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.