The unique characteristic of time as the dynamic aspect of the spacetime continuum has been largely unexplored, I believe in large part due to Minkowski's original graphic misrepresentation.
By means of a relativistic correction to the Minkowski diagram a number of clarifications and corollaries have been illustrated and propounded: The invariant length of world-lines; uniform motion in time as perpendicular to space and relative motion in spacetime as a different orientation of time to space; the misidentification of the "invariant interval"; the reason c is absolute and invariable; how two reference frames can each regard the other's clock as moving more slowly; that motion in time is absolute and dynamic, and not just the condition but the source of relative motion in space; and that the energy mis-identified with gravitation is due to continuous motion in time.
End Notes
1. The Lorentz Transformations are t' = SQRT((t-v)/(1-v2)) and x' = SQRT((x-vt)/(1-v2)), with t as time, x as distance, and v as velocity proportional to c.
2. As a matter of convenience t is generally multiplied by c so that space and time can be expressed in distances of the same scale. I prefer instead to calibrate them by giving time in seconds (sec) and space in light-seconds (ls).
3. Inertial acceleration and local gravitational influences are incidental, and need not be considered here.
References
Arnold J: Gravitation, force, and time, Eur. Sci. Journal 9, 24, (2013)
Minkowski H: Space and time, in The Principle of Relativity, H.A. Lorentz, A. Einstein, H. Minkowski, and H. Weyl, trans: W. Perrett and G.B. Jeffery, 1923 (1908)
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