Abstract
Four-vectors are defined analogously to three-vectors and provide a compact means of presenting mathematical results in relativity theory. However, the four-velocity vector does not have the same physical significance as the three-velocity vector, but assuming so has led to the declaration that there is motion through spacetime which explains special relativistic time dilation. It is shown that four-velocity cannot legitimately be employed in this manner and that the time dilation effect does not require any motion through spacetime nor any speed through time.
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