time by an interval t. If we change our frame of reference, both l and t will change in value, becoming l and t respectively, exhibiting by their changes the relativity of length and duration. In Minkowski's words, "Henceforth space and time themselves are mere shadows." On the other hand, the mathematical construct l^2 - c^2t^2 will remain invariant, and so we shall have l^2 - c^2t^2 = l'^2 - c^2t'^2. It is this invariant expression, which involves both length and duration, or both space and time, which constitutes the Einsteinian interval; and the objective world which it cannotes is the world of four-dimensional space-time. The Einsteinian interval... remains the same for all observers, just as distance alone or duration alone were mistakenly believed to remain the same for all observers in classical physics. ...the Einsteinian interval still remains an invariant as measured for all frames of reference, whether accelerated or not. In the case of accelerated frames, however, we must restrict our attention to Einsteinan intervals of infinitesimal magnitude, and then add up the intervals when finite magnitudes are involved."
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