Inside an inertial reference frame time is what a clock does. Clocks in different reference frames can only be meaningfully compared when they are local (touching). Nothing moves in spacetime - the four vector is conserved. When two inertial reference frames are in relative movement in space they have different mixes of space-like and time-like components to maintain a constant sum.

However, space and time have different units. To compare apples with apples we must measure time as distance units. Time is in seconds. Time multiplied by lightspeed, ct, is in meters. Time is thus a veeeery looong dimension. It requires a lot of space before you start to see finite tme anomalies.

[link]http://fourmilab.to/etexts/einstein/specrel/specrel.pdfl/link]

Or, you must look for very small deviations from Newton under modest circumstances. The GPS system requires a few hundred parts-per-billion relativistic corrections,

[link]http://relativity.livingreviews.org/Articles/lrr-2003-1/index.html[/link]
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