Under the Lorentz Transformation, space and time intervals turn out not to be invariant. The transformation, and the relativity of simultaneity lead observers in intertial frames of reference to see length contraction and time dilation, given by the gamma factor of (1-v2/c2)-1/2.

The spacetime interval is the quanitity that is invariant under the Lorentz Transformation, it gives a 'distance' in 4-space of two events. The interval /\s is given by:

/\s2 = (c/\t)2-(/\x2+/\y2+/\z2)

When c/\t is greater than /\x2+/\y2+/\z2, the spacetime interval is said to be 'timelike'. If those two are equal, the interval is 'lightlike'. And if c/\t is less than /\x2+/\y2+/\z2, the spacetime interval is 'spacelike', and could constitute part of the world line of a particle with rest mass.

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