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At velocities approaching the speed of light, c, mass - particles and other object bodies contract in the direction of motion as well as the fact that measurements of intervals of time dilate ( i.e., expand; the rate of clock progression slows ) as observed by an outside ( relatively ) stationary observer. In fact, the speed of light itself determines the very upper limit of velocity at which any body or mass - particle can attain since otherwise the frame of reference of such an object body ( or mass - particle ) would "outrun" any light propagation from itself. And this occurrence would thus violate the Lorentz Transformation Equations upon which all else of special relativity is predicated.
Hence, in order to preserve all that which has just been described, no simple 'Galilean addition of velocities' will suffice; but rather another sort of "Addition of Relativistic Velocities" must therefore be invoked and which inspires this following topic.
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