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-v

^{2}/c

^{2})

^{-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:

__/\__s

^{2} = (c

__/\__t)

^{2}-(

__/\__x

^{2}+

__/\__y

^{2}+

__/\__z

^{2})

When c

__/\__t is greater than

__/\__x

^{2}+

__/\__y

^{2}+

__/\__z

^{2}, the spacetime interval is said to be '

timelike'. If those two are equal, the interval is '

lightlike'. And if c

__/\__t is less than

__/\__x

^{2}+

__/\__y

^{2}+

__/\__z

^{2}, the spacetime interval is '

spacelike', and could constitute part of the

world line of a

particle with

rest mass.